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flan_v2
|
flan_v2_91133
|
[
{
"content": "instruction:\nIn this task, you will be given a set of steps that are required to answer a specific question. Your job is to generate that question. Each given step refers to either an entity (known or unknown), a propery of an entity or a query operation (count, group, union, etc.) Knowing those operations and how they appear in the input may help you generate more accurate questions.\n Select: A select step is used to return a set of objects. There are no references to previous steps in a select step. template: Return [attributes]\n Filter: A filter step is used to return results from a previous step to which a certain condition applies. template: Return [#step] [condition]\n Project: A project step should return certain attributes of the results of a previous step. template: Return [attributes] of [#step]\n Aggregate: An aggregate step returns an aggregator function applied on a step's result. template: Return the [aggregator] of [#step].\n Group: A group step is an aggregator applied on attributes. template: Return the [aggregator] of [#step] for each [attribute]\n Superlative: A superlative step is used to return the result with a highest/lowest attribute among other results. template: Return [#step1] [where] [#step2] [is] [highest / lowest]\n Comparative: A comparative step is used when we need to compare an attribute with a number to filter results. template: Return [#step1] [where] [#step2] [comparator] [number] \n Union: A union step is used to return results of two steps together. template: Return [#step1] [or / ,] [#step2]\n Intersection: An intersection step returns the result that two steps have in common. template: Return [attribute] of both [#step1] and [#step2]\n Discard: A discard step returns result of a step and excludes result of another step from it. template: Return [#step1] besides [#step2]\n Sort: A sort returns result of another step in a specific order. template: Return [#step1] [ordered / sorted by] [#step2]\n Is true: An is true step checks a condition on another result and returns a true or false. template: Return [is / if] [condition]\n Arithmetic: An arithmatic step operates an arithmatic operation on one or more steps. template: Return the [arithmetic op.] of [#step1] [and] [#step2].\nquestion:\n#1 return the objects \n#2 return #1 which is red \n#3 return #1 directly to the right of #2 \n#4 return #1 directly to the left of #2 \n#5 return #3 , #4 \n#6 return the shape of #5\nanswer:\nWhat shape is the object directly to the right and left of the red object?\n\n\nquestion:\n#1 return drivers \n#2 return pit stops of #1 \n#3 return number of #2 for each #1 \n#4 return #1 where #3 is 11 \n#5 return race results of #1 \n#6 return number of #5 for each #1 \n#7 return #1 where #6 is higher than 5 \n#8 return #1 in both #4 and #7 \n#9 return last names of #8 \n#10 return id of #8 \n#11 return #9 , #10\nanswer:\nWhat are the drivers' last names and id who had 11 pit stops and participated in more than 5 race results?\n\n\nquestion:\n#1 return the left image \n#2 return plates in #1 \n#3 return #2 that are white \n#4 return broccoli in #1 \n#5 return #3 with #4 \n#6 return number of #5 \n#7 return the right image \n#8 return plates in #7 \n#9 return #8 that are white \n#10 return broccoli in #7 \n#11 return #9 with #10 \n#12 return number of #11 \n#13 return if #6 is equal to #12\nanswer:\n",
"role": "user"
},
{
"content": "If the left and right image contains the same number of white plates with broccoli.\n\n\n",
"role": "assistant"
}
] |
cot
|
cot_86428
|
[
{
"content": "question: 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?\nOptions:\n(A) 2800\n(B) 2500\n(C) 3000\n(D) 3500\n(E) 4000\nanswer: Stream of consciousness: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144\n3x/100 + 200 – 5x/100 = 144\n2x/100 = 56 è x = 2800 The answer is (A).\nq: How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a vowel, and each letter can be used only once?\nOptions:\n(A) 20\n(B) 40\n(C) 120\n(D) 60\n(E) 10\na: Stream of consciousness: Vowel: E O\nConsonants: V R M N T\nFirst letter can be filled in 2 Ways ( As the question states that first letter has to be a vowel)\nFifth letter can be filled in 1 Ways ( As the question states that the last letter has to be a vowel)\nNow since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter\nSecond letter can be filled in 5 Ways\nThird letter can be filled in 4 Ways\nSo, Total number of ways = 2 Ways x 5 Ways x 4 ways x 1 ways = 40 The answer is (B).\nquestion: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?\nOptions:\n(A) 9\n(B) 8\n(C) 7\n(D) 6\n(E) 3\nanswer: Stream of consciousness: 1 to 9 = 9 * 9 = 81\n1 to 5 = 5 * 10 = 50\n5 to 9 = 5 * 8 = 40\n5th = 50 + 40 = 90 – 81 = 9 The answer is (A).\nq: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder K when N is divided by 30?\nOptions:\n(A) (a) 4\n(B) (b) 7\n(C) (c) 11\n(D) (d) 13\n(E) (e) 17\na: Stream of consciousness: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder K when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1. The answer is (C).\nquestion: In what time will a railway train 70 m long moving at the rate of 36 kmph pass a telegraph post on its way?\nOptions:\n(A) 5 sec\n(B) 4 sec\n(C) 3 sec\n(D) 7 sec\n(E) 1 sec\nanswer: Stream of consciousness: T = 70/36 * 18/5 = 7 sec The answer is (D).\nquestion: How many numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million?\nOptions:\n(A) 496\n(B) 486\n(C) 1084\n(D) 728\n(E) 628\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: The number of single digit numbers = 2\nThe number of 2 digit numbers = 2 × 3 = 6\nThe number of 3 digit numbers = 2 × 3 × 3 = 18\nThe number of 4 digit numbers = 2 × 3 × 3 × 3 = 54\nThe number of 5 digit numbers = 2 × 3 × 3 × 3 × 3 = 162\nThe number of 6 digit numbers = 2 × 3 × 3 × 3 × 3 × 3 = 486\nTherefore, the total numbers = 728 The answer is (D).",
"role": "assistant"
}
] |
cot
|
cot_67244
|
[
{
"content": "q: In Hockey game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?\nOptions:\n(A) 1/3\n(B) 4/9\n(C) 5/9\n(D) 2/3\n(E) 3/4\na: Stream of consciousness: In Hockey game, Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:\nP(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9. The answer is (C).\nquestion: A, B, C, and D are four points, any three of which are non-collinear. Then, the number of ways to construct three lines each joining a pair of points so that the lines do not form a triangle is\nOptions:\n(A) 7\n(B) 8\n(C) 9\n(D) 24\n(E) 23\nanswer: Stream of consciousness: To construct 2 lines, three points can be selected out of 4 in 4 x 3 x 2 = 24 ways. Now, if third line goes from the third-point to the first point, a triangle is formed, and if it goes to the fourth point, a triangle is not formed. So, there are 24 ways to form a triangle and 24 ways of avoiding triangle. The answer is (D).\nq: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?\nOptions:\n(A) 228\n(B) 162\n(C) 5528\n(D) 256\n(E) 191\na: Stream of consciousness: 12 m/s = 12 * 18/5 kmph\n3 hours 45 minutes = 3 3/4 hours = 15/4 hours\nDistance = speed * time = 12 * 18/5 * 15/4 km = 162 km. The answer is (B).\nquestion: A train running at the speed of 60 km/hr crosses a pole in 6 sec. What is the length of the train?\nOptions:\n(A) 118\n(B) 150\n(C) 277\n(D) 258\n(E) 100\nanswer: Stream of consciousness: Speed = 60 * 5/18 = 50/3 m/sec\nLength of the train = speed * time = 50/3 * 6 = 100 m The answer is (E).\nq: The average age of a family of 6 members is 24 years.If the age of the youngest member is 8 years,what was the average age of the family at the birth of the youngest member?\nOptions:\n(A) 15\n(B) 16\n(C) 21\n(D) 12\n(E) 19\na: Stream of consciousness: Present age of total members = 6 X 24 = 144\n8 yrs back their ages were = 6 x 8 = 48\nAges at the birth of youngest member = 144 - 48 = 96\nTherefore, avg age at the birth of youngest member = 96/6 = 16. The answer is (B).\nq: In 2 bags, there are to be put together 5 red and 12 white balls, neither bag being empty. How must the balls be divided so as to give a person who draws 1 ball from either bag-\nOptions:\n(A) 9/18\n(B) 9/16\n(C) 9/11\n(D) 9/12\n(E) 9/13\na:",
"role": "user"
},
{
"content": "Stream of consciousness: (1) Put 1 white in first bag, and all the remaining ball in second bag. Probability = 12×0+12×51612×0+12×516 = 532532\n(2) To maximize, we put 1 red in the first bag, and all the remaining in the second. Probability = 12×1+12×43212×1+12×432 = 9/16 The answer is (B).",
"role": "assistant"
}
] |
flan_v2
|
flan_v2_91916
|
[
{
"content": "In this task you will break down a question into the basic steps required to answer it.\n A question decomposition is a numbered list of operations that must be performed to answer the original question. Imagine explaining your question to a friendly droid by listing each action it should take in order for the question to be answered. Each step in our decomposition should refer to either an entity (known or unknown), a propery of an entity or a query operation (count, group, union, etc.)\n Here are the list of step templates and their description:\n Select: A select step is used to return a set of objects. There are no references to previous steps in a select step. template: Return [attributes]\n Filter: A filter step is used to return results from a previous step to which a certain condition applies. template: Return [#step] [condition]\n Project: A project step should return certain attributes of the results of a previous step. template: Return [attributes] of [#step]\n Aggregate: An aggregate step returns an aggregator function applied on a step's result. template: Return the [aggregator] of [#step].\n Group: A group step is an aggregator applied on attributes. template: Return the [aggregator] of [#step] for each [attribute]\n Superlative: A superlative step is used to return the result with a highest/lowest attribute among other results. template: Return [#step1] [where] [#step2] [is] [highest / lowest]\n Comparative: A comparative step is used when we need to compare an attribute with a number to filter results. template: Return [#step1] [where] [#step2] [comparator] [number] \n Union: A union step is used to return results of two steps together. template: Return [#step1] [or / ,] [#step2]\n Intersection: An intersection step returns the result that two steps have in common. template: Return [attribute] of both [#step1] and [#step2]\n Discard: A discard step returns result of a step and excludes result of another step from it. template: Return [#step1] besides [#step2]\n Sort: A sort returns result of another step in a specific order. template: Return [#step1] [ordered / sorted by] [#step2]\n Is true: An is true step checks a condition on another result and returns a true or false. template: Return [is / if] [condition]\n Arithmetic: An arithmatic step operates an arithmatic operation on one or more steps. template: Return the [arithmetic op.] of [#step1] [and] [#step2].\n\nExample Input: question: If one of the paired images contains one black brace and one white brace.\nExample Output: #1 return images \n#2 return braces in #1 \n#3 return #2 that are black \n#4 return #2 that are white \n#5 return number of #3 for each #1 \n#6 return number of #4 for each #1 \n#7 return #1 where #5 is equal to one \n#8 return #1 where #6 is equal to one \n#9 return #1 in both #7 and #8 \n#10 return number of #9 \n#11 return if #10 is equal to one\n\nExample Input: question: If an image shows at least one person in a yellow canoe on the water.\nExample Output: #1 return people \n#2 return canoe \n#3 return #2 that is yellow \n#4 return #1 in #3 \n#5 return the water \n#6 return #4 on #5 \n#7 return images of #6 \n#8 return number of #6 for each #7 \n#9 return #7 where #8 is at least one \n#10 return number of #9 \n#11 return if #10 is equal to one\n\nExample Input: question: What are the first names of the professors who do not teach a class.\nExample Output:",
"role": "user"
},
{
"content": "#1 return professors \n#2 return #1 who teach a class \n#3 return #1 besides #2 \n#4 return first names of #3\n\n",
"role": "assistant"
}
] |
cot
|
cot_70287
|
[
{
"content": "q: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 8, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created?\nOptions:\n(A) 20\n(B) 22\n(C) 24\n(D) 27\n(E) 30\na: Stream of consciousness: Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes The answer is (D).\nquestion: In 2 bags, there are to be put together 5 red and 12 white balls, neither bag being empty. How must the balls be divided so as to give a person who draws 1 ball from either bag-\nOptions:\n(A) 9/18\n(B) 9/16\n(C) 9/11\n(D) 9/12\n(E) 9/13\nanswer: Stream of consciousness: (1) Put 1 white in first bag, and all the remaining ball in second bag. Probability = 12×0+12×51612×0+12×516 = 532532\n(2) To maximize, we put 1 red in the first bag, and all the remaining in the second. Probability = 12×1+12×43212×1+12×432 = 9/16 The answer is (B).\nq: A person spends 1/3rd of the money with him on clothes, 1/5th of the remaining on food and 1/4th of the remaining on travel. Now, he is left with Rs 400. How much did he have with him in the beginning?\nOptions:\n(A) s 200\n(B) s 1000\n(C) s 300\n(D) s 450\n(E) s 550\na: Stream of consciousness: Suppose the amount in the beginning was Rs ’x’\nMoney spent on clothes = Rs 1x/3 Balance = Rs 2x/3\nMoney spent on food = 1/5 of 2x/3 = Rs 2x/15\nBalance = 2x/3 - 2x/15 = Rs 8x/15\nMoney spent on travel = 1/4 of 8x/15 = Rs 2x/15 = 8x/15 - 2x/15 = 6x/15 = Rs2x/5\nTherefore 2x/5 = 400 = 1000 The answer is (B).\nquestion: Q is a set of nine distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?\nOptions:\n(A) 2\n(B) 3\n(C) 4\n(D) 5\n(E) 7\nanswer: Stream of consciousness: 2 + 3 + 5 + 7 +11 + 13 + 17 + 23 + 29 = 100 ( sum is even)\nLeast number = 2 The answer is (A).\nq: How many three-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 2 ?\nOptions:\n(A) 8\n(B) 0\n(C) 6\n(D) 10\n(E) 12\na: Stream of consciousness: A number ending with 2 can never be a perfect square. The answer is (B).\nq: When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land once on heads and twice tails?\nOptions:\n(A) 1/3\n(B) 1/6\n(C) 1/4\n(D) 1/8\n(E) 1/5\na:",
"role": "user"
},
{
"content": "Stream of consciousness: Must be once on heads and twice on tails\n1/2*1/2*1/2 = 1/8 The answer is (D).",
"role": "assistant"
}
] |
cot
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cot_79795
|
[
{
"content": "question: If 10 crates have 98 apples each and how many apples more is required in order to make 100 apples in each crate?\nOptions:\n(A) 5\n(B) 10\n(C) 15\n(D) 20\n(E) 0\nanswer: Stream of consciousness: Each crate requires 2 apples and totally there are 10 crates so required apples = 10 * 2 = 20 The answer is (D).\nq: a certain organization has three committees. only two persons are members of all committees, but every pair of committees have three members in common. what is the least possible no of member of members on any one committee?\nOptions:\n(A) 4\n(B) 5\n(C) 6\n(D) 7\n(E) 8\na: Stream of consciousness: Total 4 members minimum required to serve only on one committee. The answer is (A).\nquestion: The Average of six numbers is 8. The average of the first two is 11 and the average of the last three is 4. What is the middle number?\nOptions:\n(A) A) 15\n(B) B) 8\n(C) C) 6\n(D) D) 14\n(E) E) 9\nanswer: Stream of consciousness: The total of six numbers = 6X8 = 48\nThe total of first 2 and last 3 numbers is = 2 X 11+3 X 4 = 34\nSo, the middle number is (48 - 34 ) = 14 The answer is (D).\nq: How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and repetition is allowed?\nOptions:\n(A) 3441\n(B) 3433\n(C) 3333\n(D) 3430\n(E) 3773\na: Stream of consciousness: Vowel: E O\nConsonants: V R M N T\nFirst letter can be filled in 2 Ways ( As the question states that first letter has to be a vowel)\nFifth letter can be filled in 5 Ways ( As the question states that the last letter has to be a consonant)\nSecond letter can be filled in 7 Ways\nThird letter can be filled in 7 Ways\nFourth letter can be filled in 7 Ways\nSo, Total number of ways = 2 Ways x 7 Ways x 7 ways x 7 ways x 5 ways = 3430 The answer is (D).\nquestion: If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?\nOptions:\n(A) 22 1/9 %\n(B) 22 2/2 %\n(C) 23 1/2 %\n(D) 22 1/2 %\n(E) 62 1/2 %\nanswer: Stream of consciousness: 9 = (1*40*R)/100\nR = 22 1/2 % The answer is (D).\nquestion: John has 10pairs of dark blue socks and 10pairs of black socks. He keeps them all in the same bag. If he picks out 3socks at random, then what is the probability thathe will get a matching pair?\nOptions:\n(A) 1\n(B) 3\n(C) 5\n(D) 6\n(E) 9\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: If he draws any combination of 3 socks he will definitely have the matching pair of either colour. The answer is (A).",
"role": "assistant"
}
] |
cot
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cot_76158
|
[
{
"content": "question: The average of 13 numbers is 60. Average of the first 7 of them is 55 and that of the last 7 is 61. Find the 8th number?\nOptions:\n(A) 32\n(B) 83\n(C) 45\n(D) 53\n(E) 64\nanswer: Stream of consciousness: Sum of all the 13 numbers = 13 * 60 = 780\nSum of the first 7 of them = 7 * 55 = 385\nSum of the last 7 of them = 7 * 61 = 427\nSo, the 8th number = 427 + 385 - 780 = 32. The answer is (A).\nq: A certain league has five divisions. The respective divisions had 6, 7, 8, 9 and 11 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?\nOptions:\n(A) 81\n(B) 83\n(C) 85\n(D) 86\n(E) 89\na: Stream of consciousness: Overall, there can be 81 minuses. Tus, it is The answer is (A).\nquestion: How many factors does 25^2 have?\nOptions:\n(A) 2\n(B) 8\n(C) 24\n(D) 25\n(E) 26\nanswer: Stream of consciousness: 36^2 = 6*6*6*6 = 2^4*3^4\nTotal factors = (4+1)*(4+1) = 4*2 = 8 The answer is (B).\nq: If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5 and 5K + 1 is 30, what is the value of K?\nOptions:\n(A) 11\n(B) 15 3/4\n(C) 22\n(D) 23\n(E) 25 3/10\na: Stream of consciousness: K + 2K +3 + 3K - 5 + 5K +1 = 11K -1\n(11K -1)/4 = 30\n11K = 30 * 4 +1 = 120 +1 = 121\nK = 121 / 11 = 11. The answer is (A).\nquestion: There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.\nWhen everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.\nSo they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.\nFinally, they woke up the 7th thief and this time the diamonds were divided equally.\nHow many diamonds did they steal in total?\nOptions:\n(A) 1560\n(B) 1561\n(C) 1559\n(D) 1557\n(E) None of the above\nanswer: Stream of consciousness: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60. The answer is (B).\nquestion: What percent is 120 of 70?\nOptions:\n(A) 133 1/3 %\n(B) 134 1/3 %\n(C) 135 1/3 %\n(D) 140 1/3 %\n(E) 171 3/7 %\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: 120/70 = 12/7\n12/7 × 100 = 1200/7 = 171 3/7 % The answer is (E).",
"role": "assistant"
}
] |
cot
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cot_59228
|
[
{
"content": "question: Solve below question 2x - 1 = 17\nOptions:\n(A) -8\n(B) -9\n(C) -5\n(D) -4\n(E) 9\nanswer: Stream of consciousness: 1. Add 1 to both sides: 2x - 1 + 1 = 17 + 1 2. Simplify both sides: 2x = 18 3. Divide both sides by 2: 4. Simplify both sides: x = 9 The answer is (E).\nq: Efrida and Frazer who live 13 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?\nOptions:\n(A) 6\n(B) 7\n(C) 8\n(D) 10\n(E) 11\na: Stream of consciousness: It's a simple geometry problem. Look at the diagram below: The answer is (E).\nquestion: The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is:\nOptions:\n(A) 279\n(B) 283\n(C) 308\n(D) 318\n(E) 328\nanswer: Stream of consciousness: Other number = (11 x 7700)/275 = 308. The answer is (C).\nq: In Cricket game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?\nOptions:\n(A) 1/3\n(B) 4/9\n(C) 5/9\n(D) 2/3\n(E) 3/4\na: Stream of consciousness: In Cricket game Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:\nP(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9. The answer is (C).\nquestion: A can do a piece of work in 10 days. He works at it for 4 days and then B finishes it in 9 days. In how many days can A and B together finish the work?\nOptions:\n(A) 6\n(B) 8\n(C) 12\n(D) 15\n(E) 20\nanswer: Stream of consciousness: 4/10+9/X = 1/x = 15\n1/10+1/15 = 1/6 = 6 days The answer is (A).\nquestion: The average of seven numbers is 4. The average of first three numbers is 2 and the average of last three numbers is 6. What is the middle number?\nOptions:\n(A) 3\n(B) 4\n(C) 6\n(D) 7\n(E) 8\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: The total of seven numbers = 7X4 = 28\nThe total of first 3 and last 3 numbers is = 3 X 2+3 X 6 = 24\nSo, the middle number is (28 - 24 ) = 4 The answer is (B).",
"role": "assistant"
}
] |
cot
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cot_92777
|
[
{
"content": "q: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 17 seconds. What is the length of the platform in meters?\nOptions:\n(A) 240 meters\n(B) 260 meters\n(C) 420 meters\n(D) 600 meters\n(E) Cannot be determined\na: Stream of consciousness: Speed of the train in metres/sec = 72000/3600 = 20\nDistance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform\nDistance travelled by train to cross the man = 17 * 20 = 340 = Length of train\nLength of platform = 600 - 340 = 260 The answer is (B).\nquestion: If x<0, y>0, and |x| < |y|, which of the following must be true?\nOptions:\n(A) x > y\n(B) y^2 > x^2\n(C) x^3 > y^2\n(D) –x < y\n(E) x < –y\nanswer: Stream of consciousness: Correct Answer: (E)\nLet’s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn’t have to be true – consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us –x > y. Remember that x < 0, so –x = |x|, and y is positive, so |y| = y. Thus –x < y is the same statement as |x| > |y|, and (D) must be true. The answer is (D).\nq: An businessman earns an income of Re 2 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 20th day of business, he earns an income of:\nOptions:\n(A) 21\n(B) 22\n(C) 36\n(D) 20\n(E) 30\na: Stream of consciousness: 2nd day he earns = 2(2 – 2)\n3rd day he earns = 2(3 – 2)\nOn 20th day he earns 2(20 -2) = 36 rupees The answer is (C).\nquestion: A frame 2 inches wide is placed around a rectangular picture with dimensions 8 inches by 12 inches. What is the area of the frame, in square inches?\nOptions:\n(A) 44\n(B) 96\n(C) 128\n(D) 144\n(E) 168\nanswer: Stream of consciousness: A frame 2 inches wide is placed around a rectangular picture with dimensions 8 inches by 12 inches. What is the area of the frame, in square inches?\n(12*16)-(8*12) = 96 The answer is (B).\nq: A password for a computer is six digits from 0 and 9. The six digit number is a prime number. What is the approximate probability that the last digit is a 3?\nOptions:\n(A) 1/4\n(B) 1/6\n(C) 1/10\n(D) 1/20\n(E) 1/50\na: Stream of consciousness: If the last digit is 0, 2, 4, 6, or 8, the number is even and therefore not prime. If the last digit is 5, the number is divisible by 5 and therefore not prime. The only possibilities are 1, 3, 7, and 9. So the probability is approximately 1/4 (answer A). We say approximately because there is a certain degree of randomness in the distribution of prime numbers. The answer is (A).\nq: A and B complete a work in 8 days. A alone can do it in 14 days. If both together can do the work in how many days?\nOptions:\n(A) 5 days\n(B) 8 days\n(C) 6 days\n(D) 3.15 days\n(E) 2.75 days\na:",
"role": "user"
},
{
"content": "Stream of consciousness: 1/8 + 1/14 = 11/56\n56/11 = 5 days The answer is (A).",
"role": "assistant"
}
] |
cot
|
cot_60164
|
[
{
"content": "q: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?\nOptions:\n(A) 9\n(B) 8\n(C) 5\n(D) 5\n(E) 4\na: Stream of consciousness: 1 to 9 = 9 * 9 = 81\n1 to 5 = 5 * 10 = 50\n5 to 9 = 5 * 8 = 40\n5th = 50 + 40 = 90 – 81 = 9 The answer is (A).\nquestion: If X is the sum of first 30 positive even integers and Y is the sum of first 30 positive odd integers, what is the value of x-y?\nPlease try to explain your answers\nOptions:\n(A) 10\n(B) 25\n(C) 30\n(D) 75\n(E) 100\nanswer: Stream of consciousness: First even minus first odd = 2-1 = 1;\nThe sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;\nThe sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;\nWe can see the patterns here, so the sum of first 30 positive even integers minus the sum of first 30 positive odd integers will be 30. The answer is (C).\nq: Steve traveled the first 2 hours of his journey at 40 mph and the last 2 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?\nOptions:\n(A) 53.33 mph\n(B) 56.67 mph\n(C) 60 mph\n(D) 64 mph\n(E) 66.67 mph\na: Stream of consciousness: Average Speed = Total distance/ Total time = (40 * 2 + 80 * 2)/(2 + 2) = 240/4 = 60 The answer is (C).\nquestion: M is 30% of Q, Q is 20% of P and N is 50% of P. What is M / N\nOptions:\n(A) 3/28\n(B) 3/27\n(C) 3/21\n(D) 3/22\n(E) 3/25\nanswer: Stream of consciousness: Take P = 100, then N = 50, Q = 20, M = 6. So M/N = 3/25 The answer is (E).\nq: A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:\nOptions:\n(A) 553681\n(B) 555181\n(C) 555681\n(D) 556581\n(E) 556881\na: Stream of consciousness: 987 = 3 x 7 x 47\nSo, the required number must be divisible by each one of 3, 7, 47\n553681->(Sum of digits = 28, not divisible by 3)\n555181->(Sum of digits = 25, not divisible by 3)\n555681 is divisible by 3, 7, 47 The answer is (C).\nq: There are 10 female and 15 male in a work place. In how many ways can a person can be selected?\nOptions:\n(A) 20\n(B) 15\n(C) 18\n(D) 40\n(E) 25\na:",
"role": "user"
},
{
"content": "Stream of consciousness: No of ways = 10+ 15 = 25 The answer is (E).",
"role": "assistant"
}
] |
cot
|
cot_70175
|
[
{
"content": "question: 4000 was divided into two parts such a way that when first part was invested at 3% and the second at 5%, the whole annual interest from both the investments is Rs.144, how much was put at 3%?\nOptions:\n(A) 2277\n(B) 2882\n(C) 2800\n(D) 2677\n(E) 2211\nanswer: Stream of consciousness: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144\n3x/100 + 200 – 5x/100 = 144\n2x/100 = 56 è x = 2800 The answer is (C).\nq: If x>0, y>0, and |x| > |y|, which of the following must be true?\nOptions:\n(A) x > y\n(B) y^2 > x^2\n(C) x^3 > y^2\n(D) –x < y\n(E) x < –y\na: Stream of consciousness: Correct Answer: (E)\nLet’s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn’t have to be true – consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us –x > y. Remember that x < 0, so –x = |x|, and y is positive, so |y| = y. Thus x > y is the same statement as |x| > |y|, and (A) must be true. The answer is (A).\nquestion: I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?\nOptions:\n(A) 5\n(B) 7\n(C) 23\n(D) 4\n(E) 2\nanswer: Stream of consciousness: Clearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5. The answer is (A).\nq: How many seconds will a train 100 meters long take to cross a bridge 180 meters long if the speed of the train is 36 kmph?\nOptions:\n(A) 54 sec\n(B) 28 sec\n(C) 25 sec\n(D) 45 sec\n(E) 24 sec\na: Stream of consciousness: D = 100 + 180 = 280\nS = 36 * 5/18 = 10 mps\nT = 280/10 = 28 sec The answer is (B).\nquestion: A daughter lent $750 to her mother to help pay her rent. At the end of the month, the daughter received y dollars more than than the amount that was lent due to interest. The mother also gave her daughter an additional $5 for goodwill. In terms of y, what fraction of the total amount that the daughter received was the goodwill amount?\nOptions:\n(A) (5y-1) /(755-y) \n(B) 5/(755+y) \n(C) 5y/(755+y) -1\n(D) 5y/(755+y) \n(E) 5y\nanswer: Stream of consciousness: The amount of money the daughter received was (750 + 5+ y) dollars. The $5 goodwill gift as a fraction of the amount received was, therefore, 5/(755+y). The answer is (B).\nquestion: A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 3 days. In how many days can they complete the remaining work?\nOptions:\n(A) 4/3 days\n(B) 2 days\n(C) 8 days\n(D) 3 days\n(E) 9 days\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: Work done by A in 3 days = 3/5\nRemaining work = 2/5\nWork done by both A and B in one day = 1/5 + 1/10 = 3/10\nRemaining work = 2/5 * 10/3 = 4/3 days. The answer is (A).",
"role": "assistant"
}
] |
flan_v2
|
flan_v2_83076
|
[
{
"content": "Detailed Instructions: In this task, you will be given a set of steps that are required to answer a specific question. Your job is to generate that question. Each given step refers to either an entity (known or unknown), a propery of an entity or a query operation (count, group, union, etc.) Knowing those operations and how they appear in the input may help you generate more accurate questions.\n Select: A select step is used to return a set of objects. There are no references to previous steps in a select step. template: Return [attributes]\n Filter: A filter step is used to return results from a previous step to which a certain condition applies. template: Return [#step] [condition]\n Project: A project step should return certain attributes of the results of a previous step. template: Return [attributes] of [#step]\n Aggregate: An aggregate step returns an aggregator function applied on a step's result. template: Return the [aggregator] of [#step].\n Group: A group step is an aggregator applied on attributes. template: Return the [aggregator] of [#step] for each [attribute]\n Superlative: A superlative step is used to return the result with a highest/lowest attribute among other results. template: Return [#step1] [where] [#step2] [is] [highest / lowest]\n Comparative: A comparative step is used when we need to compare an attribute with a number to filter results. template: Return [#step1] [where] [#step2] [comparator] [number] \n Union: A union step is used to return results of two steps together. template: Return [#step1] [or / ,] [#step2]\n Intersection: An intersection step returns the result that two steps have in common. template: Return [attribute] of both [#step1] and [#step2]\n Discard: A discard step returns result of a step and excludes result of another step from it. template: Return [#step1] besides [#step2]\n Sort: A sort returns result of another step in a specific order. template: Return [#step1] [ordered / sorted by] [#step2]\n Is true: An is true step checks a condition on another result and returns a true or false. template: Return [is / if] [condition]\n Arithmetic: An arithmatic step operates an arithmatic operation on one or more steps. template: Return the [arithmetic op.] of [#step1] [and] [#step2].\nSee one example below:\nProblem: #1 return secretaries \n#2 return #1 born in state 'Alabama \n#3 return departments managed by #2 \n#4 return distinct creation years of #3\nSolution: What are the distinct creation years of the departments managed by a secretary born in state 'Alabama'?\nExplanation: You should follow the steps in order to realize what is the asked question. In this example, the first returned entities are secretaries(based on step #1) who are born in Alabama(based on step #2). In the step #3 departments managed by step #2(which is secretaries born in Alabama. In the final steps the creation years of the departments is returned, so the question will be about the creation years of the departments. \n\nProblem: #1 return students \n#2 return sports that #1 played \n#3 return the number of #2 for each #1 \n#4 return #1 where #3 is the highest \n#5 return the first name of #4 \n#6 return the last name of #4 \n#7 return #5 , #6\nSolution:",
"role": "user"
},
{
"content": "What is the first and last name of the student who played the most sports?",
"role": "assistant"
}
] |
cot
|
cot_70361
|
[
{
"content": "q: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?\nOptions:\n(A) 9261\n(B) 1261\n(C) 9621\n(D) 9162\n(E) 5000\na: Stream of consciousness: A = 8000(21/20)3 = 9261 The answer is (A).\nquestion: If 10 crates have 95 apples each and how many apples more is required in order to make 100 apples in each crate?\nOptions:\n(A) 5\n(B) 10\n(C) 15\n(D) 50\n(E) 0\nanswer: Stream of consciousness: Each crate requires 5 apples and totally there are 10 crates so required apples = 10 * 5 = 50 The answer is (D).\nq: You have a flashlight that takes 2 working batteries. You have 8 batteries but only 4 of them work.\nWhat is the fewest number of pairs you need to test to guarantee you can get the flashlight on?\nOptions:\n(A) 5\n(B) 8\n(C) 7\n(D) 6\n(E) 4\na: Stream of consciousness: If you break the batteries into 3 groups: Two groups of 3 and one group of 2. By doing this you guarantee that one of the groups has 2 working batteries. Both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination. So, 3 + 3 + 1 = 7 tries at most to find two working batteries. The answer is (C).\nquestion: In a group of dogs and peacocks, the number of legs are 18 less than four times the number of heads How many peacocks are there in that group?\nOptions:\n(A) 9\n(B) 8\n(C) 7\n(D) 6\n(E) 5\nanswer: Stream of consciousness: Let the number of dogs be 'x' and the number of peacocks by 'y'. Then, number of legs in the group = 4x + 2y. Number of heads in the group = x+y So, 4x+2y = 4(x+y) – 18 ⇒ 2y = 18 ⇒ y = 9 Number of peacocks in that group = 9. The answer is (A).\nq: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 190 m long?\nOptions:\n(A) 40 sec\n(B) 11 sec\n(C) 88 sec\n(D) 19 sec\n(E) 44 sec\na: Stream of consciousness: Speed = 45 * 5/18 = 25/2 m/sec\nTotal distance covered = 360 + 190 = 550 m\nRequired time = 550 * 2/25 = 44 sec The answer is (E).\nq: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?\nOptions:\n(A) 226\n(B) 992 rs\n(C) 665\n(D) 771\n(E) 211\na:",
"role": "user"
},
{
"content": "Stream of consciousness: (800*3*3)/100 = 72\n920 + 72 = 992 The answer is (B).",
"role": "assistant"
}
] |
cot
|
cot_97606
|
[
{
"content": "question: A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they take to finish the work, if all the three work together?\nOptions:\n(A) 4\n(B) 9\n(C) 2\n(D) 11\n(E) None\nanswer: Stream of consciousness: 1/7 + 1/14 + 1/28 = 7/28 = 1/4\nAll three can finish the work in 4 days The answer is (A).\nq: What is the local value of 7 in the difference of 100889 and local value of 3 in 28943712?\nOptions:\n(A) 7000\n(B) 700\n(C) 70000\n(D) 70\n(E) 7\na: Stream of consciousness: 100889 - (Local value of 3) = 100889 - 3000 = 97889\nLocal value of 7 in 97889 = 7000 The answer is (A).\nquestion: An amount of money is to be divided among P, Q and R in the ratio of 4 : 9 : 16. If R gets 4 times more than P, what is Q’s share in it?\nOptions:\n(A) 1,800\n(B) 2,700\n(C) 3,600\n(D) Data inadequate\n(E) None of these\nanswer: Stream of consciousness: Here, neither the total amount nor the individual amount is given. So the share of Q cannot be determine The answer is (D).\nq: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 10(B + G) is ?\nOptions:\n(A) Equal to 3\n(B) Less than 3\n(C) More than 10\n(D) Less than 10\n(E) none of these\na: Stream of consciousness: Let number of boys = x\nLet number of girls = y\nTherefore x/y = B and y/x = G\n10(B + G) = 10[(x/y) + (y/x)] = 10[(x2 + y2)/xy] > 10 The answer is (C).\nquestion: Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?\nOptions:\n(A) 25200\n(B) 2543\n(C) 2344\n(D) 233445\n(E) 52757\nanswer: Stream of consciousness: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = (7C3 x 4C2) = ( 7 x 6 x 5 x 4 x 3 ) 3 x 2 x 1 2 x 1 = 210. Number of groups, each having 3 consonants and 2 vowels = 210. Each group contains 5 letters. Number of ways of arranging 5 letters among themselves = 5! = 5 x 4 x 3 x 2 x 1 = 120. Required number of ways = (210 x 120) = 25200. The answer is (A).\nquestion: A girl is organizing her jellybean collection in which each color has its own row. In each row, there are as many jellybeans as the number of jellybean colors. Her little brother chops each jellybean into the same number of peices as the number of jellybean colors. If the final number of jellybean pieces is m, then:\nOptions:\n(A) m is a perfect square\n(B) m is an odd number\n(C) m is an even number\n(D) m is a perfect cube.\n(E) None\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: For example, if there were 4 jellybean colors, the girl would have made a 4x4 arrangement. The boy chopped up each jellybean into 4, the number of pieces would be (4*4)*4 = 64 pieces, which is a cube of 4. The answer is (D).",
"role": "assistant"
}
] |
cot
|
cot_76421
|
[
{
"content": "Ques: There are 20 balls in a box: 11 balls are green, 6 are blue and 3 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a green ball is selected at random from the box?\nOptions:\n(A) 1/13\n(B) 10/18\n(C) 3/13\n(D) 5/13\n(E) 6/13\nAns: (B)\nCoT: If 1 green and 1 blue ball are taken from the box, then there are 10 green, 5 blue and 3 white balls, a total of 18 balls. If one ball is selected at random, the probability that it is green is given by 10 / 18\n\nQues: The average of 11 results is 44, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?\nOptions:\n(A) 122\n(B) 156\n(C) 118\n(D) 125\n(E) 123\nAns: (A)\nCoT: 1 to 11 = 11 * 44 = 484\n1 to 6 = 6 * 49 = 294\n6 to 11 = 6 * 52 = 312\n6th = 294 + 312 – 484 = 122\n\nQues: The average of seven numbers is 20. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?\nOptions:\n(A) 27\n(B) 29\n(C) 31\n(D) 41\n(E) 35\nAns: (D)\nCoT: The total of seven numbers = 7X20 = 140\nThe total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99\nSo, the middle number is (140 - 99 ) = 41\n\nQues: A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 5% on conveyance. If his savings at the end of the month is Rs. 2700, then his salary per month in rupees is:\nOptions:\n(A) 4000\n(B) 6000\n(C) 18000\n(D) 10000\n(E) None of these\nAns: (C)\n",
"role": "user"
},
{
"content": "CoT: Total expenditure = 40 + 25 + 15 + 5 = 85%\nSaving = (100 - 85) = 15%\n15/100 × Salary = 2700, Salary = 18000 Rs.",
"role": "assistant"
}
] |
cot
|
cot_58004
|
[
{
"content": "question: From a Group of 9 People, Including George and Nina, 4 people are to be selected at random to work on a certain project. What is the probability that 4 people selected will include George but not Nina\nOptions:\n(A) 5/56\n(B) 9/56\n(C) 15/56\n(D) 35/120\n(E) 25/56\nanswer: Stream of consciousness: Number of ways of selecting 4 people out of 9 people = 9C4\nIn the three members George will always be there in the team. At this step we have vacancy for 3 more members and 8 members are available. Nina cannot be there in the team. So 3 members have to be selected and the number of available members = 8 - Nina = 7\nNumber of ways to form a 4 member team that includes George and excludes Nina = 7C3\nProbability = 7C3/9C4 = 35/120 The answer is (D).\nq: A corporation triples its annual bonus to 50 of its employees. What percent Q of the employees’ new bonus is the increase?\nOptions:\n(A) 50%\n(B) 662⁄3%\n(C) 100%\n(D) 200%\n(E) 300%\na: Stream of consciousness: Q of the employees’ new bonus is the increase Hence The answer is (B).\nquestion: Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?\nOptions:\n(A) 10\n(B) 12\n(C) 7\n(D) 8\n(E) 9\nanswer: Stream of consciousness: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted. The answer is (A).\nq: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?\nOptions:\n(A) 26\n(B) 27\n(C) 29\n(D) 32\n(E) 36\na: Stream of consciousness: The total of seven numbers = 7X18 = 126\nThe total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99\nSo, the middle number is (126 - 99 ) = 27 The answer is (B).\nquestion: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 60 as remainder. Find the no. is?\nOptions:\n(A) 145646\n(B) 236578\n(C) 645353\n(D) 456546\n(E) 220060\nanswer: Stream of consciousness: (555 + 445) * 2 * 110 + 60 = 220000 + 60 = 220060 The answer is (E).\nquestion: A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?\nOptions:\n(A) 21 ½ days\n(B) 22 ½ days\n(C) 23 ½ days\n(D) 12 ½ days\n(E) none of these\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: 1/18 + 1/30 = 8/90 = 4/45\n45/4 = 11 ¼ *2 = 22 ½ days The answer is (B).",
"role": "assistant"
}
] |
cot
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cot_74923
|
[
{
"content": "question: The speed of a boat in still water is 70kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?\nOptions:\n(A) kmph\n(B) kmph\n(C) kmph\n(D) kmph\n(E) kmph\nanswer: Stream of consciousness: Speed downstream = 70 + 20 = 90 kmph\nSpeed upstream = 70 - 20 = 50 kmph The answer is (D).\nq: In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Elaine?\nOptions:\n(A) 1,008\n(B) 1,296\n(C) 1,512\n(D) 2*1008\n(E) 2,268\na: Stream of consciousness: Place D and H first: 8 options for D, 7 options for H\nWe are left with 6 empty places. A, B and C must take first 3 places and F, G, Emust take the remaining three. A, B and C can be arranged in their places in 3! ways. The same for F, G, and E\nTotal = 8*7*3!*3! = 2*1008 The answer is (D).\nquestion: Simple interest on a certain sum is 16 over 25 of the sum. Find the rate per cent and time, if both are equal.\nOptions:\n(A) 8% and 8 years\n(B) 6% and 6 years\n(C) 10% and 10 years\n(D) 12 % and 12 years\n(E) None of these\nanswer: Stream of consciousness: 16⁄25P = P×R×R/100\n⇒ R2 = 1600⁄25 ⇒ R = 40⁄5 = 8%\nAlso, time = 8 years The answer is (A).\nq: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 10 minutes, how much time will she spend doing yoga? (rounded to minutes)\nOptions:\n(A) 10 min.\n(B) 41 min.\n(C) 17 min.\n(D) 23 min.\n(E) 25 min.\na: Stream of consciousness: The ratio is 2:3 = gym:ride, so (10)(3/2) = 15 minutes at the gym, and 15 + 10 = 25 minutes exercise, so (2/3)(25) = 17 minutes yoga. The answer is (C).\nquestion: A small company employs 3 men and 5 women. If a team of 3 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?\nOptions:\n(A) 1/14\n(B) 1/7\n(C) 2/7\n(D) 5/7\n(E) 1/2\nanswer: Stream of consciousness: Total ways to choose 4 employees from 8 employees = 8C3\nTwo women = 5C2\nTwo Men = 3C1\nP = (5C2 * 3C1)/8C2 = 5/7 hence The answer is (D).\nquestion: Which of the following is equal to (x+1)!/x!\nOptions:\n(A) x-1\n(B) 1+(1/x) \n(C) x+1\n(D) 1\n(E) x\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: (x + 1)! = (x + 1) * x!\n(x + 1)!/x! = x + 1 The answer is (C).",
"role": "assistant"
}
] |
cot
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cot_97525
|
[
{
"content": "q: A river 2m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is?\nOptions:\n(A) 4500 M3\n(B) 27000 M3\n(C) 3000 M3\n(D) 2700 M3\n(E) 3700 M3\na: Stream of consciousness: (3000 * 2 * 5)/60 = 4500 M3 The answer is (A).\nquestion: CMM, EOO, GQQ, _____, KUU\nOptions:\n(A) MSQ\n(B) IPS\n(C) IIS\n(D) ISS\n(E) POL\nanswer: Stream of consciousness: The first letters are in alphabetical order with a letter skipped in between each segment: C, E, G, I, K. The second and third letters are repeated; they are also in order with a skipped letter: M, O, Q, S, U. The answer is (D).\nq: If the given two numbers are respectively 6% and 18% of a third number, then what percentage is the first of the second ?\nOptions:\n(A) 20%\n(B) 25%\n(C) 18%\n(D) 33 1/3%\n(E) none of these\na: Stream of consciousness: Here, l = 6 and m = 18\nTherefore, first number = l/m x 100% of second number = 6/18 x 100% of second number = 33 1/3% of second number The answer is (D).\nquestion: If a company allocates 15 percent of its budget to advertising, 20 percent to capital improvements, and 55 percent to salaries, what fraction of its budget remains for other allocations?\nOptions:\n(A) 4/5\n(B) 3/5\n(C) 3/10\n(D) 1/5\n(E) 1/10\nanswer: Stream of consciousness: 15 + 20 + 55 = 90% 100 - 90 = 10% to all others The answer is (E).\nq: If n is an integer, then the least possible value of |15 - 8n| is?\nOptions:\n(A) 0\n(B) 2\n(C) 1\n(D) 3\n(E) 5\na: Stream of consciousness: |15 - 8n| represents the distance between 15 and 8n on the number line. Now, the distance will be minimized when 8n, which is multiple of 8, is closest to 15. Multiple of 8 which is closest to 15 is 16 (for n = 2), so the least distance is 1: |15 - 16| = 1. The answer is (C).\nq: In what time will a railway train 40 m long moving at the rate of 36 kmph pass a telegraph post on its way?\nOptions:\n(A) 3 sec\n(B) 4 sec\n(C) 5 sec\n(D) 6 sec\n(E) 7 sec\na:",
"role": "user"
},
{
"content": "Stream of consciousness: T = 40/36 * 18/5 = 4 sec The answer is (B).",
"role": "assistant"
}
] |
cot
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cot_72559
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[
{
"content": "question: How much is 80% of 40 is greater than 4/5 of 15?\nOptions:\n(A) 12\n(B) 20\n(C) 18\n(D) 12\n(E) 81\nanswer: Stream of consciousness: (80/100) * 40 – (4/5) * 15\n32 - 12 = 20 The answer is (B).\nq: If n is an integer, then the least possible value of |15 - 8n| is?\nOptions:\n(A) 0\n(B) 2\n(C) 1\n(D) 3\n(E) 5\na: Stream of consciousness: |15 - 8n| represents the distance between 15 and 8n on the number line. Now, the distance will be minimized when 8n, which is multiple of 8, is closest to 15. Multiple of 8 which is closest to 15 is 16 (for n = 2), so the least distance is 1: |15 - 16| = 1. The answer is (C).\nquestion: Resident of town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and std deviation of 2 hrs. The number of hours that pat, a resident of town X, watched television last week was between 1 and 2 standard deviation below the mean. Which of the following could be the number of hours that Pat watched television last week?\nOptions:\n(A) 30\n(B) 20\n(C) 18\n(D) 22\n(E) 6\nanswer: Stream of consciousness: 21-12 < no of hrs < 21-2\n9< no of hrs < 19. The answer is (C).\nq: Suppose you have three identical prisms with congruent equilateral triangles as the end-polygons. Suppose you attach them by the rectangular faces so they are perfectly aligned. There will be some large faces created by two or more co-planar faces of the individual prisms: count each such large face as one. Given that, how many faces does the resultant solid have\nOptions:\n(A) 4\n(B) 6\n(C) 9\n(D) 10\n(E) 12\na: Stream of consciousness: To arrange them as described I did as follows on my scratch paper (see the file attached), where I counted 4 sides The answer is (A).\nquestion: A motorcyclist goes from Bombay to Pune, a distance of 224 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?\nOptions:\n(A) 1:2\n(B) 1:5\n(C) 4:7\n(D) 1:1\n(E) 1:8\nanswer: Stream of consciousness: T = 224/32 = 7 h\nT = 7 - 3 = 4\nTime Ratio = 7:4\nSpeed Ratio = 4:7 The answer is (C).\nquestion: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?\nOptions:\n(A) 7 1/7 sec\n(B) 7 7/2 sec\n(C) 7 1/8 sec\n(D) 7 1/2 sec\n(E) 7 3/2 sec\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: 70 + 50 = 120 * 5/18 = 100/3 mps\nD = 150 + 100 = 250 m\nT = 250 * 3/100 = 15/2 = 7 1/2 sec The answer is (D).",
"role": "assistant"
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cot
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cot_71597
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[
{
"content": "Rationale: Let number of boys = x\nLet number of girls = y\nTherefore x/y = B and y/x = G\n5(B + G) = 5[(x/y) + (y/x)] = 5[(x2 + y2)/xy] > 5\nThe answer: (E)\nQuestion: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 5 (B + G) is ?\nOptions:\n(A) Equal to 3\n(B) Less than 3\n(C) More than 3\n(D) Less than 1/3\n(E) none of these\n\n\nReasoning: Original perimeter = x\nHence original side = x/4\nNew side = 5x/4\nNew perimeter = 4*5x/4 = 5x\nAns: (C)\nQuestion: The measure of the side of a square is multiplied by 5. If x represents the perimeter of the original square, what is the value of the new perimeter?\nOptions:\n(A) 3x\n(B) 4x\n(C) 5x\n(D) 12x\n(E) 27x\n\n\nRationale: D = 130 + 150 = 280\nS = 36 * 5/18 = 10 mps\nT = 280/10 = 28 sec\nThe answer: (A)\nQuestion: How many seconds will a train 130 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?\nOptions:\n(A) 28 sec\n(B) 23 sec\n(C) 24 sec\n(D) 25 sec\n(E) 26 sec\n\n\nReasoning: It is clear that 22 x 45 = 10 x 55 + K + 11 x 40 ⇒⇒ K = 0\nAns: (B)\nQuestion: The average mark obtained by 22 candidates in an examination is 45. The average of the first ten is 55 while the last eleven is 40 .The marks obtained by the 11th candidate is ?\nOptions:\n(A) 2\n(B) 0\n(C) 9\n(D) 8\n(E) 6\n\n\nRationale: |48 - 7n| represents the distance between 48 and 7n on the number line. Now, the distance will be minimized when 7n, which is multiple of 7, is closest to 48. Multiple of 7 which is closest to 48 is 49 (for n = 7), so the least distance is 1: |48 - 49| = 1.\nThe answer: (A)\nQuestion: If n is an integer, then the least possible value of |48 - 7n| is?\nOptions:\n(A) 1\n(B) 0\n(C) 5\n(D) 4\n(E) 2\n\n\nRationale: Formula = √a×b\nA = 81 and B = 100\n√81×100 = 9 × 10 = 90\nThe answer: (E)\n",
"role": "user"
},
{
"content": "Question: Find the mean proportional between 81 & 100?\nOptions:\n(A) A) 59\n(B) B) 61\n(C) C) 63\n(D) D) 65\n(E) E) 90",
"role": "assistant"
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] |
cot
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cot_56871
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[
{
"content": "q: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?\nOptions:\n(A) 27\n(B) 29\n(C) 30\n(D) 34\n(E) 35\na: Stream of consciousness: The total of seven numbers = 7X18 = 126\nThe total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99\nSo, the middle number is (126 - 99 ) = 27 The answer is (A).\nquestion: Jasmine has a toaster with two slots that toasts one side of each piece of bread at a time, and it takes one minute to do so.\nIf she wants to make 3 pieces of toast, what is the least amount of time she needs to toast them on both sides?\nOptions:\n(A) 1\n(B) 2\n(C) 3\n(D) 4\n(E) 5\nanswer: Stream of consciousness: 3 minutes. She puts two pieces in the toaster, toasting one side of each. Then she flips one of them, takes one out, and puts the completely untoasted piece into the toaster. Finally, she takes out the toasted piece and puts the two half-toasted pieces of bread into the toaster for a minute and she's done. The answer is (C).\nq: A train 640 m in length crosses a telegraph post in 16 seconds. The speed of the train is?\nOptions:\n(A) 22 kmph\n(B) 77 kmph\n(C) 144 kmph\n(D) 71 kmph\n(E) 88 kmph\na: Stream of consciousness: S = 640/16 * 18/5 = 144 kmph The answer is (C).\nquestion: Six persons A,B,C,D,E &F went to soldier cinema. There are six consecutive seats. A sits in the first seat followed by B, followed by C and so on. If A taken on of the six seats, then B should sit adjacent to A. C should sit adjacent to A or B. D should sit adjacent to A, B or C and so on. How many possibilities are there ?\nOptions:\n(A) 30\n(B) 32\n(C) 34\n(D) 36\n(E) 38\nanswer: Stream of consciousness: First we have to arrange A, there is 1 method for it, for second person B, there are 2 methods one left and one right, for third 2 methods are there same as for B similarly for others, so total number of methods = 1*2*2*2*2*2 = 32 The answer is (B).\nq: A no.when divided by 220 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?\nOptions:\n(A) 2\n(B) 8\n(C) 9\n(D) 11\n(E) 15\na: Stream of consciousness: 220 + 43 = 263/17 = 8 (Remainder) The answer is (B).\nq: In a garden, carrots are planted in rows. In each row there are as many carrots as the number of rows in the garden. If each plant attracts as many bunnies as the number of carrots in each row and if the total number of bunnies is n, then :\nOptions:\n(A) n is a perfect square\n(B) n is an odd number\n(C) n is an even number\n(D) n is a perfect cube\n(E) none\na:",
"role": "user"
},
{
"content": "Stream of consciousness: For example, if there were 4 carrot rows, the garden would have a 4x4 arrangement. If each carrot attracts 4 bunnies, the number of bunnies would be (4*4)*4 = 64 pieces, which is a cube of 4. The answer is (D).",
"role": "assistant"
}
] |
cot
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cot_82468
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[
{
"content": "q: he population of a city is 140,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?\nOptions:\n(A) 1797787\n(B) 1597723\n(C) 159776\n(D) 159728\n(E) 157304\na: Stream of consciousness: Population after n years = P [1 + (R/100)]2\nPopulation after 2 years = 140000 * [1 + 6/100]2 = (160000 x 53/50 x 53/50) = 157304 The answer is (E).\nquestion: What is the probability that Company W's advertisement will be one of the first two be shown during the first commercial break?\nOptions:\n(A) 1/ 225\n(B) 1 / 30\n(C) 1 /15\n(D) 2 / 15\n(E) 4 /15\nanswer: Stream of consciousness: W 1/15 + (14/15) * 1/14 = 2/15 The answer is (D).\nq: A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?\nOptions:\n(A) 118\n(B) 150\n(C) 277\n(D) 200\n(E) 191\na: Stream of consciousness: Speed = 60 * 5/18 = 50/3 m/sec\nLength of the train = speed * time = 50/3 * 12 = 200 m The answer is (D).\nquestion: A, B, C, and D are four points, any three of which are non-collinear. Then, the number of ways to construct three lines each joining a pair of points so that the lines do not form a triangle is\nOptions:\n(A) 7\n(B) 8\n(C) 9\n(D) 24\n(E) 23\nanswer: Stream of consciousness: To construct 2 lines, three points can be selected out of 4 in 4 x 3 x 2 = 24 ways. Now, if third line goes from the third-point to the first point, a triangle is formed, and if it goes to the fourth point, a triangle is not formed. So, there are 24 ways to form a triangle and 24 ways of avoiding triangle. The answer is (D).\nq: A man rows his boat 105 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?\nOptions:\n(A) 5 kmph\n(B) 7 kmph\n(C) 12 kmph\n(D) 8 kmph\n(E) 1 kmph\na: Stream of consciousness: Speed downstream = d/t = 105/(2 1/2) = 42 kmph\nSpeed upstream = d/t = 45/(2 1/2) = 18 kmph\nThe speed of the stream = (42 - 18)/2 = 12 kmph The answer is (C).\nq: A sum of money doubles itself at a compound interest in 15 years . In how may years it will become 8 times ??\nOptions:\n(A) 30 years\n(B) 40 years\n(C) 45 years\n(D) 50 years\n(E) 60 years\na:",
"role": "user"
},
{
"content": "Stream of consciousness: If the sum doubles (x2) in 15 years, then it to become 2*2*2 = 8 times as large it should double three times, so three 15 years time period are needed, which is 3*15 = 45 years. The answer is (C).",
"role": "assistant"
}
] |
cot
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cot_53478
|
[
{
"content": "q: How long does a bus 100 m long traveling at 50 kmph takes to cross a bridge of 150 m in length?\nOptions:\n(A) 18\n(B) 16\n(C) 15\n(D) 11\n(E) 12\na: Stream of consciousness: D = 100 + 150 = 250 m\nS = 50 * 5/18 = 125/9\nT = 250 * 9/125 = 18 sec The answer is (A).\nquestion: Find the smallest number which should be multiplied with 36963 to make it a perfect square.\nOptions:\n(A) 4\n(B) 7\n(C) 4\n(D) 3\n(E) 6\nanswer: Stream of consciousness: 36963 = 111*111*3\nRequired smallest number = 3\n3 is the smallest number which should be multiplied with 36963 to make it a perfect square. The answer is (D).\nq: There are 4 magazines lying on a table; 2 are fashion magazines and the other 2 are sports magzines. If 1 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazine will be selected?\nOptions:\n(A) 1\n(B) 1/2\n(C) 1/4\n(D) 1/6\n(E) 1/8\na: Stream of consciousness: 1- (2c1/4c1) = 1-1/2 = 1/2 The answer is (B).\nquestion: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?\nOptions:\n(A) 226\n(B) 992\n(C) 665\n(D) 771\n(E) 211\nanswer: Stream of consciousness: (800*3*3)/100 = 72\n920 + 72 = 992 The answer is (B).\nq: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?\nOptions:\n(A) 624\n(B) 702\n(C) 756\n(D) 812\n(E) 832\na: Stream of consciousness: Total men are 7\nTotal women are 6 so we select 5 peoples in both and at least 3 are men\n7c3*6c2+7c4*6c1+7c5*6c0 then we get the 756 The answer is (C).\nq: A certain league has five divisions. The respective divisions had 6, 7, 8, 9 and 11 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?\nOptions:\n(A) 81\n(B) 83\n(C) 85\n(D) 86\n(E) 89\na:",
"role": "user"
},
{
"content": "Stream of consciousness: Overall, there can be 81 minuses. Tus, it is The answer is (A).",
"role": "assistant"
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cot
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cot_77306
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[
{
"content": "Reasoning: Answer = E\nPlease refer diagram below\n70 - 10 = 60\nAns: (E)\nQuestion: 80 white and black tiles will be used to form a 10x10 square pattern. If there must be at least one black tile in every row and at least one white tile in every column, what is the maximum difference between the number of black and white tiles that can be used?\nOptions:\n(A) 75\n(B) 80\n(C) 85\n(D) 90\n(E) 60\n\n\nRationale: Here, neither the total amount nor the individual amount is given. So the share of Q cannot be determine\nThe answer: (D)\nQuestion: An amount of money is to be divided among P, Q and R in the ratio of 4 : 9 : 16. If R gets 4 times more than P, what is Q’s share in it?\nOptions:\n(A) 1,800\n(B) 2,700\n(C) 3,600\n(D) Data inadequate\n(E) None of these\n\n\nReasoning: T = 192/32 = 6 h\nT = 6 - 3 = 3\nTime Ratio = 6:3 = 2:1\nSpeed Ratio = 1:2\nAns: (A)\nQuestion: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?\nOptions:\n(A) 1:2\n(B) 1:0\n(C) 1:87\n(D) 1:6\n(E) 1:1\n\n\nRationale: 1 to 9 = 9 * 9 = 81\n1 to 5 = 5 * 10 = 50\n5 to 9 = 5 * 8 = 40\n5th = 50 + 40 = 90 – 81 = 9\nThe answer: (A)\nQuestion: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?\nOptions:\n(A) 9\n(B) 8\n(C) 7\n(D) 6\n(E) 3\n\n\nReasoning: (555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030\nAns: (E)\nQuestion: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?\nOptions:\n(A) 124345\n(B) 234545\n(C) 165767\n(D) 144656\n(E) 220030\n\n\nReasoning: The total of thirteen numbers = 13X9 = 117\nThe total of first 6 and last 6 numbers is = 6 X 5+6 X 7 = 72\nSo, the middle number is (117 - 72 ) = 45\nAns: (B)\n",
"role": "user"
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{
"content": "Question: The average of thirteen numbers is 9. The average of first six numbers is 5 and the average of last six numbers is 7. What is the middle number?\nOptions:\n(A) 47\n(B) 45\n(C) 25\n(D) 37\n(E) 44",
"role": "assistant"
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cot
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cot_86621
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[
{
"content": "question: A certain car uses 12 gallons of gasoline in traveling 300 miles. In order for the car to travel the same distance using 10 gallons of gasoline, by how many miles per gallon must the car’s gas mileage be increased?\nOptions:\n(A) 2\n(B) 4\n(C) 5\n(D) 8\n(E) 10\nanswer: Stream of consciousness: 300/10 = 30. The difference is 30 - 25 = 5. The answer is (C).\nq: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?\nOptions:\n(A) 6 2/3%\n(B) 6 2/9%\n(C) 6 3/3%\n(D) 9 2/3%\n(E) 7 2/3%\na: Stream of consciousness: 4/9 P = (P*R*R)/100\nR = 20/3 = 6 2/3% The answer is (A).\nquestion: In how many ways can you seat 6 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?\nOptions:\n(A) 360\n(B) 1720\n(C) 2880\n(D) 5040\n(E) 10080\nanswer: Stream of consciousness: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 3 chairs to sit. The remaining 5 people can sit in 5! ways. Thus the # of arrangements is 3*5! = 360. The answer is (A).\nq: A student is ranked 13th from right and 8th from left.how many are there?\nOptions:\n(A) 18\n(B) 19\n(C) 20\n(D) 21\n(E) 22\na: Stream of consciousness: 13th from right means = x + 12\n8th from left means = 7 + x\nTotal = 12+7+1 = 20 The answer is (C).\nquestion: There are 18 balls in a jar. You take out 3 black balls without putting them back inside, and now the probability of pulling out a black ball is 1/3. How many blue balls were there in the beginning?\nOptions:\n(A) 12.\n(B) 9.\n(C) 8.\n(D) 7.\n(E) 6.\nanswer: Stream of consciousness: 8 = 3 blue balls + 15 / 3 The answer is (C).\nquestion: a student got 70% in one subject,80% in other.to get overall 75% how much he should get in third subject.\nOptions:\n(A) 65%\n(B) 75%\n(C) 85%\n(D) 95%\n(E) 88%\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: Already average of two subjects is (70+80)/2 = 75%\nTo maintain the percentage at 75%, he shouls get 75% marks in third subject The answer is (B).",
"role": "assistant"
}
] |
flan_v2
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flan_v2_90724
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[
{
"content": "In this task, you will be given a set of steps that are required to answer a specific question. Your job is to generate that question. Each given step refers to either an entity (known or unknown), a propery of an entity or a query operation (count, group, union, etc.) Knowing those operations and how they appear in the input may help you generate more accurate questions.\n Select: A select step is used to return a set of objects. There are no references to previous steps in a select step. template: Return [attributes]\n Filter: A filter step is used to return results from a previous step to which a certain condition applies. template: Return [#step] [condition]\n Project: A project step should return certain attributes of the results of a previous step. template: Return [attributes] of [#step]\n Aggregate: An aggregate step returns an aggregator function applied on a step's result. template: Return the [aggregator] of [#step].\n Group: A group step is an aggregator applied on attributes. template: Return the [aggregator] of [#step] for each [attribute]\n Superlative: A superlative step is used to return the result with a highest/lowest attribute among other results. template: Return [#step1] [where] [#step2] [is] [highest / lowest]\n Comparative: A comparative step is used when we need to compare an attribute with a number to filter results. template: Return [#step1] [where] [#step2] [comparator] [number] \n Union: A union step is used to return results of two steps together. template: Return [#step1] [or / ,] [#step2]\n Intersection: An intersection step returns the result that two steps have in common. template: Return [attribute] of both [#step1] and [#step2]\n Discard: A discard step returns result of a step and excludes result of another step from it. template: Return [#step1] besides [#step2]\n Sort: A sort returns result of another step in a specific order. template: Return [#step1] [ordered / sorted by] [#step2]\n Is true: An is true step checks a condition on another result and returns a true or false. template: Return [is / if] [condition]\n Arithmetic: An arithmatic step operates an arithmatic operation on one or more steps. template: Return the [arithmetic op.] of [#step1] [and] [#step2].\n\n[Q]: #1 return shape \n#2 return #1 that is shown the most\n[A]: What shape is shown the most?\n\n\n[Q]: #1 return dog \n#2 return #1 that is outside \n#3 return the grass \n#4 return #2 lying in #3 \n#5 return if #4 is in the image on the right\n[A]: If the dog in the image on the right is lying in the grass outside.\n\n\n[Q]: #1 return flights \n#2 return #1 from pittsburgh \n#3 return #2 to san francisco \n#4 return #3 leaving thursday evening \n#5 return information on #4\n[A]:",
"role": "user"
},
{
"content": "i would like information on any flights from pittsburgh to san francisco leaving thursday evening \n\n\n",
"role": "assistant"
}
] |
flan_v2
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flan_v2_95059
|
[
{
"content": "Rationale: Average weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 140/7 = 80 kgs\nThe answer: (B)\nQuestion: 3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 140kg then find the average weight of all the 7 rounds?\nOptions:\n(A) 98.5 kgs\n(B) 80 kgs\n(C) 76.5 kgs\n(D) 67.5 kgs\n(E) 58.2 kgs\n\n\nReasoning: The total possibilities are W@W@W@ (or) @W@W@W, where 2 blue and 1 red flowers occupy the space marked as @. Hence, the Total number of permutations is 2 x (3! / 2!) = 6.\nAns: (A)\nQuestion: One red flower, three white flowers and two blue flowers are arranged in a line such that\nI. No two adjacent flowers are of the same colour.\nII. The flowers at the two ends of the line are of different colours.\nIn how many different ways can the flowers be arranged?\nOptions:\n(A) 6\n(B) 4\n(C) 10\n(D) 12\n(E) 14\n\n\nRationale: 3!4! Required probability = 3!4!/6! = 1/5\nThe answer: (A)\nQuestion: If six persons sit in a row, then the probability that three particular persons are always together is -.\nOptions:\n(A) 1/5\n(B) 1/7\n(C) 1/9\n(D) 1/2\n(E) 2/7\n\n\nReasoning: If students are A, B, C, D, E and F; we can have 6C3 groups in all. However, if we have to count groups in which a particular student (say A) is always selected we would get 5C2 = 10 ways of doing it.\nAns: (C)\nQuestion: A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included in a particular student?\nOptions:\n(A) 6\n(B) 8\n(C) 10\n(D) 12\n(E) 15\n\n\nRationale: (x + 1)! = (x + 1) * x!\n(x + 1)!/x! = x + 1\nThe answer: (C)\nQuestion: Which of the following is equal to (x+1)!/x!\nOptions:\n(A) x-1\n(B) 1+(1/x) \n(C) x+1\n(D) 1\n(E) x\n\n\nRationale: 200/30 * 18/5 = 24 km/hr\nThe answer: (B)\n",
"role": "user"
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{
"content": "Question: A boy runs 200 metres in 30 seconds. What is his speed ?\nOptions:\n(A) 20 km/hr\n(B) 24 km/hr\n(C) 30 km/hr\n(D) 32 km/hr\n(E) 34 km/hr",
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cot
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cot_90751
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[
{
"content": "Rationale: Average weight = [(a + b + c + (a+b) + (b+c) + (c+a)+(a+b+c)] / 7 = 4 (a+b+c) /7 = 4 x 140/7 = 80 kgs\nThe answer: (B)\nQuestion: 3 friends A, B, C went for week end party to McDonald’s restaurant and there they measure there weights in some order In 7 rounds. A, B, C, AB, BC, AC, ABC. Final round measure is 140kg then find the average weight of all the 7 rounds?\nOptions:\n(A) 98.5 kgs\n(B) 80 kgs\n(C) 76.5 kgs\n(D) 67.5 kgs\n(E) 58.2 kgs\n\n\nReasoning: The total possibilities are W@W@W@ (or) @W@W@W, where 2 blue and 1 red flowers occupy the space marked as @. Hence, the Total number of permutations is 2 x (3! / 2!) = 6.\nAns: (A)\nQuestion: One red flower, three white flowers and two blue flowers are arranged in a line such that\nI. No two adjacent flowers are of the same colour.\nII. The flowers at the two ends of the line are of different colours.\nIn how many different ways can the flowers be arranged?\nOptions:\n(A) 6\n(B) 4\n(C) 10\n(D) 12\n(E) 14\n\n\nRationale: 3!4! Required probability = 3!4!/6! = 1/5\nThe answer: (A)\nQuestion: If six persons sit in a row, then the probability that three particular persons are always together is -.\nOptions:\n(A) 1/5\n(B) 1/7\n(C) 1/9\n(D) 1/2\n(E) 2/7\n\n\nReasoning: If students are A, B, C, D, E and F; we can have 6C3 groups in all. However, if we have to count groups in which a particular student (say A) is always selected we would get 5C2 = 10 ways of doing it.\nAns: (C)\nQuestion: A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included in a particular student?\nOptions:\n(A) 6\n(B) 8\n(C) 10\n(D) 12\n(E) 15\n\n\nRationale: (x + 1)! = (x + 1) * x!\n(x + 1)!/x! = x + 1\nThe answer: (C)\nQuestion: Which of the following is equal to (x+1)!/x!\nOptions:\n(A) x-1\n(B) 1+(1/x) \n(C) x+1\n(D) 1\n(E) x\n\n\nRationale: 200/30 * 18/5 = 24 km/hr\nThe answer: (B)\n",
"role": "user"
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{
"content": "Question: A boy runs 200 metres in 30 seconds. What is his speed ?\nOptions:\n(A) 20 km/hr\n(B) 24 km/hr\n(C) 30 km/hr\n(D) 32 km/hr\n(E) 34 km/hr",
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cot
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cot_55405
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[
{
"content": "q: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?\nOptions:\n(A) 6 2/3%\n(B) 6 2/9%\n(C) 6 3/3%\n(D) 9 2/3%\n(E) 7 2/3%\na: Stream of consciousness: 4/9 P = (P*R*R)/100\nR = 20/3 = 6 2/3% The answer is (A).\nquestion: What is the sum of all the composite numbers up to 20?\nOptions:\n(A) 130\n(B) 132\n(C) 124\n(D) 145\n(E) 166\nanswer: Stream of consciousness: 4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 = 132 The answer is (B).\nq: A man pointing to a photo says \"The lady in the photograph is my nephew’s maternal grandmother\". How is the lady in the photograph related to the man’s sister who has no other sister ?\nOptions:\n(A) Cousin\n(B) Sister-in-law\n(C) Mother\n(D) Mother-in-law\n(E) None of these\na: Stream of consciousness: Since the man is referring to his nephew, the nephew’s parent has to be a sibling to the man. Now the last part says that the man’s sister has no other sister and hence the brother-sister relationship is established between the man and his nephew’s mother. Now the lady in the picture is the grandmother of the nephew and hence she is the mother of the man’s sister. The answer is (C).\nquestion: If n is an integer, then the least possible value of |35 - 6n| is?\nOptions:\n(A) 2\n(B) 3\n(C) 5\n(D) 0\n(E) 1\nanswer: Stream of consciousness: |35 - 6n| represents the distance between 35 and 6n on the number line. Now, the distance will be minimized when 6n, which is multiple of 6, is closest to 35. Multiple of 6 which is closest to 35 is 36 (for n = 6), so the least distance is 1: |35 - 36| = 1. The answer is (E).\nq: Efrida and Frazer who live 12 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?\nOptions:\n(A) 6\n(B) 7\n(C) 8\n(D) 10\n(E) 11\na: Stream of consciousness: It's a simple geometry problem. Look at the diagram below: The answer is (D).\nq: How many seconds will a train 120 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?\nOptions:\n(A) 27 sec\n(B) 23 sec\n(C) 24 sec\n(D) 25 sec\n(E) 26 sec\na:",
"role": "user"
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{
"content": "Stream of consciousness: D = 120 + 150 = 270\nS = 36 * 5/18 = 10 mps\nT = 270/10 = 27 sec The answer is (A).",
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cot
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cot_56358
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[
{
"content": "question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?\nOptions:\n(A) 6 kmph\n(B) 5 kmph\n(C) 2 kmph\n(D) 8 kmph\n(E) 1 kmph\nanswer: Stream of consciousness: Speed downstream = d/t = 85/(2 1/2) = 34 kmph\nSpeed upstream = d/t = 45/(2 1/2) = 18 kmph\nThe speed of the stream = (34 - 18)/2 = 8 kmph The answer is (D).\nq: A rat is placed at the beginning of a maze and must make it to the end. There are four paths at the start that he has an equal chance of taking: path A takes 5 minutes and leads to the end, path B takes 8 minutes and leads to the start, path C takes 3 minutes and leads to the end, and path D takes 2 minutes and leads to the start.\nWhat is the expected amount of time it will take for the rat to finish the maze?\nOptions:\n(A) 5min\n(B) 6min\n(C) 7min\n(D) 8min\n(E) 9min\na: Stream of consciousness: Each path has an equal chance of occurring and if B or D are chosen they will just add 8 or 2 minutes to the time because the rat must restart the maze: time = (1/4)*5 + (1/4)*(8 + time) + (1/4)*(3) + (1/4)*(2 + time). Time = 9 minutes. The answer is (E).\nquestion: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?\nOptions:\n(A) 81000\n(B) 22887\n(C) 26877\n(D) 26771\n(E) 17121\nanswer: Stream of consciousness: 64000* 9/8 * 9/8 = 81000 The answer is (A).\nq: The average of 9 results is 50. The average of first four results is 52 and average of last four results is 49 . what is the fifth result?\nOptions:\n(A) 22\n(B) 27\n(C) 29\n(D) 46\n(E) 92\na: Stream of consciousness: Total of results = 50 x 9 = 450\nTotal of first four results = 52 x 4 = 208\nTotal of Last four results = 49 x 4 = 196\nHence the fifth result = 450 - (208 + 196) = 46 The answer is (D).\nquestion: The number N is 6,2X4, where X represents the ten's digit. If N is divisible by 9, what is the value of X?\nOptions:\n(A) 1\n(B) 3\n(C) 5\n(D) 7\n(E) 6\nanswer: Stream of consciousness: Integer is divisible by 9 - Sum of digits is divisible by 9 The answer is (E).\nquestion: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.\nOptions:\n(A) 150\n(B) 88\n(C) 2767\n(D) 288\n(E) 712\nanswer:",
"role": "user"
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{
"content": "Stream of consciousness: Speed = 60*(5/18) m/sec = 50/3 m/sec\nLength of Train (Distance) = Speed * Time\n(50/3) * 9 = 150 meter The answer is (A).",
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cot
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cot_61045
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[
{
"content": "q: A rat is placed at the beginning of a maze and must make it to the end. There are four paths at the start that he has an equal chance of taking: path A takes 5 minutes and leads to the end, path B takes 8 minutes and leads to the start, path C takes 3 minutes and leads to the end, and path D takes 2 minutes and leads to the start.\nWhat is the expected amount of time it will take for the rat to finish the maze?\nOptions:\n(A) 5min\n(B) 6min\n(C) 7min\n(D) 8min\n(E) 9min\na: Stream of consciousness: Each path has an equal chance of occurring and if B or D are chosen they will just add 8 or 2 minutes to the time because the rat must restart the maze: time = (1/4)*5 + (1/4)*(8 + time) + (1/4)*(3) + (1/4)*(2 + time). Time = 9 minutes. The answer is (E).\nquestion: A pipe can fill a cistern in 20 minutes whereas the cistern when full can be emptied by a leak in 28 minutes. When both pipes are opened, find when the cistern will be full?\nOptions:\n(A) 17\n(B) 16\n(C) 70\n(D) 13\n(E) 12\nanswer: Stream of consciousness: 1/20 - 1/28 = 1/70\n70 minutes The answer is (C).\nq: If one type of tobacco costs Re.1/- per kg and other type costs Rs. 5/- per kg. What quantity of first type and second type are mixed so that 100 kg of mixture costs Rs. 100/-?\nOptions:\n(A) 50 kg\n(B) 100 kg\n(C) 150 kg\n(D) 200 kg\n(E) 250 kg\na: Stream of consciousness: 100 kg of first type. The answer is (B).\nquestion: If 5 spiders can catch five flies in five minutes, how many flies can hundred spiders catch in 100 minutes?\nOptions:\n(A) 100\n(B) 1000\n(C) 500\n(D) 2000\n(E) None\nanswer: Stream of consciousness: 5 × 5 × x = 100 × 100 × 5 ⇒ x = 2000. The answer is (D).\nq: If M is the least positive integer that is divisible by every integer from 4 to 12 inclusive, then M/11 is =\nOptions:\n(A) 40320\n(B) 27720\n(C) 20160\n(D) 6720\n(E) 2520\na: Stream of consciousness: The integer should be divisible by: 4, 5, 6, 7, 8, 9, 10, 11 and 12, that is 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 3*2^2. The least common multiple of these integers is the product of 11, 7, 5, 3^2 and 2^3. Then, M/11 is (11 * 7 * 5 * 3^2 * 2^3)/11 = 7*5*9*8 = 2520. The answer is (E).\nq: What should come in place of the question mark (?) in the following equation?\n5978 + 6134 + 7014 = ?\nOptions:\n(A) 19226\n(B) 16226\n(C) 19216\n(D) 19126\n(E) None of these\na:",
"role": "user"
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{
"content": "Stream of consciousness: ? = 5978 + 6134 + 7014 = 19126 The answer is (D).",
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cot
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cot_62496
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[
{
"content": "Rationale: Sum of all the 13 results = 13 * 20 = 260\nSum of the first 7 of them = 8 * 20 = 160\nSum of the last 7 of them = 8 * 40 = 320\nSo, the 8th number = 260 + 160 - 320 = 100.\nThe answer: (E)\nQuestion: The average of 13 result is 20. Average of the first 8 of them is 20 and that of the last 8 is 40. Find the 8th result?\nOptions:\n(A) 35\n(B) 37\n(C) 46\n(D) 90\n(E) 100\n\n\nReasoning: If students are A, B, C, D, E and F; we can have 6C3 groups in all. However, if we have to count groups in which a particular student (say A) is always selected we would get 5C2 = 10 ways of doing it.\nAns: (C)\nQuestion: A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included in a particular student?\nOptions:\n(A) 6\n(B) 8\n(C) 10\n(D) 12\n(E) 15\n\n\nRationale: Multiple of 6 and 7 with difference 1 are 36 and 35\nSo the number of students in the class is 37\nThe answer: (C)\nQuestion: In a class if 1 is absent the rest of them can be divided into 6 equal groups and if two are absent can be divided into 7 equal groups. Find the minimum number of students in the class\nOptions:\n(A) 35\n(B) 36\n(C) 37\n(D) 38\n(E) 39\n\n\nReasoning: I = (300*9*6)/100 = 162\nAns: (C)\nQuestion: Find the simple interest on Rs.300 for 9 months at 6 paisa per month?\nOptions:\n(A) 142\n(B) 152\n(C) 162\n(D) 172\n(E) 182\n\n\nRationale: Number of ways of selecting 3 people out of 10 people = 10C3\nIn the three members George will always be there in the team. At this step we have vacancy for 2 more members and 9 members are available. Lina cannot be there in the team. So 2 members have to be selected and the number of available members = 9 - Nina = 8\nNumber of ways to form a 3 member team that includes George and excludes Nina = 8C2\nProbability = 8C2/10C3 = 28/120\nThe answer: (C)\nQuestion: From a Group of 10 People, Including George and Nina, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include George but not Nina\nOptions:\n(A) 5/56\n(B) 9/56\n(C) 28/120\n(D) 21/56\n(E) 25/56\n\n\nRationale: Using question number 11 and 12, we get the probability as\n1 - (1/36 + 5/9) = 5/12\nThe answer: (B)\n",
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{
"content": "Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is\nOptions:\n(A) 5/18\n(B) 5/12\n(C) 5/19\n(D) 5/15\n(E) 5/11",
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cot
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cot_97151
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[
{
"content": "Rationale: 14*13*12/3*2*1 = 364\nThe answer: (D)\nQuestion: A company organized a recruiting process for 3 vacant positions of assistant manager for its product launches. The company's efforts yielded 14 eligible candidates. How many sets of 3 candidates can the company choose to fill the 3 assistant manager positions?\nOptions:\n(A) 2,060\n(B) 1,320\n(C) 545\n(D) 364\n(E) 220\n\n\nReasoning: 45789+ 34567 = 610+ ?\n45789+ 34567 – 610 = 79746\nAns: (E)\nQuestion: What should come in place of the question mark (?) in the following equation?\n45789+ 34567 = 610+ ?\nOptions:\n(A) 96543\n(B) 13678\n(C) 23456\n(D) 56789\n(E) 79746\n\n\nRationale: If 1 green and 1 blue ball are taken from the box, then there are 10 green, 5 blue and 3 white balls, a total of 18 balls. If one ball is selected at random, the probability that it is green is given by 10 / 18\nThe answer: (B)\nQuestion: There are 20 balls in a box: 11 balls are green, 6 are blue and 3 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a green ball is selected at random from the box?\nOptions:\n(A) 1/13\n(B) 10/18\n(C) 3/13\n(D) 5/13\n(E) 6/13\n\n\nReasoning: 1/3: 1/6: 1/1 = 2:1:6\nAns: (C)\nQuestion: The inverse ratio of 3: 6: 1 is?\nOptions:\n(A) 2:3:7\n(B) 2:3:9\n(C) 2:1:6\n(D) 2:3:6\n(E) 2:3:1\n\n\nRationale: Let number of boys = x\nLet number of girls = y\nTherefore x/y = B and y/x = G\n7(B + G) = 7[(x/y) + (y/x)] = 7[(x2 + y2)/xy] > 7\nThe answer: (A)\nQuestion: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 7 (B + G) is ?\nOptions:\n(A) more than 7\n(B) Less than 3\n(C) More than 3\n(D) Less than 1/3\n(E) none of these\n\n\nRationale: 10 * 145 = 1450\n3 * 100 + 5 * 150 = 1050\n1450 – 1050 = 400\nThe answer: (A)\n",
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"content": "Question: A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.145. Find the unknown rate of two towels?\nOptions:\n(A) A) 400\n(B) B) 450\n(C) C) 500\n(D) D) 550\n(E) E) 600",
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cot
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cot_96816
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[
{
"content": "Rationale: Each path has an equal chance of occurring and if B or D are chosen they will just add 8 or 2 minutes to the time because the rat must restart the maze: time = (1/4)*5 + (1/4)*(8 + time) + (1/4)*(3) + (1/4)*(2 + time). Time = 9 minutes.\nThe answer: (E)\nQuestion: A rat is placed at the beginning of a maze and must make it to the end. There are four paths at the start that he has an equal chance of taking: path A takes 5 minutes and leads to the end, path B takes 8 minutes and leads to the start, path C takes 3 minutes and leads to the end, and path D takes 2 minutes and leads to the start.\nWhat is the expected amount of time it will take for the rat to finish the maze?\nOptions:\n(A) 5min\n(B) 6min\n(C) 7min\n(D) 8min\n(E) 9min\n\n\nReasoning: Correct Answer: (E)\nLet’s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn’t have to be true – consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us –x > y. Remember that x < 0, so –x = |x|, and y is positive, so |y| = y. Thus x < y is the same statement as |x| > |y|, and (D) must be true.\nAns: (D)\nQuestion: If x<0, y<0, and |x| > |y|, which of the following must be true?\nOptions:\n(A) x > y\n(B) y^2 > x^2\n(C) x^3 > y^2\n(D) x < y\n(E) x < –y\n\n\nRationale: 1/15 + 1/25 = 8/75\n75/8 = 9 3/8 days\nThe answer: (A)\nQuestion: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?\nOptions:\n(A) 9 3/8 days\n(B) 4 2/8 days\n(C) 17 9/8 days\n(D) 12 7/8 days\n(E) 16 9/8 days\n\n\nReasoning: Speed downstream = d/t = 85/(2 1/2) = 34 kmph\nSpeed upstream = d/t = 45/(2 1/2) = 18 kmph\nThe speed of the stream = (34 - 18)/2 = 8 kmph\nAns: (D)\nQuestion: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?\nOptions:\n(A) 6 kmph\n(B) 5 kmph\n(C) 2 kmph\n(D) 8 kmph\n(E) 1 kmph\n\n\nRationale: T = 192/32 = 6 h\nT = 6 - 3 = 3\nTime Ratio = 6:3 = 2:1\nSpeed Ratio = 1:2\nThe answer: (A)\nQuestion: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?\nOptions:\n(A) 1:2\n(B) 1:9\n(C) 1:1\n(D) 1:9\n(E) 3:2\n\n\nRationale: Given that 8th Feb, 2005 was Tuesday\nNumber of days from 8th Feb, 2004 to 7th Feb, 2005 = 366 (Since Feb 2004 has 29 days as it is a leap year)\n366 days = 2 odd days\nHence 8th Feb, 2004 = (Tuesday - 2 odd days) = Sunday\nThe answer: (A)\n",
"role": "user"
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"content": "Question: On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?\nOptions:\n(A) Sunday\n(B) Friday\n(C) Saturday\n(D) Monday\n(E) Tuesday",
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cot
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cot_80678
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[
{
"content": "Q: There are 4 magazines lying on a table; 2 are fashion magazines and the other 2 are sports magzines. If 1 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazine will be selected?\nOptions:\n(A) 1\n(B) 1/2\n(C) 1/4\n(D) 1/6\n(E) 1/8\nA: OK... Stream of consciousness: 1- (2c1/4c1) = 1-1/2 = 1/2\nThe answer is (B).\n\nQ: From a Group of 9 People, Including George and Nina, 4 people are to be selected at random to work on a certain project. What is the probability that 4 people selected will include George but not Nina\nOptions:\n(A) 5/56\n(B) 9/56\n(C) 15/56\n(D) 35/120\n(E) 25/56\nA: OK... Stream of consciousness: Number of ways of selecting 4 people out of 9 people = 9C4\nIn the three members George will always be there in the team. At this step we have vacancy for 3 more members and 8 members are available. Nina cannot be there in the team. So 3 members have to be selected and the number of available members = 8 - Nina = 7\nNumber of ways to form a 4 member team that includes George and excludes Nina = 7C3\nProbability = 7C3/9C4 = 35/120\nThe answer is (D).\n\nQ: The area of a triangle is with base 18m and height 6m?\nOptions:\n(A) 88 m2\n(B) 10 m2\n(C) 66 m2\n(D) 54 m2\n(E) 31 m2\nA: OK... Stream of consciousness: 1/2 * 18 * 6 = 54 m2\nThe answer is (D).\n\nQ: A train 210 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 120 meters long is?\nOptions:\n(A) 29\n(B) 22\n(C) 48\n(D) 99\n(E) 11\nA:",
"role": "user"
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"content": "OK... Stream of consciousness: D = 210 + 120 = 330\nS = 54 * 5/18 = 15 mps\nT = 330/15 = 22 sec\nThe answer is (B).",
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cot_93902
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[
{
"content": "Rationale: 4/9 P = (P*R*R)/100\nR = 20/3 = 6 2/3%\nThe answer: (A)\nQuestion: The simple interest on a sum of money is 4/9 of the principal and the number of years is equal to the rate percent. Find the rate and the time?\nOptions:\n(A) 6 2/3%\n(B) 6 2/7%\n(C) 6 2/2%\n(D) 6 3/3%\n(E) 6 5/3%\n\n\nReasoning: (y + 1)! = (y + 1) * x!\n(y + 1)!/y! = y + 1\nAns: (D)\nQuestion: Which of the following is equal to (y+1)!/y!?\nOptions:\n(A) y-1\n(B) 1+(1/y) \n(C) 1\n(D) y+1\n(E) y\n\n\nRationale: Integer is divisible by 9 - Sum of digits is divisible by 9\nThe answer: (E)\nQuestion: The number N is 6,2X4, where X represents the ten's digit. If N is divisible by 9, what is the value of X?\nOptions:\n(A) 1\n(B) 3\n(C) 5\n(D) 7\n(E) 6\n\n\nReasoning: Of the 15 marbles we are wanting red:\nProbability of choosing 1st red marble: 5/15\nProbability of Choosing 2nd red marble: 4/14\nMultiply and you get 20/210 simplified to 2/21\nAns: (B)\nQuestion: A marble shop contains 5 blue marbles, 5 red marbles, and 5 green marbles. If 2 marbles are purchased at random from the shop, what is the probability that the 2 marbles will be of the red?\nOptions:\n(A) 5/15\n(B) 2/21\n(C) 20/15\n(D) 5/210\n(E) 4/14\n\n\nRationale: Average of 20 numbers = 0\nSum of 20 numbers = (0 * 20) = 0\nIt is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).\nThe answer: (D)\nQuestion: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?\nOptions:\n(A) 7\n(B) 4\n(C) 12\n(D) 19\n(E) 28\n\n\nRationale: Speed downstream = 60 + 20 = 80 kmph\nSpeed upstream = 60 - 20 = 40 kmph\nThe answer: (D)\n",
"role": "user"
},
{
"content": "Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?\nOptions:\n(A) 40, 68 kmph\n(B) 40, 30 kmph\n(C) 90, 60 kmph\n(D) 40, 60 kmph\n(E) 20, 60 kmph",
"role": "assistant"
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cot
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cot_92787
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[
{
"content": "q: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?\nOptions:\n(A) 122456\n(B) 145778\n(C) 456678\n(D) 235467\n(E) 220030\na: Stream of consciousness: (555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030 The answer is (E).\nquestion: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?\nOptions:\n(A) 2\n(B) 3\n(C) 6\n(D) 8\n(E) 9\nanswer: Stream of consciousness: Work done by X in 1 day = 1/18\nWork done by Y in 1 day = 1/15\nWork done by Y in 10 days = 10/15 = 2/3\nRemaining work = 1 – 2/3 = 1/3\nNumber of days in which X can finish the remaining work = (1/3) / (1/18) = 6 The answer is (C).\nq: A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?\nOptions:\n(A) 31 inches\n(B) 32 inches\n(C) 33 inches\n(D) 34 inches\n(E) 35 inches\na: Stream of consciousness: 7 ft 9 in is 84 + 9 = 93 inches. so 93/3 = 31 inches or 2 ft. 7 inch. The answer is (A).\nquestion: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?\nOptions:\n(A) 1\n(B) 2\n(C) 3\n(D) 5\n(E) 6\nanswer: Stream of consciousness: (1056 / 23) gives remainder 21\n21 + 2 = 23, So we need to add 2 The answer is (B).\nq: 189. The inside dimensions of a rectangular wooden box\nare 10 inches by 12 inches by 14 inches. A cylindrical\ncanister is to be placed inside the box so that it stands\nupright when the closed box rests on one of its six\nfaces. Of all such canisters that could be used, what is\nthe radius, in inches, of the one that has maximum\nvolume?\nOptions:\n(A) 3\n(B) 4\n(C) 5\n(D) 6\n(E) 8\na: Stream of consciousness: Since the radius is squared, the biggest volume cylinder will have the biggest possible radius. To achieve that, let the smaller dimension of the rectangular box be the height. So, it will have 14x12 width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 12, so the radius will be 6. The answer is (D).\nq: The length of each side of an equilateral triangle having an area of 4√3 cm2 is?\nOptions:\n(A) 1/8\n(B) 1/9\n(C) 1/5\n(D) 1/23\n(E) 1/2\na:",
"role": "user"
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{
"content": "Stream of consciousness: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5 The answer is (C).",
"role": "assistant"
}
] |
cot
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cot_83696
|
[
{
"content": "Reasoning: 12 = 3 blue balls + 18 / 2\nAns: (A)\nQuestion: There are 20 balls in a jar. You take out 2 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning?\nOptions:\n(A) 12.\n(B) 9.\n(C) 8.\n(D) 7.\n(E) 6.\n\n\nRationale: Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes only the product of 333 and will be odd, the remaining 26 will have either 2 or 4 in them, which ensures that their product will be even. Therefore the number of codes where the product of the digits is even = (total) - (restriction) = 27 - 1 = 26.\nThe answer: (C)\nQuestion: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 6, 4 and 3, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created?\nOptions:\n(A) 20\n(B) 22\n(C) 26\n(D) 24\n(E) 30\n\n\nReasoning: Clearly, 37 is a prime number.\nAns: (A)\nQuestion: Find a a prime number from the options below.\nOptions:\n(A) 37\n(B) 38\n(C) 39\n(D) 40\n(E) 42\n\n\nRationale: It's a simple geometry problem. Look at the diagram below:\nThe answer: (D)\nQuestion: Efrida and Frazer who live 12 miles apart, meet at a restaurant that is directly north of Efrida's home and directly east of Frazer's home. If the restaurant is two miles closer to Efrida's home, than to Frazer's home, how many miles is the restaurant from Frazer's home?\nOptions:\n(A) 6\n(B) 7\n(C) 8\n(D) 10\n(E) 11\n\n\nReasoning: These 5 tasks can be arranged in 5! = 120 ways. In half of them invites are sentafterthe guest list is decided and in half of them before. So, there are total of 120/2 = 60 ways to arrange the task so that the invites are sent after the guest list is decided.\nAns: (C)\nQuestion: Joey is planning to throw a small party and for that he needs to do the following tasks:\nI. Decide guest list\nII. Send invites\nIII. Arrange catering\nIV. Decide the venue\nV. Rent a music system\nThe tasks can be done in any order as long as the invites are sent after the guest list is decided. In how many ways can Joey do the five tasks listed above?\nOptions:\n(A) 24\n(B) 48\n(C) 60\n(D) 120\n(E) 240\n\n\nReasoning: Total boxes = 23\nFilled with toys = 16\nFilled with appliance = 7\nTotal boxes for sale = 8\nToy boxes for sale = 6\nAppliance boxes for sale = 2\nAppliance boxes not for sale = 7 - 2 = 5\nAns: (E)\n",
"role": "user"
},
{
"content": "Question: In Sam's hanger there are 23 boxes, 16 out of the boxes are filled with toys and the rest are filled with electrical appliances. 8 boxes are for sale, 6 of them are filled with toys. How many boxes with electrical appliances are in Sam's hanger that is not for sale?\nOptions:\n(A) 1.\n(B) 2.\n(C) 3.\n(D) 4.\n(E) 5.",
"role": "assistant"
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flan_v2
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flan_v2_89082
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[
{
"content": "In this task, you will be given a set of steps that are required to answer a specific question. Your job is to generate that question. Each given step refers to either an entity (known or unknown), a propery of an entity or a query operation (count, group, union, etc.) Knowing those operations and how they appear in the input may help you generate more accurate questions.\n Select: A select step is used to return a set of objects. There are no references to previous steps in a select step. template: Return [attributes]\n Filter: A filter step is used to return results from a previous step to which a certain condition applies. template: Return [#step] [condition]\n Project: A project step should return certain attributes of the results of a previous step. template: Return [attributes] of [#step]\n Aggregate: An aggregate step returns an aggregator function applied on a step's result. template: Return the [aggregator] of [#step].\n Group: A group step is an aggregator applied on attributes. template: Return the [aggregator] of [#step] for each [attribute]\n Superlative: A superlative step is used to return the result with a highest/lowest attribute among other results. template: Return [#step1] [where] [#step2] [is] [highest / lowest]\n Comparative: A comparative step is used when we need to compare an attribute with a number to filter results. template: Return [#step1] [where] [#step2] [comparator] [number] \n Union: A union step is used to return results of two steps together. template: Return [#step1] [or / ,] [#step2]\n Intersection: An intersection step returns the result that two steps have in common. template: Return [attribute] of both [#step1] and [#step2]\n Discard: A discard step returns result of a step and excludes result of another step from it. template: Return [#step1] besides [#step2]\n Sort: A sort returns result of another step in a specific order. template: Return [#step1] [ordered / sorted by] [#step2]\n Is true: An is true step checks a condition on another result and returns a true or false. template: Return [is / if] [condition]\n Arithmetic: An arithmatic step operates an arithmatic operation on one or more steps. template: Return the [arithmetic op.] of [#step1] [and] [#step2].\nOne example is below.\nQ: #1 return secretaries \n#2 return #1 born in state 'Alabama \n#3 return departments managed by #2 \n#4 return distinct creation years of #3\nA: What are the distinct creation years of the departments managed by a secretary born in state 'Alabama'?\nRationale: You should follow the steps in order to realize what is the asked question. In this example, the first returned entities are secretaries(based on step #1) who are born in Alabama(based on step #2). In the step #3 departments managed by step #2(which is secretaries born in Alabama. In the final steps the creation years of the departments is returned, so the question will be about the creation years of the departments. \nQ: #1 return Rashard Mendenhall \n#2 return tds of #1 \n#3 return yards of #2 \n#4 return #3 that are equal to one \n#5 return number of #4\nA:",
"role": "user"
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{
"content": "How many one yard tds did Rashard Mendenhall score?",
"role": "assistant"
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cot
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cot_55584
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[
{
"content": "question: A racng car travels k kilometres in n hours. How many miles will it travel in x hours at the same rate?\nOptions:\n(A) knx\n(B) k⁄n\n(C) kn⁄x\n(D) kx\n(E) kx⁄n\nanswer: Stream of consciousness: Given Speed = k/n\nTo Find distance in x hours with same speed\nDistance = speed * time\nDistance = k/n*x = kx/n The answer is (E).\nq: Which one of the following is a prime number?\nOptions:\n(A) 10\n(B) 61\n(C) 49\n(D) 75\n(E) 91\na: Stream of consciousness: 61 is divisible by 1, and itself. So, it is a prime number. The answer is (B).\nquestion: Find the least number must be subtracted from 5474827 so that remaining no.is divisible by 12?\nOptions:\n(A) 3\n(B) 5\n(C) 4\n(D) 7\n(E) 2\nanswer: Stream of consciousness: On dividing 5474827 by 12 we get the remainder 7, so 7 should be subtracted The answer is (D).\nq: A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?\nOptions:\n(A) 6\n(B) 2\n(C) 3\n(D) 4\n(E) 98\na: Stream of consciousness: Work done by A in 2 days = 2/5\nRemaining work = 3/5\nWork done by both A and B in one day = 1/5 + 1/10 = 3/10\nRemaining work = 3/5 * 10/3 = 2 day The answer is (B).\nquestion: In a certain lottery drawing, two balls are selected at random from a container with 10 balls, numbered from 1 to 10, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner?\nOptions:\n(A) $9 x 10^4\n(B) $9.90 x 10^6\n(C) $1.00 x 10^7\n(D) $1.05 x 10^7\n(E) $9.90 x 10^7\nanswer: Stream of consciousness: The max product of any two balls can be 9 * 10 = 9900 = 9 * 10\nIf we multiply it by $1000 the max amount will be 9 * 10^4. The answer is (A).\nquestion: 80 370 860 1550 ? 3530\nOptions:\n(A) 900\n(B) 2440\n(C) 750\n(D) 244\n(E) 960\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: 10^2 - 20 = 80\n20^2 - 30 = 370\n30^2 - 40 = 860\n40^2 - 50 = 1550\n50^2 - 60 = 2440\n60^2 - 70 = 3530. The answer is (B).",
"role": "assistant"
}
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cot
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cot_79717
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[
{
"content": "If n is an integer, then the least possible value of |33 - 5n| is?\nOptions:\n(A) 0\n(B) 1\n(C) 2\n(D) 3\n(E) 4\n\n|33 - 5n| represents the distance between 33 and 5n on the number line. Now, the distance will be minimized when 5n, which is multiple of 5, is closest to 33. Multiple of 5 which is closest to 33 is 35 (for n = 7), so the least distance is 2: |33 - 35| = 2. So the answer is: (C).\n\nThe average of 13 numbers is 60. Average of the first 7 of them is 56 and that of the last 7 is 61. Find the 8th number?\nOptions:\n(A) 39\n(B) 83\n(C) 45\n(D) 53\n(E) 64\n\nSum of all the 13 numbers = 13 * 60 = 780\nSum of the first 7 of them = 7 * 56 = 392\nSum of the last 7 of them = 7 * 61 = 427\nSo, the 8th number = 427 + 392 - 780 = 39. So the answer is: (A).\n\nThe price of a T.V. set worth Rs. 40000 is to be paid in 20 installments of Rs. 2500 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?\nOptions:\n(A) 29997\n(B) 28088\n(C) 27098\n(D) 37500\n(E) 2799\n\nMoney paid in cash = Rs. 2500\nBalance payment = (40000- 2500) = Rs. 37500. So the answer is: (D).\n\nA can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately?\nOptions:\n(A) 7 days\n(B) 8 days\n(C) 5 days\n(D) 4 days\n(E) 2 days\n\n",
"role": "user"
},
{
"content": "A + B = 1/20 + 1/15 = 7/60\nA + C = 1/20 + 1/12 = 8/60\n7/60 + 8/60 = 15/60 = 1/4\n4 days * 2 = 8 days So the answer is: (B).",
"role": "assistant"
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cot
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cot_73272
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[
{
"content": "Reasoning: This alternating addition series begins with 3; then 1 is added to give 4; then 3 is added to give 7; then 1 is added, and so on.\nAns: (A)\nQuestion: Look at this series: 3, 4, 7, 8, 11, 12, ... What number should come next?\nOptions:\n(A) 15\n(B) 14\n(C) 17\n(D) 12\n(E) 19\n\n\nRationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m\nNo. of days required to paint 36 m cloth by 6 men = 72/ 6 × 6 = 2 day.\nThe answer: (B)\nQuestion: If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 72 m long cloth in\nOptions:\n(A) 1 day\n(B) 2 days\n(C) 3 days\n(D) 4 days\n(E) 5 days\n\n\nReasoning: Bass = 2/7 = 10/35\nTuna = 1/5 = 7/35\nTrout = 1/7 = 5/35\nCatfish = 1 - (10/35 +7/35 + 5/35) = 13/35\nPurchased: Tuna = 7/35 - (7/35)(1/7) = 6/35, and\nCatfish = 13/35 - (13/35)(1/7) = 12/35\nStocked: doubling the number of bass (2)(10/35) = 20/35\nNow: 20 + 6 + 5 + 12 = 43\nTrout proportion is now 5/43.\nAns: (C)\nQuestion: At the A-Street Fish Market a vendor sells fresh caught fish. His store is filled with 2/7 bass, 1/5 tuna, 1/7 trout, and the rest are catfish. If a customer just bought 1/7 of all the tuna and 1/7 of all the catfish, and a fisherman arrived to restock the bass, doubling the number of bass, what proportion of fish now in the store are trout?\nOptions:\n(A) 30/71\n(B) 4/7\n(C) 5/43\n(D) 1/2\n(E) 1/5\n\n\nRationale: (800*3*3)/100 = 72\n920 + 72 = 992\nThe answer: (D)\nQuestion: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?\nOptions:\n(A) 288\n(B) 200\n(C) 279\n(D) 992\n(E) 208\n\n\nReasoning: Hundreds digit can be 7 or 8\nIf the hundreds digit is 7, then the tens digit has to be 8 and the units digit has to be 9\nIf the hundreds digit is 8, then the tens digit has to be 9 and the units digit has to be 10\nA digit has to fall between 0 and 9, so 10 cannot be a digit\nThe number is 789\nTotal numbers between 700 and 899 = (899-700)+1 = 200\nProbability = 1/200\nAns: (E)\nQuestion: If a 3-digit integer is selected at random from the integers 700 through 899, inclusive, what is the probability that the second digit is one greater then the first digit, and the third digit is one greater than the second digit?\nOptions:\n(A) 2/225\n(B) 2/200\n(C) 8/700\n(D) 1/50\n(E) 1/200\n\n\nReasoning: Overall, there can be 47 minuses. Tus, it is\nAns: (D)\n",
"role": "user"
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{
"content": "Question: A certain league has two divisions. The respective divisions had 11 and 13 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?\nOptions:\n(A) 41\n(B) 42\n(C) 45\n(D) 47\n(E) 49",
"role": "assistant"
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cot
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cot_73107
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[
{
"content": "Question: There were 180 apples in each crate. 12 such crates of apples were delivered to a factory. 160 apples were rotten and had to be thrown away. The remaining apples were packed into boxes of 20 apples each. How many boxes of apples were there?\nAnswer: The total number of apples delivered was: 180 apples x 12 crates = 2160 apples. So, the number of remaining apples after throwing away the rotten ones was: 2160 apples – 160 apples = 2000 apples. And now, we can find the total number of boxes of apples by dividing the remaining number of apples by the number of apples per box: 2000 apples / 20 apples / box = 100 boxes of apples. The answer is 100.\n[Question]Mark bought a shirt, pants, and shoes for $340. What is the price of the pants knowing that the price of a shirt is three-quarters of the price of the pants and that the price of a shoe is ten dollars more than the price of the pants?\n[Answer]Let X be the price of the pants. The price of the shirt is 3 / 4 * X. The price of the shoes is X + 10. The total amount paid is X + 3 / 4 * X + X + 10 = $340. Combining like terms we get X * 11 / 4 + 10 = $340. Subtracting 10 from both sides we get X * 11 / 4 = $330. Dividing both sides by 11 / 4 we get X = $120. The answer is 120.\nQ: For every black & white cookie that Elsa makes, she has to make the batter, bake the cookies for 15 minutes and then allow to cool. She then has to dip the cookies in white icing and allow the icing to harden for 30 minutes. Then she has to re-dip them in chocolate icing and allowed to harden for an additional 30 minutes. If it takes her 2 hours to make the cookies from start to finish, how long does it take to make the dough and cool the cookies before she can start dipping them?\nA: It takes 15 minutes to bake, 30 minutes for the white icing to harden and 30 minutes for the chocolate icing to harden so it takes 15 + 30 + 30 = 75 minutes. Every hour has 60 minutes and it takes her 2 hours so it takes 60 * 2 = 120 minutes to make the cookies. It takes 120 minutes to make the cookies from start to finish and she spends 75 minutes baking and hardening icing so it takes her 120 - 75 = 45 minutes to make the batter and cool the cookies. The answer is 45.\nQuestion: The area of square A is 25. The area of square B is 81. What's the length difference between the sides of square A and B?\nAnswer: The area of a square is calculated as length * width. Because all a square has all sides equal then we can say that given a side S, the area is S * S. For square A of sides A, the area is A * A = 25 or A^2 = 25. Solving for A we know that A = 5. For square B of sides B, the area is B * B = 81 or B^2 = 81. Solving for B we know that B = 9. The side difference between A and B is 9 - 5 = 4. The answer is 4.\n[Question]Jeremy loves to play Scrabble. He once played a three-letter word on a triple word score to earn thirty points. If before the word score was tripled, the first and third letters were each valued at one point apiece, how much was the middle letter valued at before the word score was tripled?\n[Answer]Since the word score after being tripled was 30 points, then the word score before tripling was 30 / 3 = 10 points. If before the word score was tripled, the first and third letters were each valued at one point apiece, then the value of the middle letter was 10 - 1 - 1 = 8 points. The answer is 8.\n[Question]Betty is planning to host her friends over for a party. She buys drinks, cakes, and ice creams at a unit cost of $2, $10, and $5 respectively. How much does she spend if she buys 10 drinks, 5 cakes, and 100 ice creams?\n[Answer]\n",
"role": "user"
},
{
"content": "The amount she spends on buying drinks is $2 * 10 = $20. The amount she spends on buying cakes is $10 * 5 = $50. The amount she spends on buying ice creams is $5 * 100 = $500. The total amount she spends is $20 + $50 + $500 = $570. The answer is 570.",
"role": "assistant"
}
] |
flan_v2
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flan_v2_94805
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[
{
"content": "Question: There were 180 apples in each crate. 12 such crates of apples were delivered to a factory. 160 apples were rotten and had to be thrown away. The remaining apples were packed into boxes of 20 apples each. How many boxes of apples were there?\nAnswer: The total number of apples delivered was: 180 apples x 12 crates = 2160 apples. So, the number of remaining apples after throwing away the rotten ones was: 2160 apples – 160 apples = 2000 apples. And now, we can find the total number of boxes of apples by dividing the remaining number of apples by the number of apples per box: 2000 apples / 20 apples / box = 100 boxes of apples. The answer is 100.\n[Question]Mark bought a shirt, pants, and shoes for $340. What is the price of the pants knowing that the price of a shirt is three-quarters of the price of the pants and that the price of a shoe is ten dollars more than the price of the pants?\n[Answer]Let X be the price of the pants. The price of the shirt is 3 / 4 * X. The price of the shoes is X + 10. The total amount paid is X + 3 / 4 * X + X + 10 = $340. Combining like terms we get X * 11 / 4 + 10 = $340. Subtracting 10 from both sides we get X * 11 / 4 = $330. Dividing both sides by 11 / 4 we get X = $120. The answer is 120.\nQ: For every black & white cookie that Elsa makes, she has to make the batter, bake the cookies for 15 minutes and then allow to cool. She then has to dip the cookies in white icing and allow the icing to harden for 30 minutes. Then she has to re-dip them in chocolate icing and allowed to harden for an additional 30 minutes. If it takes her 2 hours to make the cookies from start to finish, how long does it take to make the dough and cool the cookies before she can start dipping them?\nA: It takes 15 minutes to bake, 30 minutes for the white icing to harden and 30 minutes for the chocolate icing to harden so it takes 15 + 30 + 30 = 75 minutes. Every hour has 60 minutes and it takes her 2 hours so it takes 60 * 2 = 120 minutes to make the cookies. It takes 120 minutes to make the cookies from start to finish and she spends 75 minutes baking and hardening icing so it takes her 120 - 75 = 45 minutes to make the batter and cool the cookies. The answer is 45.\nQuestion: The area of square A is 25. The area of square B is 81. What's the length difference between the sides of square A and B?\nAnswer: The area of a square is calculated as length * width. Because all a square has all sides equal then we can say that given a side S, the area is S * S. For square A of sides A, the area is A * A = 25 or A^2 = 25. Solving for A we know that A = 5. For square B of sides B, the area is B * B = 81 or B^2 = 81. Solving for B we know that B = 9. The side difference between A and B is 9 - 5 = 4. The answer is 4.\n[Question]Jeremy loves to play Scrabble. He once played a three-letter word on a triple word score to earn thirty points. If before the word score was tripled, the first and third letters were each valued at one point apiece, how much was the middle letter valued at before the word score was tripled?\n[Answer]Since the word score after being tripled was 30 points, then the word score before tripling was 30 / 3 = 10 points. If before the word score was tripled, the first and third letters were each valued at one point apiece, then the value of the middle letter was 10 - 1 - 1 = 8 points. The answer is 8.\n[Question]Betty is planning to host her friends over for a party. She buys drinks, cakes, and ice creams at a unit cost of $2, $10, and $5 respectively. How much does she spend if she buys 10 drinks, 5 cakes, and 100 ice creams?\n[Answer]\n",
"role": "user"
},
{
"content": "The amount she spends on buying drinks is $2 * 10 = $20. The amount she spends on buying cakes is $10 * 5 = $50. The amount she spends on buying ice creams is $5 * 100 = $500. The total amount she spends is $20 + $50 + $500 = $570. The answer is 570.",
"role": "assistant"
}
] |
cot
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cot_66828
|
[
{
"content": "question: CMM, EOO, GQQ, _____, KUU\nOptions:\n(A) MSQ\n(B) IPS\n(C) IIS\n(D) ISS\n(E) POL\nanswer: Stream of consciousness: The first letters are in alphabetical order with a letter skipped in between each segment: C, E, G, I, K. The second and third letters are repeated; they are also in order with a skipped letter: M, O, Q, S, U. The answer is (D).\nq: What is the units digit of the expression 14^7−16^4?\nOptions:\n(A) 0\n(B) 3\n(C) 8\n(D) 6\n(E) 4\na: Stream of consciousness: I think answer on this one should be C too. Since we know that 14^7>16^4, as Will said one should always check if the number is positive. The answer is (C).\nquestion: If six persons sit in a row, then the probability that three particular persons are always together is -.\nOptions:\n(A) 1/5\n(B) 1/7\n(C) 1/9\n(D) 1/2\n(E) 2/7\nanswer: Stream of consciousness: 3!4! Required probability = 3!4!/6! = 1/5 The answer is (A).\nq: If X is the sum of first 40 positive even integers and Y is the sum of first 40 positive odd integers, what is the value of x-y?\nPlease try to explain your answers\nOptions:\n(A) 0\n(B) 25\n(C) 40\n(D) 75\n(E) 100\na: Stream of consciousness: First even minus first odd = 2-1 = 1;\nThe sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;\nThe sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;\nWe can see the patterns here, so the sum of first 40 positive even integers minus the sum of first 40 positive odd integers will be 40. The answer is (C).\nquestion: An analyst will recommend a combination of 2 industrial stocks, 3 transportation stocks, and 3 utility stocks. If the analyst can choose from 6 industrial stocks, 3 transportation stocks, and 4 utility stocks, how many different combinations of 9 stocks are possible?\nOptions:\n(A) 12\n(B) 19\n(C) 60\n(D) 180\n(E) 720\nanswer: Stream of consciousness: 6C2 * 3C3 * 4C3 = 15*1*4 = 60. The answer is (C).\nquestion: Amy, Bob, Cindy, and Daniel all have the same birthday, but they are all different ages. Today is their birthday. Cindy's age is divisible by Bob's age, and Amy's age is divisible by Cindy's age. If A is Amy's age in years, B is Bob's age, and C is Cindy's age, which of the following CANNOT be Daniel's age?\nOptions:\n(A) AC/B\n(B) (A+C) /B\n(C) (A+B) /C\n(D) AB/C\n(E) (A-C) /B\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: Since today's is Daniel's birthday, his age must be an integer. As per the question, let A = 12, B = 2, and C = 6. Plugging these into the answer choices, only C does not yield an integer. The answer is (C).",
"role": "assistant"
}
] |
cot
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cot_68958
|
[
{
"content": "Q: The average of seven numbers is 9. The average of first three numbers is 7 and the average of last three numbers is 11. What is the middle number?\nOptions:\n(A) 7\n(B) 8\n(C) 9\n(D) 11\n(E) 10\nA: OK... Stream of consciousness: The total of seven numbers = 7X9 = 63\nThe total of first 3 and last 3 numbers is = 3 X 7+3 X 11 = 54\nSo, the middle number is (63 - 54 ) = 9\nThe answer is (C).\n\nQ: Rs.600 amounts to Rs.900 in 3 years at simple interest. If the interest is increased by 4%, it would amount to how much?\nOptions:\n(A) 672\n(B) 246\n(C) 258\n(D) 856\n(E) 653\nA: OK... Stream of consciousness: (600*3*4)/100 = 72\n600 + 72 = 672\nThe answer is (A).\n\nQ: If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 72 m long cloth in\nOptions:\n(A) 1 day\n(B) 2 days\n(C) 3 days\n(D) 4 days\n(E) 5 days\nA: OK... Stream of consciousness: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m\nNo. of days required to paint 36 m cloth by 6 men = 72/ 6 × 6 = 2 day.\nThe answer is (B).\n\nQ: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?\nOptions:\n(A) 5 kmph\n(B) 6 kmph\n(C) 7 kmph\n(D) 8 kmph\n(E) 9 kmph\nA:",
"role": "user"
},
{
"content": "OK... Stream of consciousness: Speed downstream = d/t = 85/(2 1/2) = 34 kmph\nSpeed upstream = d/t = 45/(2 1/2) = 18 kmph\nThe speed of the stream = (34 - 18)/2 = 8 kmph\nThe answer is (D).",
"role": "assistant"
}
] |
cot
|
cot_78841
|
[
{
"content": "question: What is the units digit of the expression 14^7−15^4?\nOptions:\n(A) 0\n(B) 8\n(C) 4\n(D) 6\n(E) 3\nanswer: Stream of consciousness: I think answer on this one should be B too. Since we know that 14^7>15^4, as Will said one should always check if the number is positive. The answer is (B).\nq: What is the Mode of the following data set S- {1,2,6,9,6,6,10}\nOptions:\n(A) 9\n(B) 6\n(C) 10\n(D) 1\n(E) 2\na: Stream of consciousness: Mode of a set is the data point that is repeated the most number of times. In the set given, 6 is repeated. The answer is (B).\nquestion: A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?\nOptions:\n(A) 229\n(B) 108\n(C) 278\n(D) 126\n(E) 112\nanswer: Stream of consciousness: S = 180/6 * 18/5 = 108 kmph The answer is (B).\nq: Three grades of milk are 2 percent, 3 percent and 5 percent fat by volume. If x gallons of the 2 percent grade, y gallons of the 3 percent grade, and z gallons of the 5 percent grade are mixed to give x+y+z gallons of a 4 percent grade, what is x in terms of y and z?\nOptions:\n(A) y + 3z\n(B) (y +z) / 4\n(C) 2y + 3z\n(D) z/2\n(E) 3y + 4.5z\na: Stream of consciousness: Based on the given information, the following equation could be dervied: 2% * x + 4% * y + 5% * z = 4% * (x+y+z) Then use algebra to figure out -2%*x = 0%*y - 1%*z. Thus, 2x = z. The answer is (D).\nquestion: There are 10 flavors of ice cream, 3 types of nuts and 5 types of fruit at an ice cream store. If a person can choose 2 ice cream flavors as base, 2 types of nuts and 2 types of fruit. How many different variations are possible if repetition is allowed ?\nOptions:\n(A) 150\n(B) 250\n(C) 22500\n(D) 225\n(E) 225000\nanswer: Stream of consciousness: Ice cream flavors: 10x10 = 100\nNuts: 3x3 = 9\nFruit: 5x5 = 25\nTotal = 22500 The answer is (C).\nquestion: An urn contains 6 red, 5 blue and 2 green marbles. If 2 marbles are picked at random, what is the probability that both are red?\nOptions:\n(A) 6/13\n(B) 5/26\n(C) 6/26\n(D) 9/26\n(E) 10/27\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: Option(B) is correct\nP(Both are red), 6C2/13C2 = 5/26 The answer is (B).",
"role": "assistant"
}
] |
cot
|
cot_72201
|
[
{
"content": "question: In a bucket there are 3 green balls and 2 yellow balls. What is the probability of drawing at least one green ball when drawing two consecutive balls randomly?\nOptions:\n(A) 16/20\n(B) 9/10\n(C) 2/5\n(D) 3/5\n(E) ½\nanswer: Stream of consciousness: P(at least one green) = 1 - P(no green, so 2 yellow) = 1- 2/5*1/4 = 9/10. The answer is (B).\nq: A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?\nOptions:\n(A) 22\n(B) 66\n(C) 28\n(D) 41\n(E) 61\na: Stream of consciousness: (1 man + 1 woman)'s 1 day work = (1/3 + 1/4) = 7/12 Work done by 1 man and 1 woman in 1/4 day = (7/12 * 1/4) = 7/48\nRemaining work = (1 - 7/48) = 41/48\nWork done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48\nNumber of boys required = 41/48 * 41 = 41. The answer is (D).\nquestion: An equity analyst needs to select 4 stocks for the upcoming year and rank these securities in terms of their investment potential. If the analyst has narrowed down the list of potential stocks to 8, in how many ways can she choose and rank her top 4 picks?\nOptions:\n(A) 1200\n(B) 1680\n(C) 2102\n(D) 4020\n(E) 1840\nanswer: Stream of consciousness: Number of ways of choosing 4 stocks = 8C4\nNumber of ways of ranking the chosen stocks = 4!\nHence total ways of chosing and ranking = 8C4 * 4! = 1680 The answer is (B).\nq: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?\nOptions:\n(A) 11\n(B) 77\n(C) 12\n(D) 99\n(E) 02\na: Stream of consciousness: A's 1 hour work = 1/4;\n(B + C)'s 1 hour work = 1/3;\n(A + C)'s 1 hour work = 1/2\n(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12\nB's 1 hour work = (7/12 + 1/2) = 1/12\nB alone will take 12 hours to do the work. The answer is (C).\nquestion: A shipment of 8 TV sets contains 5 black and white sets and 3 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set?\nOptions:\n(A) 1/7\n(B) 1/4\n(C) 5/14\n(D) 25/28\n(E) 13/28\nanswer: Stream of consciousness: 3/8 * 2/7 = 6/56\n1-(6/56) = 50/56 = 25/28 The answer is (D).\nquestion: In case N is the only individual sewing on committee B, which among the following shouldserve on committee A?\nOptions:\n(A) V and U\n(B) V and T\n(C) U and S\n(D) O and P\n(E) T and U\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: O and P should serve on A The answer is (D).",
"role": "assistant"
}
] |
cot
|
cot_92256
|
[
{
"content": "q: A password for a computer is six digits from 0 and 9. The six digit number is a prime number. What is the approximate probability that the last digit is a 3?\nOptions:\n(A) 1/4\n(B) 1/6\n(C) 1/10\n(D) 1/20\n(E) 1/50\na: Stream of consciousness: If the last digit is 0, 2, 4, 6, or 8, the number is even and therefore not prime. If the last digit is 5, the number is divisible by 5 and therefore not prime. The only possibilities are 1, 3, 7, and 9. So the probability is approximately 1/4 (answer A). We say approximately because there is a certain degree of randomness in the distribution of prime numbers. The answer is (A).\nquestion: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?\nOptions:\n(A) 18\n(B) 16\n(C) 17\n(D) 19\n(E) 13\nanswer: Stream of consciousness: Average of 20 numbers = 0\nSum of 20 numbers = (0 * 20) = 0\nIt is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a). The answer is (D).\nq: In Badminton game, one player throws two fair, six-sided die at the same time. If the player receives at least a five or a one on either die, that player wins. What is the probability that a player wins after playing the game once?\nOptions:\n(A) 1/3\n(B) 4/9\n(C) 5/9\n(D) 2/3\n(E) 3/4\na: Stream of consciousness: In Badminton game, Probably the easiest approach would be to find the probability of the opposite event and subtract it from 1:\nP(win) = 1- P(not win) = 1 - 4/6*4/6 = 5/9. The answer is (C).\nquestion: A train 260 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?\nOptions:\n(A) 40 sec\n(B) 50 sec\n(C) 32 sec\n(D) 49 sec\n(E) 60 sec\nanswer: Stream of consciousness: Speed = 45 * 5/18 = 25/2 m/sec\nTotal distance covered = 260 + 140 = 400 m\nRequired time = 400 * 2/25 = 32 se The answer is (C).\nq: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?\nOptions:\n(A) 22\n(B) 28\n(C) 25\n(D) 77\n(E) 88\na: Stream of consciousness: D = 100 + 150 = 250\nS = 36 * 5/18 = 10 mps\nT = 250/10 = 25 se The answer is (C).\nq: John makes $40 a week from his job. He earns a raise and now makes $70 a week. What is the % increase?\nOptions:\n(A) 16%\n(B) 16.66%\n(C) 18%\n(D) 21%\n(E) 75%\na:",
"role": "user"
},
{
"content": "Stream of consciousness: Increase = (30/40)*100 = 75%. The answer is (E).",
"role": "assistant"
}
] |
flan_v2
|
flan_v2_89802
|
[
{
"content": "In this task you will break down a question into the basic steps required to answer it.\n A question decomposition is a numbered list of operations that must be performed to answer the original question. Imagine explaining your question to a friendly droid by listing each action it should take in order for the question to be answered. Each step in our decomposition should refer to either an entity (known or unknown), a propery of an entity or a query operation (count, group, union, etc.)\n Here are the list of step templates and their description:\n Select: A select step is used to return a set of objects. There are no references to previous steps in a select step. template: Return [attributes]\n Filter: A filter step is used to return results from a previous step to which a certain condition applies. template: Return [#step] [condition]\n Project: A project step should return certain attributes of the results of a previous step. template: Return [attributes] of [#step]\n Aggregate: An aggregate step returns an aggregator function applied on a step's result. template: Return the [aggregator] of [#step].\n Group: A group step is an aggregator applied on attributes. template: Return the [aggregator] of [#step] for each [attribute]\n Superlative: A superlative step is used to return the result with a highest/lowest attribute among other results. template: Return [#step1] [where] [#step2] [is] [highest / lowest]\n Comparative: A comparative step is used when we need to compare an attribute with a number to filter results. template: Return [#step1] [where] [#step2] [comparator] [number] \n Union: A union step is used to return results of two steps together. template: Return [#step1] [or / ,] [#step2]\n Intersection: An intersection step returns the result that two steps have in common. template: Return [attribute] of both [#step1] and [#step2]\n Discard: A discard step returns result of a step and excludes result of another step from it. template: Return [#step1] besides [#step2]\n Sort: A sort returns result of another step in a specific order. template: Return [#step1] [ordered / sorted by] [#step2]\n Is true: An is true step checks a condition on another result and returns a true or false. template: Return [is / if] [condition]\n Arithmetic: An arithmatic step operates an arithmatic operation on one or more steps. template: Return the [arithmetic op.] of [#step1] [and] [#step2].\n--------\nQuestion: question: What is the shape of the only matte finish object?\n\nAnswer: #1 return objects \n#2 return finishes of #1 \n#3 return #1 where #2 is matte \n#4 return the shape of #3\n\n\nQuestion: question: How many poins were scored in the first half?\n\nAnswer: #1 return the first half \n#2 return poins scored of #1 \n#3 return number of #2\n\n\nQuestion: question: At which restaurant did the students spend the least amount of time? List restaurant and the time students spent on in total.\n\nAnswer:",
"role": "user"
},
{
"content": "#1 return restaurants \n#2 return time students spent in #1 \n#3 return sum of #2 for each #1 \n#4 return #1 where #3 is highest \n#5 return time students spent in #4 \n#6 return sum of #5 \n#7 return #4 , #6\n\n\n",
"role": "assistant"
}
] |
cot
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cot_88604
|
[
{
"content": "question: What is the probability that Company G's advertisement will be one of the first two be shown during the first commercial break?\nOptions:\n(A) 1/ 225\n(B) 1 / 30\n(C) 1 /15\n(D) 2 / 15\n(E) 4 /15\nanswer: Stream of consciousness: G 1/15 + (14/15) * 1/14 = 2/15 The answer is (D).\nq: An design manager has 10patterns of chairs & 9patterns of tables. In how many ways can he make a pair of table & chair?\nOptions:\n(A) 20\n(B) 40\n(C) 80\n(D) 90\n(E) 100\na: Stream of consciousness: He has has ten patterns of chairs and eight patterns of tables\nHence, A chair can be arranged in 10 ways and\nA table can be arranged in 9 ways\nHence one chair and one table can be arranged in 10 x 9 ways = 90 ways The answer is (D).\nquestion: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?\nOptions:\n(A) 2450\n(B) 2560\n(C) 2650\n(D) 3500\n(E) 5184\nanswer: Stream of consciousness: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184\n432 12 x 62 The answer is (E).\nq: A shipment of 8 TV sets contains 4 black and white sets and 4 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set?\nOptions:\n(A) 1/7\n(B) 11/14\n(C) 5/14\n(D) 11/28\n(E) 13/28\na: Stream of consciousness: 4/8 * 3/7 = 12/56\n1-(12/56) = 44/56 = 11/14 The answer is (B).\nquestion: A motorcyclist goes from Bombay to Pune, a distance of 128 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?\nOptions:\n(A) 1:3\n(B) 1:5\n(C) 1:4\n(D) 1:1\n(E) 1:8\nanswer: Stream of consciousness: T = 128/32 = 4 h\nT = 4 - 3 = 1\nTime Ratio = 4:1 = 4:1\nSpeed Ratio = 1:4 The answer is (C).\nquestion: The ratio of males and females in a city is 7 : 8 and the percentage of children among males and females is 25% and 20% respectively. If the number of adult females in the city is 156800 what is the total population?\nOptions:\n(A) 245000\n(B) 367500\n(C) 196000\n(D) 171500\n(E) None of these\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: Number of females = 156800 × 100⁄80 = 196000\n\\ Number of males = 7⁄8 × 196000 = 171500\n\\ Total population = 196000 + 171500 = 367500 The answer is (B).",
"role": "assistant"
}
] |
cot
|
cot_82508
|
[
{
"content": "question: There are 4 magazines lying on a table; 2 are fashion magazines and the other 2 are sports magzines. If 1 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazine will be selected?\nOptions:\n(A) 1\n(B) 1/2\n(C) 1/4\n(D) 1/6\n(E) 1/8\nanswer: Stream of consciousness: 1- (2c1/4c1) = 1-1/2 = 1/2 The answer is (B).\nq: Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 30, and 40 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?\nOptions:\n(A) 4/11\n(B) 1/2\n(C) 15/22\n(D) 120/7\n(E) 11/4\na: Stream of consciousness: P1 takes 12 hrs\nRate for P2P3 together = 1/30 + 1/40 = 7/120\nTherefore they take 120/7\nRatio = 120/7 = The answer is (D).\nquestion: Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They each took a test 4 times, and no one scored below 450 or over 650. If the individual ranges of the three people's scores in those 4 practice tests were 30, 80 and 110, what is the difference between the maximum and minimum possible ranges of all their scores put together.\nOptions:\n(A) 90\n(B) 120\n(C) 50\n(D) 70\n(E) 100\nanswer: Stream of consciousness: According to the information in the question the maximum range would be between 450 and 650(200). The minimum range would be the greatest range for any one individual, which is listed in the problem as 110. So the difference between these would be 200-110 or 90. The answer is (A).\nq: An analyst will recommend a combination of 2 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 6 industrial stocks, 5 transportation stocks, and 4 utility stocks, how many different combinations of 6 stocks are possible?\nOptions:\n(A) 1200\n(B) 900\n(C) 600\n(D) 180\n(E) 720\na: Stream of consciousness: 6C2 * 5C2 * 4C2 = 15*10*6 = 900. The answer is (C).\nquestion: For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 90 Θ 33 ) Θ 17 ) - ( 99 Θ (33 Θ 17)) ?\nOptions:\n(A) 10\n(B) 8\n(C) 6\n(D) 4\n(E) 2\nanswer: Stream of consciousness: (( 90 Θ 33 ) Θ 17 )\nThe remainder of 90 divided by 33 is 24;\nThe remainder of 24 divided by 17 is 7;\n( 99 Θ (33 Θ 17))\nThe remainder of 33 divided by 17 is 16;\n7 - 3 = 4. The answer is (D).\nquestion: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?\nOptions:\n(A) 1\n(B) 2\n(C) 3\n(D) 4\n(E) 5\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: (1056 / 23) gives remainder 21\n21 + 2 = 23, So we need to add 2 The answer is (B).",
"role": "assistant"
}
] |
cot
|
cot_70594
|
[
{
"content": "q: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?\nOptions:\n(A) 10000\n(B) 28869\n(C) 10002\n(D) 18089\n(E) 10004\na: Stream of consciousness: 100 * 100 = 10000\n125 * 80 = 10000 The answer is (A).\nquestion: A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?\nOptions:\n(A) 15\n(B) 66\n(C) 88\n(D) 1\n(E) 12\nanswer: Stream of consciousness: 90 * 10/60 = 15 kmph The answer is (A).\nq: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?\nOptions:\n(A) 9\n(B) 8\n(C) 7\n(D) 6\n(E) 4\na: Stream of consciousness: 1 to 9 = 9 * 9 = 81\n1 to 5 = 5 * 10 = 50\n5 to 9 = 5 * 8 = 40\n5th = 50 + 40 = 90 – 81 = 9 The answer is (A).\nquestion: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much? Look at this series: 120, 30, 240, 25, ___, 20, 480, 15... Which number is missing?\nOptions:\n(A) 120\n(B) 360\n(C) 340\n(D) 960\n(E) 280\nanswer: Stream of consciousness: B 360\nThis is an alternating addition and subtraction series. In the first pattern, 120 is added to each number to arrive at the next. In the second, 5 is subtracted from each number to arrive at the next. The answer is (B).\nq: How much is 80% of 40 is greater than 4/5 of 15?\nOptions:\n(A) 12\n(B) 20\n(C) 18\n(D) 12\n(E) 81\na: Stream of consciousness: (80/100) * 40 – (4/5) * 15\n32 - 12 = 20 The answer is (B).\nq: During a sale, the price of a pair of shoes is marked down 10% from the regular price. After the sale ends, the price goes back to the original price. What is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes?\nOptions:\n(A) 9%\n(B) 10%\n(C) 11%\n(D) 15%\n(E) 90%\na:",
"role": "user"
},
{
"content": "Stream of consciousness: Assume the price = 100\nPrice during sale = 90\nPrice after sale = 100\nPercent increase = 10/90*100 = 11% approx. The answer is (C).",
"role": "assistant"
}
] |
cot
|
cot_70989
|
[
{
"content": "question: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 20 minutes, how much time will she spend doing yoga? (rounded to minutes)\nOptions:\n(A) 10 min.\n(B) 33 min.\n(C) 17 min.\n(D) 23 min.\n(E) 25 min.\nanswer: Stream of consciousness: The ratio is 2:3 = gym:ride, so (20)(3/2) = 30 minutes at the gym, and 30 + 20 = 50 minutes exercise, so (2/3)(50) = 33 minutes yoga. The answer is (B).\nq: A person borrowed Rs.600 @ 3% per annum S.I and Rs.800 @ 4½ % per annum on the agreement that the whole sum will be returned only when the total interest becomes Rs.246. The number of years, after which the borrowed sum is to be returned, is\nOptions:\n(A) 2 years\n(B) 3years\n(C) 4 years\n(D) 5 years\n(E) 6 years\na: Stream of consciousness: Let the time be x years. Then (600 *3* x)/100 + (800*9*x)/(2*100) = 24\n18x+ 36x = 246 ; x = 246/54 = 4 years\nRequired time = 4 years The answer is (C).\nquestion: A scientist was researching into animal behavior in his laboratory. He was very interested in studying the behavior of bears. He travelled a mile to the north and reached the north pole. There he saw a bear. He then followed the bear for an 1 hour to the east with a speed of 2km/hr. After that he travelled south and reached his laboratory in 2 hours. What was the colour of the bear?\nOptions:\n(A) Black\n(B) White\n(C) Red\n(D) Blue\n(E) None\nanswer: Stream of consciousness: This question is based on bear on poles so it should be polo bear and the color of polo bear is white. The answer is (B).\nq: The no. of girls in a class are 7times the no. of boys, which value cannever be the of total students?\nOptions:\n(A) 20\n(B) 35\n(C) 30\n(D) 40\n(E) 42\na: Stream of consciousness: Let the boys are X, then girls are 7X, total = X+7X = 8X\nSo it should be multiple of 8, 30 is not a multiple of 8. The answer is (C).\nquestion: The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir?\nOptions:\n(A) 20\n(B) 24\n(C) 30\n(D) 32\n(E) 34\nanswer: Stream of consciousness: Use simultaneous equations / By combination\n4x = 5y + 4\n5x = 6y + 6\nMultiply (1) by 6\nMultiply (2) by -5\nGet rid of y, and x = 6\nThen 5x = 30 The answer is (C).\nquestion: If a man walks to his office at 3/4 of his usual rate, he reaches office 1/3 of an hour later than usual. What is his usual time to reach office.\nOptions:\n(A) 1⁄2 hr\n(B) 1 hr\n(C) 3⁄4 hr\n(D) 2 hrs\n(E) None of these\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: If new speed is a⁄b of original speed, then usual time × (b⁄a - 1) = change in time\n∴ usual time × (4⁄3 - 1) = 1⁄3\n⇒ usual time = 1⁄3 × 3 = 1 hr The answer is (B).",
"role": "assistant"
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cot
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cot_75589
|
[
{
"content": "question: What amount does Kiran get if he invests Rs. 18000 at 12% p.a. simple interest for four years?\nOptions:\n(A) 29893\n(B) 26640\n(C) 29989\n(D) 28800\n(E) 29883\nanswer: Stream of consciousness: Simple interest = (18000 * 4 * 12)/100 = Rs. 8640\nAmount = P + I = 18000 + 8640 = Rs. 26640 The answer is (B).\nq: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 4 utility stocks, how many different combinations of 7 stocks are possible?\n--\nOptions:\n(A) 12\n(B) 360\n(C) 60\n(D) 180\n(E) 720\na: Stream of consciousness: 5C3 * 4C2 * 4C2 = 10*6*6 = 360. The answer is (B).\nquestion: If J is the least positive integer that is divisible by every integer from 10 to 15 inclusive, then J/26 is =\nOptions:\n(A) 1155\n(B) 2310\n(C) 4620\n(D) 30030\n(E) 60060\nanswer: Stream of consciousness: The integer should be divisible by: 10, 11, 12, 13, 14 and 15, that is 5*2, 11, 3*2^2, 13, 2*7, and 3*5. The least common multiple of these integers is the product of 13, 11, 7, 5, 3 and 2^2. Then, R/26 is (13 * 11 * 7 * 5 * 3 * 2^2)/2 * 13 = 11*7*5*3*2 = 2310. The answer is (B).\nq: A family with 1 mother, 1 father, and 4 children sit in a car with 2 front seats and 4 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other three children on either side of him, how many seating arrangements are possible?\nOptions:\n(A) 3\n(B) 4\n(C) 6\n(D) 24\n(E) 10\na: Stream of consciousness: Mother has a fixed place and father, so there are 4! ways to arrange the children, hence The answer is (D).\nquestion: Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 40, and 50 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?\nOptions:\n(A) 4/11\n(B) 1/2\n(C) 15/22\n(D) 200/9\n(E) 11/4\nanswer: Stream of consciousness: P1 takes 12 hrs\nRate for P2P3 together = 1/40 + 1/50 = 9/200\nTherefore they take 200/9\nRatio = 200/9 = The answer is (D).\nquestion: There are 100 employees in a room. 99% are managers. How many managers must leave the room to bring down the percentage of manager to 98%?\nOptions:\n(A) 1\n(B) 2\n(C) 50\n(D) 49\n(E) 97\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: We have 99 managers and 1 director. That 1 director to compose 2% of the total number of people, there must be 50 people in the room, hence 50 managers must leave. The answer is (C).",
"role": "assistant"
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cot
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cot_52354
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[
{
"content": "Reasoning: The prime factorization of a square has to have even powers of all its prime factors. If the original number has a factor, say of 7, then when it’s squared, the square will have a factor of 7^2. Another way to say that is: any positive integer all of whose prime factors have even powers must be a perfect square of some other integer. Look at the prime factorization of 432\n432 = (2^4)*(3^3)\nThe factor of 2 already has an even power —- that’s all set. The factor of 3 currently has an odd power. If n = 3, then 432*n would have an even power of 2 and an even power of 3; therefore, it would be a perfect square. Thus, n = 3 is a choice that makes 432*n a perfect square.\nAns: (B)\nQuestion: If n is the smallest integer such that 432 times n is the square of an integer, what is the value of n?\nOptions:\n(A) 2\n(B) 3\n(C) 6\n(D) 12\n(E) 24\n\n\nRationale: Speed = 60 * 5/18 = 50/3 m/sec\nLength of the train = speed * time = 50/3 * 12 = 250 m\nThe answer: (C)\nQuestion: A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?\nOptions:\n(A) 287\n(B) 699\n(C) 250\n(D) 168\n(E) 150\n\n\nReasoning: Number of ways of selecting 4 people out of 9 people = 9C4\nIn the three members George will always be there in the team. At this step we have vacancy for 3 more members and 8 members are available. Nina cannot be there in the team. So 3 members have to be selected and the number of available members = 8 - Nina = 7\nNumber of ways to form a 4 member team that includes George and excludes Nina = 7C3\nProbability = 7C3/9C4 = 35/120\nAns: (D)\nQuestion: From a Group of 9 People, Including George and Nina, 4 people are to be selected at random to work on a certain project. What is the probability that 4 people selected will include George but not Nina\nOptions:\n(A) 5/56\n(B) 9/56\n(C) 15/56\n(D) 35/120\n(E) 25/56\n\n\nRationale: Original perimeter = x\nHence original side = x/4\nNew side = 3x/4\nNew perimeter = 4*3x/4 = 3x\nThe answer: (A)\nQuestion: The measure of the side of a square is tripled. If x represents the perimeter of the original square, what is the value of the new perimeter?\nOptions:\n(A) 3x\n(B) 4x\n(C) 9x\n(D) 12x\n(E) 27x\n\n\nReasoning: A's 1 hour work = 1/4;\n(B + C)'s 1 hour work = 1/3;\n(A + C)'s 1 hour work = 1/2\n(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12\nB's 1 hour work = (7/12 + 1/2) = 1/12\nB alone will take 12 hours to do the work.\nAns: (C)\nQuestion: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?\nOptions:\n(A) 15 hours\n(B) 14 hours\n(C) 12 hours\n(D) 74 hours\n(E) 79 hours\n\n\nReasoning: P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*1/8*5/7 + 1/5*7/8*2/7 + 4/5*1/8*2/7 = 27/280.\nAns: (C)\n",
"role": "user"
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{
"content": "Question: Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 1/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?\nOptions:\n(A) 3/140\n(B) 1/280\n(C) 27/280\n(D) 3/35\n(E) 7/56",
"role": "assistant"
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cot
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cot_69190
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[
{
"content": "q: A, B, C, and D are four points, any three of which are non-collinear. Then, the number of ways to construct three lines each joining a pair of points so that the lines do not form a triangle is\nOptions:\n(A) 7\n(B) 8\n(C) 9\n(D) 24\n(E) 23\na: Stream of consciousness: To construct 2 lines, three points can be selected out of 4 in 4 x 3 x 2 = 24 ways. Now, if third line goes from the third-point to the first point, a triangle is formed, and if it goes to the fourth point, a triangle is not formed. So, there are 24 ways to form a triangle and 24 ways of avoiding triangle. The answer is (D).\nquestion: A, B and C can do a work in 4 days, 8 days and 12 days respectively. In how many days can all three of them working together, complete the work?\nOptions:\n(A) 2 2/3\n(B) 2 2/8\n(C) 2 2/0\n(D) 2 2/2\n(E) 2 2/11\nanswer: Stream of consciousness: Work done by all three of them in one day = 1/4 + 1/8 + 1/12 = 11/24\nThe number of days required = 24/11 = 2 2/11 days. The answer is (E).\nq: In wardrobe Marry has 3trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4shirts. One of them is grey and the other 3are white. He openshiswardrobe in the dark and pick out one shirt trouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey?\nOptions:\n(A) 1/2\n(B) 2/3\n(C) 3/5\n(D) 4/7\n(E) 4/9\na: Stream of consciousness: Probability that trouser is not grey = 2/3\nProbability that shirt is not grey = 3/4\n∴ Required probability = 2/3 x 3/4 = 1/2 The answer is (A).\nquestion: 80 ? 860 1550 2440 3530\nOptions:\n(A) 370\n(B) 840\n(C) 750\n(D) 860\n(E) 960\nanswer: Stream of consciousness: 10^2 - 20 = 80\n20^2 - 30 = 370\n30^2 - 40 = 860\n40^2 - 50 = 1550\n50^2 - 60 = 2440\n60^2 - 70 = 3530. The answer is (A).\nq: If 85 percent of the test takers taking an old paper and pencil GMAT exam answered the first question on a given math section correctly, and 75 percent of the test takers answered the second question correctly, and 15 percent of the test takers answered neither question correctly, what percent answered both correctly?\nOptions:\n(A) 60 %\n(B) 65 %\n(C) 70%\n(D) 75%\n(E) 80%\na: Stream of consciousness: {Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}\n100 = 85 + 75 - {Both correctly} + 15\n{Both correctly} = 75. The answer is (D).\nq: In a race with 30 runners where 3 trophies will be given to the top 5 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?\nOptions:\n(A) 5^3 ways\n(B) 8^9 ways\n(C) 7^8 ways\n(D) 8^7 ways\n(E) 8^6 ways\na:",
"role": "user"
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{
"content": "Stream of consciousness: 5 people can be prized with 3 distinct prizes in 5^3 ways The answer is (A).",
"role": "assistant"
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cot
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cot_77480
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[
{
"content": "q: How many positive integers less than 50 have a reminder 01 when divided by 5?\nOptions:\n(A) 10\n(B) 14\n(C) 15\n(D) 16\n(E) 17\na: Stream of consciousness: 1 also gives the remainder of 1 when divided by 5. So, there are total of 10 numbers. The answer is (A).\nquestion: Which of the following is a prime number ?\nOptions:\n(A) 27\n(B) 45\n(C) 97\n(D) 98\n(E) 100\nanswer: Stream of consciousness: Clearly, 97 is a prime number. The answer is (C).\nq: The average of 13 result is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th result?\nOptions:\n(A) 35\n(B) 37\n(C) 46\n(D) 48\n(E) 50\na: Stream of consciousness: Sum of all the 13 results = 13 * 60 = 780\nSum of the first 7 of them = 7 * 57 = 399\nSum of the last 7 of them = 7 * 61 = 427\nSo, the 8th number = 427 + 399 - 780 = 46. The answer is (C).\nquestion: Sum of the local value and the face value of 4 in the numeral 153489216 is\nOptions:\n(A) 40004\n(B) 4004\n(C) 4000004\n(D) 400004\n(E) 44\nanswer: Stream of consciousness: (Local value of 4) + (Face value of 4) = (400000 + 4) = 400004 The answer is (D).\nq: In wardrobe Marry has 3 trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4 shirts. One of them is grey and the other 3are white. He opens hiswardrobe in the dark and pick out one shirt trouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey?\nOptions:\n(A) 1/2\n(B) 2/3\n(C) 3/5\n(D) 3/7\n(E) 4/9\na: Stream of consciousness: Probability that trouser is not grey = 2/3\nProbability that shirt is not grey = 3/4\n∴ Required probability = 2/3 x 3/4 = 1/2 The answer is (A).\nq: If the ratio of boys to girls in a class is B and the ratio of girls to boys is G; then 5 (B + G) is ?\nOptions:\n(A) Equal to 3\n(B) Less than 5\n(C) More than 5\n(D) Less than 1/5\n(E) none of these\na:",
"role": "user"
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{
"content": "Stream of consciousness: Let number of boys = x\nLet number of girls = y\nTherefore x/y = B and y/x = G\n5(B + G) = 5[(x/y) + (y/x)] = 5[(x2 + y2)/xy] > 5 The answer is (A).",
"role": "assistant"
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flan_v2
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flan_v2_82351
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[
{
"content": "Teacher: In this task, you will be given a set of steps that are required to answer a specific question. Your job is to generate that question. Each given step refers to either an entity (known or unknown), a propery of an entity or a query operation (count, group, union, etc.) Knowing those operations and how they appear in the input may help you generate more accurate questions.\n Select: A select step is used to return a set of objects. There are no references to previous steps in a select step. template: Return [attributes]\n Filter: A filter step is used to return results from a previous step to which a certain condition applies. template: Return [#step] [condition]\n Project: A project step should return certain attributes of the results of a previous step. template: Return [attributes] of [#step]\n Aggregate: An aggregate step returns an aggregator function applied on a step's result. template: Return the [aggregator] of [#step].\n Group: A group step is an aggregator applied on attributes. template: Return the [aggregator] of [#step] for each [attribute]\n Superlative: A superlative step is used to return the result with a highest/lowest attribute among other results. template: Return [#step1] [where] [#step2] [is] [highest / lowest]\n Comparative: A comparative step is used when we need to compare an attribute with a number to filter results. template: Return [#step1] [where] [#step2] [comparator] [number] \n Union: A union step is used to return results of two steps together. template: Return [#step1] [or / ,] [#step2]\n Intersection: An intersection step returns the result that two steps have in common. template: Return [attribute] of both [#step1] and [#step2]\n Discard: A discard step returns result of a step and excludes result of another step from it. template: Return [#step1] besides [#step2]\n Sort: A sort returns result of another step in a specific order. template: Return [#step1] [ordered / sorted by] [#step2]\n Is true: An is true step checks a condition on another result and returns a true or false. template: Return [is / if] [condition]\n Arithmetic: An arithmatic step operates an arithmatic operation on one or more steps. template: Return the [arithmetic op.] of [#step1] [and] [#step2].\nTeacher: Now, understand the problem? If you are still confused, see the following example:\n#1 return secretaries \n#2 return #1 born in state 'Alabama \n#3 return departments managed by #2 \n#4 return distinct creation years of #3\nSolution: What are the distinct creation years of the departments managed by a secretary born in state 'Alabama'?\nReason: You should follow the steps in order to realize what is the asked question. In this example, the first returned entities are secretaries(based on step #1) who are born in Alabama(based on step #2). In the step #3 departments managed by step #2(which is secretaries born in Alabama. In the final steps the creation years of the departments is returned, so the question will be about the creation years of the departments. \n\nNow, solve this instance: #1 return organisms \n#2 return #1 that are floating freely \n#3 return number of #2 \n#4 return if #3 is equal to one\nStudent:",
"role": "user"
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{
"content": "If exactly one organism is floating freely.",
"role": "assistant"
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flan_v2
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flan_v2_84492
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[
{
"content": "In this task, you will be given a set of steps that are required to answer a specific question. Your job is to generate that question. Each given step refers to either an entity (known or unknown), a propery of an entity or a query operation (count, group, union, etc.) Knowing those operations and how they appear in the input may help you generate more accurate questions.\n Select: A select step is used to return a set of objects. There are no references to previous steps in a select step. template: Return [attributes]\n Filter: A filter step is used to return results from a previous step to which a certain condition applies. template: Return [#step] [condition]\n Project: A project step should return certain attributes of the results of a previous step. template: Return [attributes] of [#step]\n Aggregate: An aggregate step returns an aggregator function applied on a step's result. template: Return the [aggregator] of [#step].\n Group: A group step is an aggregator applied on attributes. template: Return the [aggregator] of [#step] for each [attribute]\n Superlative: A superlative step is used to return the result with a highest/lowest attribute among other results. template: Return [#step1] [where] [#step2] [is] [highest / lowest]\n Comparative: A comparative step is used when we need to compare an attribute with a number to filter results. template: Return [#step1] [where] [#step2] [comparator] [number] \n Union: A union step is used to return results of two steps together. template: Return [#step1] [or / ,] [#step2]\n Intersection: An intersection step returns the result that two steps have in common. template: Return [attribute] of both [#step1] and [#step2]\n Discard: A discard step returns result of a step and excludes result of another step from it. template: Return [#step1] besides [#step2]\n Sort: A sort returns result of another step in a specific order. template: Return [#step1] [ordered / sorted by] [#step2]\n Is true: An is true step checks a condition on another result and returns a true or false. template: Return [is / if] [condition]\n Arithmetic: An arithmatic step operates an arithmatic operation on one or more steps. template: Return the [arithmetic op.] of [#step1] [and] [#step2].\nOne example: #1 return secretaries \n#2 return #1 born in state 'Alabama \n#3 return departments managed by #2 \n#4 return distinct creation years of #3\nSolution is here: What are the distinct creation years of the departments managed by a secretary born in state 'Alabama'?\nExplanation: You should follow the steps in order to realize what is the asked question. In this example, the first returned entities are secretaries(based on step #1) who are born in Alabama(based on step #2). In the step #3 departments managed by step #2(which is secretaries born in Alabama. In the final steps the creation years of the departments is returned, so the question will be about the creation years of the departments. \n\nNow, solve this: #1 return ships \n#2 return names of #1 \n#3 return tonnages of #1 \n#4 return #2 sorted by #3 ascending\nSolution:",
"role": "user"
},
{
"content": "what are the names of the ships ordered by ascending tonnage?",
"role": "assistant"
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cot
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cot_59200
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[
{
"content": "q: A man pointing to a photo says \"The lady in the photograph is my nephew’s maternal grandmother\". How is the lady in the photograph related to the man’s sister who has no other sister ?\nOptions:\n(A) Cousin\n(B) Sister-in-law\n(C) Mother\n(D) Mother-in-law\n(E) None of these\na: Stream of consciousness: Since the man is referring to his nephew, the nephew’s parent has to be a sibling to the man. Now the last part says that the man’s sister has no other sister and hence the brother-sister relationship is established between the man and his nephew’s mother. Now the lady in the picture is the grandmother of the nephew and hence she is the mother of the man’s sister. The answer is (C).\nquestion: In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Elaine?\nOptions:\n(A) 1,008\n(B) 1,296\n(C) 1,512\n(D) 2*1008\n(E) 2,268\nanswer: Stream of consciousness: Place D and H first: 8 options for D, 7 options for H\nWe are left with 6 empty places. A, B and C must take first 3 places and F, G, Emust take the remaining three. A, B and C can be arranged in their places in 3! ways. The same for F, G, and E\nTotal = 8*7*3!*3! = 2*1008 The answer is (D).\nq: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?\nOptions:\n(A) 29\n(B) 18\n(C) 48\n(D) 99\n(E) 11\na: Stream of consciousness: D = 540 + 180 = 720\nS = 54 * 5/18 = 15 mps\nT = 720/15 = 48 se The answer is (C).\nquestion: From among the 35 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?\nOptions:\n(A) 1360\n(B) 1260\n(C) 1060\n(D) 1190\n(E) 1460\nanswer: Stream of consciousness: There are 35 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 35 ways. When one person is appointed as leader, we are left with 35 students. Out of these 34 teachers, we can select one class representative. So, a class representative can be selected in 34 ways. Hence, the number of ways in which a leader and class representative can be selected = 35 x 34 = 1190 The answer is (D).\nq: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?\nOptions:\n(A) 3 4/9 days\n(B) 8 4/9 days\n(C) 9 3/8 days\n(D) 6 3/8 days\n(E) none of these\na: Stream of consciousness: 1/15 + 1/25 = 8/75\n75/8 = 9 3/8 days The answer is (C).\nq: Which of the following is not divisible by 8?\nOptions:\n(A) 10032\n(B) 21192\n(C) 47816\n(D) 91232\n(E) 72034\na:",
"role": "user"
},
{
"content": "Stream of consciousness: Divisibility rule of 8: Last three digits of the number should be divisible by 8\nOption A: 10032, last three digits = 032. Divisible by 8\nOption B: 21192, last three digits = 192. Divisible by 8\nOption C: 47816, last three digits = 816. Divisible by 8\nOption D: 91232, last three digits = 232. Divisible by 8\nOption E: 72034, last three digits = 034. Not divisible by 8. Hence 72034 is not divisible by 8 The answer is (E).",
"role": "assistant"
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cot
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cot_58394
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[
{
"content": "q: At 15:00 there were 20 students in the computer lab. At 15:03 and every three minutes after that, 3 students entered the lab. If at 15:10 and every ten minutes after that 7 students left the lab, how many students were in the computer lab at 15:44 ?\nOptions:\n(A) 7\n(B) 14\n(C) 25\n(D) 27\n(E) 30\na: Stream of consciousness: Initial no of students + 3 * (1 + No of possible 3 minute intervals between 15:03 and 15:44) -\n8 *(1 + No of possible 10 minute intervals between 15:10 and 15:44)\n20 + 3*14 -8 * 4 = 25 The answer is (C).\nquestion: What is the sum of the 1st 5 prime numbers greater than 20?\nOptions:\n(A) 121\n(B) 151\n(C) 168\n(D) 164\n(E) 161\nanswer: Stream of consciousness: Required sum = (23 + 29 + 31 + 37 + 41) = 161\nNote: 1 is not a prime number The answer is (E).\nq: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?\nOptions:\n(A) 3\n(B) 5\n(C) 6\n(D) 8\n(E) 9\na: Stream of consciousness: Work done by X in 1 day = 1/18\nWork done by Y in 1 day = 1/15\nWork done by Y in 10 days = 10/15 = 2/3\nRemaining work = 1 – 2/3 = 1/3\nNumber of days in which X can finish the remaining work = (1/3) / (1/18) = 6 The answer is (C).\nquestion: How many terminating zeroes Q does 200! have?\nOptions:\n(A) 40\n(B) 48\n(C) 49\n(D) 55\n(E) 64\nanswer: Stream of consciousness: You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros. The answer is (C).\nq: Look at this series: 36, 34, 30, 28, 24, ... What number should come next?\nOptions:\n(A) 20\n(B) 22\n(C) 25\n(D) 24\n(E) 26\na: Stream of consciousness: This is an alternating number subtraction series. First, 2 is subtracted, then 4, then 2, and so on. The answer is (B).\nq: Which of the following is equal to the average (arithmetic mean) of (x+1)^2 and (x-1)^2?\nOptions:\n(A) x^2\n(B) x^2+1\n(C) x^2 +4\n(D) x^2+2x\n(E) x^2+4x\na:",
"role": "user"
},
{
"content": "Stream of consciousness: Avg = [(x+1)^2 + (x-1)^2] / 2\nExpanding and simplifying, (x^2 + 2x + 1 + x^2 -2x + 1 ) / 2 = x^2 + 1 The answer is (B).",
"role": "assistant"
}
] |
cot
|
cot_88781
|
[
{
"content": "q: A password for a computer is six digits from 0 and 9. The six digit number is a prime number. What is the approximate probability that the last digit is a 3?\nOptions:\n(A) 1/4\n(B) 1/6\n(C) 1/10\n(D) 1/20\n(E) 1/50\na: Stream of consciousness: If the last digit is 0, 2, 4, 6, or 8, the number is even and therefore not prime. If the last digit is 5, the number is divisible by 5 and therefore not prime. The only possibilities are 1, 3, 7, and 9. So the probability is approximately 1/4 (answer A). We say approximately because there is a certain degree of randomness in the distribution of prime numbers. The answer is (A).\nquestion: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?\nOptions:\n(A) 27\n(B) 30\n(C) 31\n(D) 33\n(E) 34\nanswer: Stream of consciousness: The total of seven numbers = 7X18 = 126\nThe total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99\nSo, the middle number is (126 - 99 ) = 27 The answer is (A).\nq: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 1 year the amount to be paid is?\nOptions:\n(A) 3377\n(B) 2688\n(C) 2688\n(D) 7800\n(E) 1268\na: Stream of consciousness: A = 7500(26/25)^1 = 7800 The answer is (D).\nquestion: The average of first 16 even numbers is?\nOptions:\n(A) 19\n(B) 18\n(C) 16\n(D) 11\n(E) 17\nanswer: Stream of consciousness: Sum of 16 even numbers = 16 * 17 = 272\nAverage = 272/16 = 17 The answer is (E).\nq: Find the largest 4 digit number which isexactly divisible by 88?\nOptions:\n(A) 8765\n(B) 9543\n(C) 9944\n(D) 1012\n(E) 2465\na: Stream of consciousness: Largest 4 digit number is 9999\nAfter doing 9999 ÷ 88 we get remainder 55\nHence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 The answer is (C).\nq: How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 3 ?\nOptions:\n(A) 4\n(B) 0\n(C) 3\n(D) 2\n(E) 1\na:",
"role": "user"
},
{
"content": "Stream of consciousness: A number ending with 3 can never be a perfect square. The answer is (B).",
"role": "assistant"
}
] |
cot
|
cot_72961
|
[
{
"content": "q: What is the are of an equilateral triangle of side 24 cm?\nOptions:\n(A) 66√3 cm2\n(B) 74√3 cm2\n(C) 64√3 cm2\n(D) 64√5 cm2\n(E) 144√3 cm2\na: Stream of consciousness: Area of an equilateral triangle = √3/4 S2\nIf S = 24, Area of triangle = √3/4 * 24 * 24 = 144√3 cm2; The answer is (E).\nquestion: If x<0, y<0, and |x| > |y|, which of the following must be true?\nOptions:\n(A) x > y\n(B) y^2 > x^2\n(C) x^3 > y^2\n(D) x < y\n(E) x < –y\nanswer: Stream of consciousness: Correct Answer: (E)\nLet’s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn’t have to be true – consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us –x > y. Remember that x < 0, so –x = |x|, and y is positive, so |y| = y. Thus x < y is the same statement as |x| > |y|, and (D) must be true. The answer is (D).\nq: If 40 per cent of a number is added to an other number then it becomes 125 per cent of itself. What will be the ratio of first and second numbers?\nOptions:\n(A) 8 : 5\n(B) 5 : 7\n(C) 5 : 8\n(D) Data inadequate\n(E) None of these\na: Stream of consciousness: 40x⁄100 + y = 125x⁄100 ⇒ x⁄y = 20⁄17 The answer is (E).\nquestion: In what time a sum of money double itself at 8% per annum simple interest?\nOptions:\n(A) 33 1/8%\n(B) 33 1/3%\n(C) 33 7/3%\n(D) 32 1/3%\n(E) 12 1/2%\nanswer: Stream of consciousness: P = (P*8*R)/100\nR = 12 1/2% The answer is (E).\nq: If 14m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?\nOptions:\n(A) 2m −1\n(B) 4m\n(C) 5m\n(D) m/5\n(E) 6m/5\na: Stream of consciousness: 14m - n = p\nAdd n to both sides:\n14m = n + p\nAdd m to both sides:\n15m = n + p + m\nNow, divide both sides by 3\n5m = (n + p + m)/3 = the average of n, p, and m The answer is (C).\nq: Three grades of milk are 1 percent, 5 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 5 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 7 percent grade, what is x in terms of y and z?\nOptions:\n(A) -1y - 2z\n(B) (y +z) / 4\n(C) 2y + 3z\n(D) 3y + z\n(E) 3y + 4.5z\na:",
"role": "user"
},
{
"content": "Stream of consciousness: Based on the given information, the following equation could be dervied: 1% * x + 5% * y + 3% * z = 7% * (x+y+z)\nThen use algebra to figure out 6%*x = -2%*y - 4%*z. Thus, 3x = -1y - 2z. The answer is (A).",
"role": "assistant"
}
] |
cot
|
cot_65570
|
[
{
"content": "question: A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?\nOptions:\n(A) 720\n(B) 760\n(C) 680\n(D) 780\n(E) 880\nanswer: Stream of consciousness: On first wheel there can be 10 digits. On the second wheel there will be one of the 9 digits and on the third wheel there will be 8 digits. Therefore, the number of numbers is\n10 x 9 x 8 = 720 The answer is (A).\nq: The sale price shirts listed for Rs.400 after successive discount is 10% and 5% is?\nOptions:\n(A) 280\n(B) 290\n(C) Rs.342\n(D) 250\n(E) 253\na: Stream of consciousness: 400*(90/100)* (95/100) = 342 The answer is (C).\nquestion: Four of the following five parts numbered (a), (b), (c), (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.\nOptions:\n(A) xy2 – x2y + 2x2y2\n(B) xy2(1 – 2x) + x2y(2y – 1) \n(C) xy2(1 + x) – x2y(1 – y) \n(D) xy[y(1 + x) – x(1 – y) ]\n(E) xy(y – x + 2xy) \nanswer: Stream of consciousness: The other parts are equal to xy2 – x2y + 2x2y2. The answer is (B).\nq: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?\nOptions:\n(A) 6 ½ sec\n(B) 9 ½ sec\n(C) 3 ½ sec\n(D) 7 ½ sec\n(E) 2 ½ sec\na: Stream of consciousness: \\70 + 50 = 120 * 5/18 = 100/3 mps\nD = 150 + 100 = 250 m\nT = 250 * 3/100 = 15/2 = 7 ½ sec The answer is (D).\nquestion: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?\nOptions:\n(A) 19 1/7 min\n(B) 15 1/7 min\n(C) 17 1/7 min\n(D) 7 1/7 min\n(E) 7 2/7 min\nanswer: Stream of consciousness: 1/20 + 1/30 - 1/40 = 7/120\n120/7 = 17 1/7 The answer is (C).\nquestion: The radius of a cylinder is 2 r units and height is 3 r units. Find the curved surface?\nOptions:\n(A) 27\n(B) 16\n(C) 12\n(D) 18\n(E) 11\nanswer:",
"role": "user"
},
{
"content": "Stream of consciousness: 2 * π * 2r * 3r = 12 πr2 The answer is (C).",
"role": "assistant"
}
] |
cot
|
cot_51412
|
[
{
"content": "What is the sum of the local values of the digits 2, 3, 4, 5 in the number 2345?\nOptions:\n(A) 2345\n(B) 4500\n(C) 5000\n(D) 6000\n(E) 7000\n\n2000 + 300 + 40 + 5 = 2345 So the answer is: (A).\n\nA password of a computer consists of five digits 1 through 6. What is the probability that all digits are divisible by 3 ?\nOptions:\n(A) 1/3\n(B) 1/6\n(C) 1/27\n(D) 1/243\n(E) 1/486\n\nFor each digit there are six possibilities. Two of them (3 and 6) are divisible by three, so there is a one in three chance for each digit, and since the digits are independent of each other, overall probability is 1 / 3^5 or So the answer is: (D).\n\nIf the personal income tax rate is lowered from 46% to 32%, what is the differential savings for a tax payer having an annual income before tax to the tune of $36000?\nOptions:\n(A) $3500\n(B) $5040\n(C) $3150\n(D) $7000\n(E) $10000\n\nSaving = (46-32)% of 36000 = 5040. So the answer is: (B).\n\nWorking alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 40, and 50 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?\nOptions:\n(A) 4/11\n(B) 1/2\n(C) 15/22\n(D) 200/9\n(E) 11/4\n\n",
"role": "user"
},
{
"content": "P1 takes 12 hrs\nRate for P2P3 together = 1/40 + 1/50 = 9/200\nTherefore they take 200/9\nRatio = 200/9 = So the answer is: (D).",
"role": "assistant"
}
] |
flan_v2
|
flan_v2_86011
|
[
{
"content": "In this task, you will be given a set of steps that are required to answer a specific question. Your job is to generate that question. Each given step refers to either an entity (known or unknown), a propery of an entity or a query operation (count, group, union, etc.) Knowing those operations and how they appear in the input may help you generate more accurate questions.\n Select: A select step is used to return a set of objects. There are no references to previous steps in a select step. template: Return [attributes]\n Filter: A filter step is used to return results from a previous step to which a certain condition applies. template: Return [#step] [condition]\n Project: A project step should return certain attributes of the results of a previous step. template: Return [attributes] of [#step]\n Aggregate: An aggregate step returns an aggregator function applied on a step's result. template: Return the [aggregator] of [#step].\n Group: A group step is an aggregator applied on attributes. template: Return the [aggregator] of [#step] for each [attribute]\n Superlative: A superlative step is used to return the result with a highest/lowest attribute among other results. template: Return [#step1] [where] [#step2] [is] [highest / lowest]\n Comparative: A comparative step is used when we need to compare an attribute with a number to filter results. template: Return [#step1] [where] [#step2] [comparator] [number] \n Union: A union step is used to return results of two steps together. template: Return [#step1] [or / ,] [#step2]\n Intersection: An intersection step returns the result that two steps have in common. template: Return [attribute] of both [#step1] and [#step2]\n Discard: A discard step returns result of a step and excludes result of another step from it. template: Return [#step1] besides [#step2]\n Sort: A sort returns result of another step in a specific order. template: Return [#step1] [ordered / sorted by] [#step2]\n Is true: An is true step checks a condition on another result and returns a true or false. template: Return [is / if] [condition]\n Arithmetic: An arithmatic step operates an arithmatic operation on one or more steps. template: Return the [arithmetic op.] of [#step1] [and] [#step2].\nExample: #1 return secretaries \n#2 return #1 born in state 'Alabama \n#3 return departments managed by #2 \n#4 return distinct creation years of #3\nExample solution: What are the distinct creation years of the departments managed by a secretary born in state 'Alabama'?\nExample explanation: You should follow the steps in order to realize what is the asked question. In this example, the first returned entities are secretaries(based on step #1) who are born in Alabama(based on step #2). In the step #3 departments managed by step #2(which is secretaries born in Alabama. In the final steps the creation years of the departments is returned, so the question will be about the creation years of the departments. \n\nProblem: #1 return left image \n#2 return pelican in #1 \n#3 return pole in #1 \n#4 return If #2 perches on #3\n",
"role": "user"
},
{
"content": "Solution: If a pelican perches on a pole in the image on the left.",
"role": "assistant"
}
] |
cot
|
cot_56825
|
[
{
"content": "q: The average of seven numbers is 21. The average of first three numbers is 19 and the average of last three numbers is 23. What is the middle number?\nOptions:\n(A) 20\n(B) 22\n(C) 18\n(D) 19\n(E) 21\na: Stream of consciousness: The total of seven numbers = 7X21 = 147\nThe total of first 3 and last 3 numbers is = 3 X 19+3 X 23 = 126\nSo, the middle number is (147 - 126 ) = 21 The answer is (E).\nquestion: Ronald and Elan are working on an assignment. Ronald takes 6 hrs to type 32 pages on a computer, while Elan takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?\nOptions:\n(A) 8 hrs 18 min\n(B) 8 hrs 85 min\n(C) 8 hrs 15 min\n(D) 7 hrs 15 min\n(E) 8 hrs 25 min\nanswer: Stream of consciousness: Number of pages typed by Ronald in 1 hour = 32/6 = 16/3\nNumber of pages typed by Elan in 1 hour = 40/5 = 8\nNumber of pages typed by both in 1 hour = (16/3 + 8) = 40/3\nTime taken by both to type 110 pages = (110 * 3/40) = 8 1/4 = 8 hrs 15 min The answer is (C).\nq: There are seven thieves. They stole diamonds from a diamond merchant and ran away. While running, night sets in and they decide to rest in the jungle.\nWhen everybody was sleeping, two of them woke up and decided to divide the diamonds equally among themselves. But when they divided the diamonds equally, one diamond is left.\nSo they woke up the 3rd thief and tried to divide the diamonds equally again but still one diamond was left. Then they woke up the 4th thief to divide the diamonds equally again, and again one diamond was left. This happened with the 5th and 6th thief – one diamond was still left.\nFinally, they woke up the 7th thief and this time the diamonds were divided equally.\nHow many diamonds did they steal in total?\nOptions:\n(A) 2397\n(B) 2401\n(C) 2411\n(D) 2423\n(E) None of the above\na: Stream of consciousness: We need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2, 3, 4, 5, and 6. The least common multiple of these numbers is 60. So, we need a multiple of 7 that is 1 greater than a multiple of 60. The answer is (B).\nquestion: On a clock, how many times a day do the minute and hour hand overlap?\nOptions:\n(A) 10\n(B) 11\n(C) 20\n(D) 22\n(E) 24\nanswer: Stream of consciousness: 22 times: 12:00:00, 1:05:27, 2:10:55, 3:16:22, 4:21:49, 5:27:16, 6:32:44, 7:38:11, 8:43:38, 9:49:05, 10:54:33. Each twice a day. The answer is (D).\nq: A man rows his boat 95 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?\nOptions:\n(A) 10 kmph\n(B) 6 kmph\n(C) 5 kmph\n(D) 8 kmph\n(E) 7 kmph\na: Stream of consciousness: Speed downstream = d/t = 95/(2 1/2) = 38 kmph\nSpeed upstream = d/t = 45/(2 1/2) = 18 kmph\nThe speed of the stream = (38 - 18)/2 = 10 kmph The answer is (A).\nq: 10 men and 15 women together can complete a work in 5 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?\nOptions:\n(A) 127 days\n(B) 150 days\n(C) 177 days\n(D) 187 days\n(E) 225 days\na:",
"role": "user"
},
{
"content": "Stream of consciousness: 1 man's 1 day work = 1/100\n(10 men + 15 women)'s 1 day work = 1/5\n15 women's 1 day work = (1/5 - 10/100) = 1/10\n1 woman's 1 day work = 1/150\n1 woman alone can complete the work in 150 days. The answer is (B).",
"role": "assistant"
}
] |
cot
|
cot_94182
|
[
{
"content": "Reasoning: The integer should be divisible by: 2, 3, 4, 5, 6, 7, 8 and 9, that is 2, 3, 2^2, 5, 2*3, 7, 2^3 and 3^2. The least common multiple of these integers is the product of 7, 5, 3^2 and 2^3. Then, L/2 is (7 * 5 * 3^2 * 2^3)/2 = 7*5*9*4 = 1260.\nAns: (D)\nQuestion: If L is the least positive integer that is divisible by every integer from 1 to 9 inclusive, then L/2 is =\nOptions:\n(A) 5040\n(B) 2520\n(C) 1890\n(D) 1260\n(E) 630\n\n\nRationale: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder X when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.\nThe answer: (C)\nQuestion: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder X when N is divided by 30?\nOptions:\n(A) (a) 4\n(B) (b) 7\n(C) (c) 11\n(D) (d) 13\n(E) (e) 17\n\n\nReasoning: Speed = 63 * 5/18 = 35/2 m/sec\nTime taken = 280 * 2/35 = 16 sec\nAns: (B)\nQuestion: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?\nOptions:\n(A) 11\n(B) 16\n(C) 18\n(D) 10\n(E) 14\n\n\nRationale: (800*3*3)/100 = 72\n920 + 72 = 992\nThe answer: (D)\nQuestion: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?\nOptions:\n(A) 3387\n(B) 277\n(C) 223\n(D) 992\n(E) 213\n\n\nReasoning: 20m - n = p\nAdd n to both sides:\n20m = n + p\nAdd m to both sides:\n21m = n + p + m\nNow, divide both sides by 3\n7m = (n + p + m)/3 = the average of n, p, and m\nAns: (D)\nQuestion: If 20m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?\nOptions:\n(A) 2m −1\n(B) 4m\n(C) 6m\n(D) 7m\n(E) 6m/5\n\n\nReasoning: Speed = 63 * 5/18 = 35/2 m/sec\nTime taken = 280 * 2/35 = 16 sec\nAns: (B)\n",
"role": "user"
},
{
"content": "Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?\nOptions:\n(A) 15 sec\n(B) 16 sec\n(C) 18 sec\n(D) 20 sec\n(E) 25 sec",
"role": "assistant"
}
] |
cot
|
cot_52081
|
[
{
"content": "Reasoning: 1 to 11 = 11 * 48 = 528\n1 to 6 = 6 * 49 = 294\n6 to 11 = 6 * 52 = 312\n6th = 294 + 312 – 528 = 78\nAns: (C)\nQuestion: The average of 11 results is 48, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?\nOptions:\n(A) 21\n(B) 56\n(C) 78\n(D) 25\n(E) 23\n\n\nRationale: (1056 / 28) gives remainder 20\n20 + 8 = 28, So we need to add 8\nThe answer: (E)\nQuestion: What is the least number should be added to 1056, so the sum of the number is completely divisible by 28?\nOptions:\n(A) 1\n(B) 2\n(C) 3\n(D) 4\n(E) 8\n\n\nReasoning: The ratio is 2:3 = gym:ride, so (16)(3/2) = 24 minutes at the gym, and 24 + 16 = 40 minutes exercise, so (2/3)(40) = 27 minutes yoga.\nAns: (C)\nQuestion: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 16 minutes, how much time will she spend doing yoga? (rounded to minutes)\nOptions:\n(A) 10 min.\n(B) 41 min.\n(C) 27 min.\n(D) 23 min.\n(E) 25 min.\n\n\nRationale: The max product of any two balls can be 9 * 10 = 9900 = 9 * 10\nIf we multiply it by $1000 the max amount will be 9 * 10^4.\nThe answer: (A)\nQuestion: In a certain lottery drawing, two balls are selected at random from a container with 10 balls, numbered from 1 to 10, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner?\nOptions:\n(A) $9 x 10^4\n(B) $9.90 x 10^6\n(C) $1.00 x 10^7\n(D) $1.05 x 10^7\n(E) $9.90 x 10^7\n\n\nReasoning: Money paid in cash = Rs. 1000\nBalance payment = (40000 - 1000) = Rs. 39000\nAns: (E)\nQuestion: The price of a T.V. set worth Rs. 40000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?\nOptions:\n(A) 22678\n(B) 26699\n(C) 26788\n(D) 19000\n(E) 39000\n\n\nReasoning: 223 + 43 = 266/17 = 11 (Remainder)\nAns: (D)\n",
"role": "user"
},
{
"content": "Question: A no.when divided by 223 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?\nOptions:\n(A) 2\n(B) 7\n(C) 9\n(D) 11\n(E) 15",
"role": "assistant"
}
] |
cot
|
cot_87950
|
[
{
"content": "Reasoning: Work done by X in 1 day = 1/18\nWork done by Y in 1 day = 1/15\nWork done by Y in 10 days = 10/15 = 2/3\nRemaining work = 1 – 2/3 = 1/3\nNumber of days in which X can finish the remaining work = (1/3) / (1/18) = 6\nAns: (C)\nQuestion: X can finish a work in 18 days. Y can finish the same work in 15 days. Yworked for 10 days and left the job. how many days does X alone need to finish the remaining work?\nOptions:\n(A) 3\n(B) 5\n(C) 6\n(D) 7\n(E) 9\n\n\nRationale: A 54 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 54 matches were played.\nThe answer: (A)\nQuestion: Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 55 players took part in that tournament. How many matches were played?\nOptions:\n(A) 90 matches\n(B) 95 matches\n(C) 99 matches\n(D) 85 matches\n(E) 87 matches\n\n\nReasoning: There are altogether three arrangements, which are we can select two members each from team A and B, each from team A and C, and each from team B and C. For each arrangement, there are altogether 64 possibilities (8*8) since each team has 8 players. So there are a total of 192 possibilities (64*3). I hope this method is easier for you to understand.\nAns: (C)\nQuestion: There are 3 teams each with 8 basket players. How many combinations are there if we were to pick 2 players from the 3 teams such that no team was picked twice?\nOptions:\n(A) 50\n(B) 23\n(C) 192\n(D) 28\n(E) 45\n\n\nRationale: ? ≈ 16 × 23 + 1490 – 250 ≈ 1600\nThe answer: (A)\nQuestion: What approximate value should come in place of the question mark (?) in the following equation?\n16√524 + 1492 - 250.0521?\nOptions:\n(A) 1600\n(B) 1800\n(C) 1900\n(D) 2400\n(E) 1400\n\n\nReasoning: The integer should be divisible by: 2, 3, 4, 5, 6, 7, 8 and 9, that is 2, 3, 2^2, 5, 2*3, 7, 2^3 and 3^2. The least common multiple of these integers is the product of 7, 5, 3^2 and 2^3. Then, L/2 is (7 * 5 * 3^2 * 2^3)/2 = 7*5*9*4 = 1260.\nAns: (D)\nQuestion: If L is the least positive integer that is divisible by every integer from 1 to 9 inclusive, then L/2 is =\nOptions:\n(A) 5040\n(B) 2520\n(C) 1890\n(D) 1260\n(E) 630\n\n\nReasoning: Let the time taken to reach the destination be 3x hours. Total distance = 40 * 3x = 120x km\nHe covered 2/3 * 120x = 80x km in 1/3 * 3x = x hours So, the remaining 40x km, he has to cover in 2x hours. Required speed = 40x/2x = 20 kmph.\nAns: (A)\n",
"role": "user"
},
{
"content": "Question: By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?\nOptions:\n(A) 20\n(B) 99\n(C) 88\n(D) 77\n(E) 61",
"role": "assistant"
}
] |
cot
|
cot_68421
|
[
{
"content": "q: There are 100 employees in a room. 99% are President. How many managers must leave the room to bring down the percentage of President to 98%?\nOptions:\n(A) 1\n(B) 2\n(C) 46\n(D) 50\n(E) 97\na: Stream of consciousness: We have 99 Presidents and 1 director. That 1 director to compose 2% of the total number of people, there must be 50 people in the room, hence 50 Presidents must leave. The answer is (B).\nquestion: Calculate the speed of a boat in still water (in km/hr) if in one hour, the boat goes 15 km/hr downstream and 7 km/hr upstream.\nOptions:\n(A) 12 kmph\n(B) 13 kmph\n(C) 14 kmph\n(D) 15 kmph\n(E) 11 kmph\nanswer: Stream of consciousness: Speed in still water = (15 + 7)1/2 kmph = 11 kmph. The answer is (E).\nq: The average of seven numbers is 22. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?\nOptions:\n(A) 25\n(B) 27\n(C) 29\n(D) 32\n(E) 55\na: Stream of consciousness: The total of seven numbers = 7X22 = 154\nThe total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99\nSo, the middle number is (154 - 99 ) = 55 The answer is (E).\nquestion: In how many ways can you seat 4 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?\nOptions:\n(A) 720\n(B) 1720\n(C) 2880\n(D) 6\n(E) 10080\nanswer: Stream of consciousness: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 1 chairs to sit. The remaining 3 people can sit in 3! ways. Thus the # of arrangements is 1*3! = 6. The answer is (D).\nq: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?\nOptions:\n(A) 2234\n(B) 4350\n(C) 4560\n(D) 5132\n(E) y=5184\na: Stream of consciousness: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184\n432 12 x 62 The answer is (E).\nq: How much is 80% of 40 is greater than 4/5 of 25?\nOptions:\n(A) 229\n(B) 87\n(C) 26\n(D) 12\n(E) 667\na:",
"role": "user"
},
{
"content": "Stream of consciousness: (80/100) * 40 – (4/5) * 25\n32 - 20 = 12 The answer is (D).",
"role": "assistant"
}
] |
flan_v2
|
flan_v2_90594
|
[
{
"content": "In this task, you will be given a set of steps that are required to answer a specific question. Your job is to generate that question. Each given step refers to either an entity (known or unknown), a propery of an entity or a query operation (count, group, union, etc.) Knowing those operations and how they appear in the input may help you generate more accurate questions.\n Select: A select step is used to return a set of objects. There are no references to previous steps in a select step. template: Return [attributes]\n Filter: A filter step is used to return results from a previous step to which a certain condition applies. template: Return [#step] [condition]\n Project: A project step should return certain attributes of the results of a previous step. template: Return [attributes] of [#step]\n Aggregate: An aggregate step returns an aggregator function applied on a step's result. template: Return the [aggregator] of [#step].\n Group: A group step is an aggregator applied on attributes. template: Return the [aggregator] of [#step] for each [attribute]\n Superlative: A superlative step is used to return the result with a highest/lowest attribute among other results. template: Return [#step1] [where] [#step2] [is] [highest / lowest]\n Comparative: A comparative step is used when we need to compare an attribute with a number to filter results. template: Return [#step1] [where] [#step2] [comparator] [number] \n Union: A union step is used to return results of two steps together. template: Return [#step1] [or / ,] [#step2]\n Intersection: An intersection step returns the result that two steps have in common. template: Return [attribute] of both [#step1] and [#step2]\n Discard: A discard step returns result of a step and excludes result of another step from it. template: Return [#step1] besides [#step2]\n Sort: A sort returns result of another step in a specific order. template: Return [#step1] [ordered / sorted by] [#step2]\n Is true: An is true step checks a condition on another result and returns a true or false. template: Return [is / if] [condition]\n Arithmetic: An arithmatic step operates an arithmatic operation on one or more steps. template: Return the [arithmetic op.] of [#step1] [and] [#step2].\n\nExample Input: #1 return drivers \n#2 return races that #1 have participated \n#3 return number of #2 for each #1 \n#4 return #1 where #3 is at least 2 \n#5 return id of #4 \n#6 return races of #4 \n#7 return number of #6 \n#8 return forename of #4 \n#9 return #5 , #8 , #7\nExample Output: What is the id, forename, and number of races for all drivers that have participated in at least 2 races?\n\nExample Input: #1 return light source \n#2 return laptop \n#3 return #1 that is attached to #2 \n#4 return number of #3 \n#5 return if #4 is at least one\nExample Output: If a light source is attached to a laptop\n\nExample Input: #1 return left image \n#2 return warthogs of #1 \n#3 return the number of #2 \n#4 return if #3 is equal to one\nExample Output:",
"role": "user"
},
{
"content": "If the image on the left shows a single warthog.\n\n",
"role": "assistant"
}
] |
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