[User]
Rationale: 300/(900 - 300) = 50%.
The answer: (D)
Question: A cricket bat is sold for $900, making a profit of $300. The profit percentage would be
Options:
(A) 24%
(B) 25%
(C) 30%
(D) 50%
(E) 40%

Reasoning: Speed downstream = d/t = 105/(2 1/2) = 42 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (42 - 18)/2 = 12 kmph
Ans: (C)
Question: 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?
Options:
(A) 5 kmph
(B) 7 kmph
(C) 12 kmph
(D) 8 kmph
(E) 1 kmph

Rationale: {Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}
100 = 80 + 75 - {Both correctly} + 5
{Both correctly} = 60.
The answer: (A)
Question: If 80 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 5 percent of the test takers answered neither question correctly, what percent answered both correctly?
Options:
(A) 60 %
(B) 65 %
(C) 70%
(D) 75%
(E) 80%

Reasoning: 10 * 154 = 1540
3 * 100 + 5 * 150 = 1050
1540 – 1050 = 490
Ans: (C)
Question: A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.154. Find the unknown rate of two blankets?
Options:
(A) 420
(B) 550
(C) 490
(D) 450
(E) 457

Rationale: Sum of all the 13 results = 15 * 60 = 900
Sum of the first 7 of them = 10 * 10 = 100
Sum of the last 7 of them = 10 * 80 = 800
So, the 8th number = 900 + 100 - 800 = 200.
The answer: (B)
Question: The average of 15 result is 60. Average of the first 10 of them is 10 and that of the last 10 is 80. Find the 8th result?
Options:
(A) 35
(B) 200
(C) 150
(D) 250
(E) 300

Rationale: 12x = 16y = 28z
3x = 4y = 7z
3(4*7) = 4(3*7) = 7(3*4)
Addition = 28+21+12 = 61
Answer would be multiple of 61 which is 122
The answer: (C)

[Assistant]
Question: If 12x = 16y = 28z, then what is a possible sum of positive integers x, y, and z?
Options:
(A) 52
(B) 58
(C) 122
(D) 84
(E) 168


[User]
Largest 6 digit number is 999999
After doing 999999 ÷ 88 we get remainder 55
Hence largest 6 digit number exactly divisible by 88 = 999999 - 55 = 999944
This justifies what answer for what question? Q & A:

[Assistant]
Find the largest 6 digit number which is exactly divisible by 88?
Options:
(A) 998765
(B) 998907
(C) 999944
(D) 999954
(E) 999990
(C)


[User]
[Ans] (D)
[Question] If 12 men can reap 120 acres of land in 16 days, how many acres of land can 36 men reap in 32 days?
Options:
(A) 269
(B) 512
(C) 369
(D) 720
(E) 450
[CoT] 12 men 120 acres 16 days
36 men ? 32 days
120 * 36/12 * 32/16
120 * 3 * 2
120 * 6 = 720

[Ans] (C)
[Question] 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?
Options:
(A) (a)  4
(B) (b)  7
(C) (c)  11
(D) (d)  13
(E) (e)  17
[CoT] 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.

[Ans] (B)
[Question]

[Assistant]
Guna has 8 flavors of ice cream in him parlor. How many options are there for Thilak to pick a one-flavor, two-flavor, three-flavor, four-flavor, five-flavor, six-flavor,seven-flavor or eight-flavor order?
Options:
(A) 223
(B) 395
(C) 448
(D) 774
(E) 835
[CoT] 8C1 + 8C2+ 8C3+8C4+8C5+8C6+8C7+8C8 = 395.


[User]
What was the question for this implicit rationale, and corresponding answer?
Distance traveled by Eddy = 450 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 450/3 = 150 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 150/75 = 2
 The answer: (B)

[Assistant]
The question: Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 450 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Freddy)
Options:
(A) 8/3
(B) 2
(C) 8/5
(D) 5/8
(E) 5/3


[User]
Question. Maximum no of unsuccessful attempts, a thief can do in order to break a number locking system of 4 digits.
Options:
(A) 9988
(B) 9999
(C) 9799
(D) 9685
(E) 6545
Answer. (B)
What step-by-step reasoning justifies that answer?

[Assistant]
Reasoning: From 0 to 9999 there are 10000 four digit numbers
So maximum number of unsuccessful attempts = 10000 - 1 = 9999


[User]
Rationale: 36^2 = 6*6*6*6 = 2^4*3^4
Total factors = (4+1)*(4+1) = 6*6 = 36
The answer: (E)
Question: How many factors does 49^2 have?
Options:
(A) 2
(B) 8
(C) 24
(D) 25
(E) 36

Reasoning: The total number of arrangements is
5P5 = 5! = 120
Ans: (B)
Question: In how many different ways can the letters of the word "CLAIM" be rearrangement?
Options:
(A) 110
(B) 120
(C) 125
(D) 130
(E) 140

Rationale: Mother has a fixed place and father, so there are 2! ways to arrange the children, hence
The answer: (A)
Question: A family with 1 mother, 1 father, and 2 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other two children on either side of him, how many seating arrangements are possible?
Options:
(A)  2
(B)  4
(C)  6
(D)  8
(E)  10

Reasoning: T = 60/36 * 18/5 = 6 sec
Ans: (D)
Question: n what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
(A) 2
(B) 7
(C) 8
(D) 6
(E) 9

Rationale: Already average of two subjects is (70+80)/2 = 75%
To maintain the percentage at 75%, he shouls get 75% marks in third subject
The answer: (B)
Question: a student got 70% in one subject,80% in other.to get overall 75% how much he should get in third subject.
Options:
(A) 65%
(B) 75%
(C) 85%
(D) 95%
(E) 88%

Rationale: A prime factors are 3 and 11. 33<sqrt(99)? no
B prime factors are 2 and 7. 14<sqrt(98)? no
C prime number. its sqrt is never greater than itself
D A prime factors are 2 and 6. 6<sqrt(96)? yes
E prime factors are 5 and 19. 45<sqrt(95)? no
The answer: (D)

[Assistant]
Question: A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two digit prime saturated integer ?
Options:
(A) 99
(B) 98
(C) 97
(D) 96
(E) 95


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: 720 * 5/18 = 200 mps
 The question and answer:

[Assistant]
Express a speed of 720 kmph in meters per second?
Options:
(A) 120 mps
(B) 200 mps
(C) 181 mps
(D) 190 mps
(E) 125 mps
The answer is (B)


[User]
Consider the question. 396, 462, 572, 427, 671, 264
Options:
(A) 396
(B) 427
(C) 671
(D) 264
(E) 572
 If the answer is '(B)'; explain the reasoning:

[Assistant] In each number except 427, the middle digit is the sum of other two.


[User]
Rationale: Average = (76 + 65 + 82 + 67 + 85)/5 = 375/5 = 75.
The answer: (E)
Question: Dacid obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
(A) 32
(B) 88
(C) 77
(D) 99
(E) 75

Reasoning: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20 = 40 kmph
Ans: (B)
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?
Options:
(A) 30/90 kmph
(B) 80,40 kmph
(C) 24,98 kmph
(D) 30,54 kmph
(E) 45.98 kmph

Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter
The answer: (A)
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
(A) 150
(B) 781
(C) 767
(D) 277
(E) 266

Reasoning: D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 se
Ans: (C)
Question: 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?
Options:
(A) 65 sec
(B) 88 sec
(C) 25 sec
(D) 88 sec
(E) 55 sec

Rationale: Only 4 cubes situated at the corners of the cuboid will have 4 coloured and 2 non-coloured sides.
The answer: (B)
Question: How many cubes will have 4 coloured sides and two non-coloured sides ?
Options:
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1

Rationale: P(at least one gold ball) = 1 - P(no golf ball, so 2 ping pong balls) = 1- 2/5*1/4 = 9/10.
The answer: (D)

[Assistant]
Question: In a jar there are 3 golf balls and 2 ping pong balls. What is the probability of drawing at least one golf ball when drawing two consecutive balls randomly?
Options:
(A) 1/4
(B) 1/2
(C) 3/5
(D) 9/10
(E) 16/20


[User]
Ques: Find the average of the first 23 natural numbers?
Options:
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Ans: (E)
CoT: Average of the first 'n' natural numbers = (n + 1)/2
We get (23 + 1)/2 = 12

Ques: From among the 31 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
Options:
(A) 1360
(B) 1260
(C) 1060
(D) 1160
(E) 930
Ans: (E)
CoT: There are 31 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 31 ways. When one person is appointed as leader, we are left with 35 students. Out of these 30 teachers, we can select one class representative. So, a class representative can be selected in 30 ways. Hence, the number of ways in which a leader and class representative can be selected = 31 x 30 = 930

Ques: The area of a triangle is with base 10m and height 5m?
Options:
(A) 11
(B) 25
(C) 787
(D) 122
(E) 12
Ans: (B)
CoT: 1/2 * 10 * 5 = 25 m2

Ques: The average of 11 results is 49, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
(A) 21
(B) 67
(C) 18
(D) 25
(E) 23
Ans: (B)

[Assistant]
CoT: 1 to 11 = 11 * 49 = 539
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 â€“ 539 = 67


[User]
Consider the question. Find the mean proportional between 81 & 100?
Options:
(A) A) 59
(B) B) 61
(C) C) 63
(D) D) 65
(E) E) 90
 What is the step-by-step reasoning process to arrive at the answer: (E)?

[Assistant]
Formula = √a×b
A = 81 and B = 100
√81×100 = 9 × 10 = 90


[User] Creatively image a question and justification for this answer: (C)

[Assistant]
The question is: The average of nine numbers is 15. The average of first four numbers is 11 and the average of last four numbers is 14. What is the middle number?
Options:
(A) 19
(B) 20
(C) 35
(D) 31
(E) 27
Step-by-step reasoning process: The total of nine numbers = 9X15 = 135
The total of first 4 and last 4 numbers is = 4 X 11+4 X 14 = 100
So, the middle number is (135 - 100 ) = 35


[User]
Consider the question. How much 60% of 50 is greater than 40% of 30?
Options:
(A) 18
(B) 99
(C) 77
(D) 66
(E) 12
 What is the step-by-step reasoning process to arrive at the answer: (A)?

[Assistant]
(60/100) * 50 – (40/100) * 30
30 - 12 = 18ch 60% of 50 is greater than 40% of 30?


[User]
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
The answer: (C)
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
Options:
(A) 34%
(B) 54%
(C) 57%
(D) 78%
(E) 87%

Reasoning: Simple interest = (18000 * 2 * 15)/100 = Rs. 5400
Amount = P + I = 18000 + 5400 = Rs. 23400
Ans: (E)
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for two years?
Options:
(A) 29893
(B) 27773
(C) 29989
(D) 28800
(E) 23400

Rationale: 12 Rupees = 1200 paisa's
36/1200 × 100 = 3/12
12/3 = 3 %
The answer: (B)
Question: What percent is 36 paisa's of 12 rupees?
Options:
(A) 2 %
(B) 3 %
(C) 4 %
(D) 5 %
(E) 6 %

Reasoning: Correct Answer: (E)
Let’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.
Ans: (D)
Question: If x<0, y>0, and |x| < |y|, which of the following must be true?
Options:
(A) x > y
(B) y^2 > x^2
(C) x^3 > y^2
(D) –x < y
(E) x < –y

Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 460 + 140 = 600 m
Required time = 600 * 2/25 = 48 se
The answer: (C)
Question: A train 460 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
(A) 40
(B) 87
(C) 48
(D) 21
(E) 14

Rationale: 6a2 = 6 * 2a * 2a = 24a2
The answer: (D)

[Assistant]
Question: The edge of a cube is 2a cm. Find its surface?
Options:
(A) 24a8
(B) 24a4
(C) 24a1
(D) 24a2
(E) 24a7


[User] Creatively image a question and justification for this answer: (D)

[Assistant]
The question is: 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 8 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?
Options:
(A) 30
(B) 20
(C) 18
(D) 12
(E) 6
Step-by-step reasoning process: 21-12 < no of hrs < 21-8
9< no of hrs < 13.


[User]
Consider the question. Which of the following is equal to the average (arithmetic mean) of (y+4)^2 and (y-4)^2?
Options:
(A) x^2
(B) x^2+2
(C) x^2 +12
(D) x^2+21
(E) y^2+16
 If the answer is '(E)'; explain the reasoning:

[Assistant]
Avg = [(y+4)^2 + (y-4)^2] / 2
Expanding and simplifying, (y^2 + 8y + 16 + y^2 - 8y + 16 ) / 2 = y^2 + 16


[User]
Correct Answer: (E)
Let’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.
If x<0, y<0, and |x| > |y|, which of the following must be true?
Options:
(A) x > y
(B) y^2 > x^2
(C) x^3 > y^2
(D) x < y
(E) x < –y
(D)

400*(90/100)*(95/100) = 342
The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
Options:
(A) 338
(B) 277
(C) 342
(D) 882
(E) 212
(C)

1/18 + 1/30 = 8/90 = 4/45
45/4 = 11 1/4 *2 = 22 1/2 days

[Assistant]
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?
Options:
(A) 22 1/8 days
(B) 22 1/2 days
(C) 22 6/2 days
(D) 72 1/2 days
(E) 23 1/2 days
(B)


[User]
Q: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
Options:
(A) 9 sec
(B) 6 sec
(C) 8 sec
(D) 10 sec
(E) 11 sec
A: (B)
Explain how we arrive at this answer:

[Assistant] Explanation: T = 60/36 * 18/5 = 6 sec


[User]
Rationale: Any number multiplied by 2 has to be an even number henc
The answer: (E)
Question: If x and y are unique prime integers, which of the following must be odd?
Options:
(A) xy^2
(B) 2x+2y
(C) 2x−2y
(D) 2x/2y
(E) x−y

Reasoning: T = 160/32 = 5 h
T = 5 - 3 = 2
Time Ratio = 5:2 = 5:2
Speed Ratio = 2:5
Ans: (B)
Question: A motorcyclist goes from Bombay to Pune, a distance of 160 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?
Options:
(A) 1:2
(B) 2:5
(C) 1:4
(D) 1:1
(E) 1:6

Rationale: Total boxes = 23
Filled with toys = 19
Filled with appliance = 4
Total boxes for sale = 8
Toy boxes for sale = 5
Appliance boxes for sale = 3
Appliance boxes not for sale = 4 - 3 = 1
The answer: (A)
Question: In Sam's hanger there are 23 boxes, 19 out of the boxes are filled with toys and the rest are filled with electrical appliances. 8 boxes are for sale, 5 of them are filled with toys. How many boxes with electrical appliances are in Sam's hanger that is not for sale?
Options:
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.

Reasoning: The total distance D traveled by John is given by
D = 45 * 2 + 3 * 55 = 255 miles.
Ans: (C)
Question: John left home and drove at the rate of 45 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination. How many miles did John drive?
Options:
(A) 235 miles.
(B) 245 miles.
(C) 255 miles.
(D) 265 miles.
(E) 275 miles.

Rationale: 2/3 * 6/7 * 4/3 * 1/8 = 48/504 = 2/21
The answer: (A)
Question: The compound ratio of 2/3, 6/7, 4/3 and 1/8 is given by?
Options:
(A) 2/21
(B) 1/48
(C) 1/98
(D) 1/96
(E) 1/68

Rationale: S = 400/10 * 18/5 = 144 kmph
The answer: (A)

[Assistant]
Question: A 400 meter long train crosses a man standing on the platform in 10 sec. What is the speed of the train?
Options:
(A) 144
(B) 108
(C) 278
(D) 126
(E) 112


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: Increase = (30/40)*100 = (3/4)*100 = 75%.
 The question and answer:

[Assistant]
John makes $40 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?
Options:
(A) 16%
(B) 16.66%
(C) 76.69%
(D) 76.98%
(E) 75%
The answer is (E)


[User]
Reconstruct a question, answer pair from this explanation: D = 1400+100 = 1500 m
S = 72 * 5/18 = 20
T = 1500 * 1/20 = 75 sec

[Assistant]
Q:How long does a train 100 m long traveling at 72 kmph takes to cross a tunnel of 1400 m in length?
Options:
(A) 70 sec
(B) 60sec
(C) 82 sec
(D) 75 sec
(E) 62 sec
A:(D)


[User]
Reasoning: There are 38 students and every one has equal chance of being selected as a leader. Hence, the leader can be appointed in 38 ways. When one person is appointed as leader, we are left with 35 students. Out of these 37 teachers, we can select one class representative. So, a class representative can be selected in 37 ways. Hence, the number of ways in which a leader and class representative can be selected = 38 x 37 = 1406
Ans: (E)
Question: From among the 38 students in a class, one leader and one class representative are to be appointed. In how many ways can this be done?
Options:
(A) 1360
(B) 1260
(C) 1060
(D) 1160
(E) 1406

Rationale: Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
The answer: (C)
Question: Find the largest 4 digit number which isexactly divisible by 88?
Options:
(A) 7890
(B) 8900
(C) 9944
(D) 9976
(E) 10000

Reasoning: (12/170)/(4/50) = 15/17 = 88% it means that 12/170 represents only 88%. Therefore a decrease of 12%.
Ans: (A)
Question: A pharmaceutical company received $4 million in royalties on the first $50 million in sales of and then $12 million in royalties on the next $170 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $50 million in sales to the next $170 million in sales?
Options:
(A) 12%
(B) 15%
(C) 45%
(D) 52%
(E) 56%

Rationale: Since the man can go in 4 ways and can back in 3 ways. Therefore total number of ways are 4 x3 = 12ways.
The answer: (C)
Question: 4 buses runs between Chennai and Mysore. If a man goes from Chennai to Mysore by a bus and comes back to Mysore by another bus, then the total possible ways are
Options:
(A) 4
(B) 8
(C) 12
(D) 16
(E) None of these

Reasoning: Time = (100 x 100)/(1000 x 5) years = 2 years.
Ans: (C)
Question: How much time will it take for an amount of 1000 to yield 100 as interest at 5% per annum of simple interest?
Options:
(A) 3 years
(B) 4 years
(C) 2 years
(D) 5 years
(E) 7 years

Reasoning: Speed = 99 * 5/18 = 55/2 m/sec
Total distance covered = 300 + 195 = 495 m
Required time = 495 * 2/55 = 18 sec
Ans: (B)

[Assistant]
Question: A train 300 m long is running at a speed of 99 km/hr. In what time will it pass a bridge 195 m long?
Options:
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21


[User] The other parts are equal to (a + b)2.is the reasoning for what question and answer pair?

[Assistant]
Q: Four of the 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.
Options:
(A) (a – b) 2 + 4ab
(B) a(a + b)  + b(a + b)
(C) (a2 – b2)  + 2b(b + a)
(D) (a – b) b + (a + b) 2b
(E) (a + b) 2 – 2a(a – b)  + a(2a – 2b)
A: (D)


[User]
Reconstruct a question, answer pair from this explanation: 60/360 = 1/6
1/6 of total area = 5
5/6 of total area = 5*5 = 25

[Assistant]
Q:If O is the center of the circle in the figure above and the area of the unshaded sector is 5, what is the area of the shaded region?
Options:
(A) 25/√π
(B) 30/√π
(C) 20
(D) twenty five (25)
(E) 30
A:(D)


[User] Come up with a question and reasoning that would justify this answer: (B)

[Assistant]
The question is: The average height in a group of 4 people is 175 cm. If the average height increased when 2 more people were added to the group, which of the following cannot be the heights of the two new people?
Options:
(A) 179 cm and 172 cm
(B) 181 cm and 169 cm
(C) 173 cm and 178 cm
(D) 176 cm and 176 cm
(E) 174 cm and 177 cm
Step-by-step reasoning process: Denote X as the sum of the heights of the two new people. From the stem it follows that (700+X)6>175. This reduces to X>350. Only the heights from B add up to 350 cm. All other pairs add up to more than 350 cm.


[User]
Given the following reasoning and answer, what was the question? 2/3 * 6/7 * 4/3 * 1/8 = 48/504 = 2/21
 The answer: (A)

[Assistant]
The question The compound ratio of 2/3, 6/7, 4/3 and 1/8 is given by?
Options:
(A) 2/21
(B) 1/48
(C) 1/98
(D) 1/96
(E) 1/68


[User]
Rationale: My ans is 15C4 = 1365
The answer: (E)
Question: Fifteen telegenic contestants with a variety of personality disorders are to be divided into two “tribes” of four members each, tribe A and tribe B, for a competition. How many distinct groupings of two tribes are possible?
Options:
(A) 120
(B) 126
(C) 252
(D) 1200
(E) 1365

Rationale: 3 feet = 1 yard
12 inches = 1 foot
The answer: (A)
Question: Which is longest: a foot, a yard or an inch?
Options:
(A) a yard
(B) inch
(C) foot
(D) feet
(E) cm

Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780 = 46.
The answer: (A)

[Assistant]
Question: The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
Options:
(A) 46
(B) 82
(C) 45
(D) 43
(E) 53


[User]
[Ques]: Look at this series: 1.25, 7.5, ____, 270, 1620, ... What number should fill the blank?
Options:
(A) 50
(B) 65
(C) 45
(D) 55
(E) 40
*Ans*: (C)
--CoT--: This is a simple multiplication series. Each number is 6 times greater than the previous number.

[Ques]: A and B complete a work in 9 days. A alone can do it in 18 days. If both together can do the work in how many days?
Options:
(A) 6 days
(B) 8 days
(C) 5 days
(D) 7 days
(E) 15 days
*Ans*: (A)
--CoT--: 1/9 + 1/18 = 1/6
6/1 = 6 days

[Ques]: The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was :
Options:
(A) 12000
(B) 10000
(C) 15000
(D) 20000
(E) 25000
*Ans*: (A)
--CoT--: Purchase = 8748/(1-10/100^3) = 12000

[Ques]: A train running at the speed of 60 km/hr crosses a pole in 3 sec. What is the length of the train?
Options:
(A) 85 m
(B) 70 m
(C) 115 m
(D) 50 m
(E) 150 m
*Ans*: (D)

[Assistant]
--CoT--: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 3 = 50 m


[User] Creatively image a question and justification for this answer: (D)

[Assistant]
The question is: Grace has 17 jellybeans in her pocket. She has 9 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
Options:
(A) 4
(B) 8
(C) 12
(D) 14
(E) 16
Step-by-step reasoning process: The worst scenario is when she takes 9 red and 4 green, total of 13 jellybeans, and still doesn't have 3 distinct colors. But the next draw (14th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.


[User] Imagine a question and stream-of-consciousness explanation for which this is the answer: (C)

[Assistant]
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
Options:
(A) 337
(B) 267
(C) 342
(D) 287
(E) 261
Stream-of-consciousness: 400*(90/100)*(95/100) = 342


[User]
(Ans). (A)
(Question). Every year an amount increases by 1/6th of itself. How much will it be after two years if its present value is Rs.64000?
Options:
(A) 87111
(B) 81007
(C) 81008
(D) 81066
(E) 81022
(CoT). 64000* 7/6 * 7/6 = 87111

(Ans). (C)
(Question). 10 books are placed at random in a shelf. The probability that a pair of books will always be together is?
Options:
(A) 1/6
(B) 1/7
(C) 1/5
(D) 1/9
(E) 1/2
(CoT). 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5

(Ans). (E)
(Question). What is the greatest positive integer x such that 4^x is a factor of 64^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
(CoT). 64^10 = (4^3)^10 = 4^30

(Ans). (A)
(Question).

[Assistant]
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?
Options:
(A) 1:2
(B) 1:5
(C) 1:3
(D) 1:1
(E) 1:7
(CoT). T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2


[User]
Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 70 * 2/35 = 16 sec
This justifies what answer for what question? Q & A:

[Assistant]
A train 70 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
(A) 4 sec
(B) 16 sec
(C) 6 sec
(D) 20 sec
(E) 8 sec
(A)


[User]
Reasoning: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 – 5x/100 = 144
2x/100 = 56 è x = 2800
Ans: (C)
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%?
Options:
(A) 2178
(B) 1087
(C) 2800
(D) 2689
(E) 2081

Rationale: Average Speed = Total distance/ Total time = (40 * 5 + 80 * 3)/(5 + 3) = 440/5 = 88
The answer: (B)
Question: Steve traveled the first 5 hours of his journey at 40 mph and the last 3 hours of his journey at 80 mph. What is his average speed of travel for the entire journey?
Options:
(A) 53.33 mph
(B) 88 mph
(C) 60 mph
(D) 64 mph
(E) 66.67 mph

Reasoning: 72nd/75th/83rd/85th/94th
Ans: (B)
Question: John's grade was 80th percentile of the 100 grades for his class. Of the 60 grades from another class, 20 were higher than John's, and the rest were lower. If no other grade was the same as John's grade, then John's grade was what percentile of the grades of the two classes of two classes combined?
Options:
(A) 72nd
(B) 75th
(C) 83rd
(D) 85th
(E) 94th

Rationale: 1 to 11 = 11 * 53 = 583
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 583 = 23
The answer: (B)
Question: The average of 11 results is 53, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
(A) A) 46
(B) B) 23
(C) C) 66
(D) D) 76
(E) E) 74

Reasoning: D = 1400+100 = 1500 m
S = 72 * 5/18 = 20
T = 1500 * 1/20 = 75 sec
Ans: (D)
Question: How long does a train 100 m long traveling at 72 kmph takes to cross a tunnel of 1400 m in length?
Options:
(A) 70 sec
(B) 60sec
(C) 82 sec
(D) 75 sec
(E) 62 sec

Reasoning: (1-(1/16))(1-(1/15))(1-(5/7)) of Income = 50
Hence income = 200
Ans: (B)

[Assistant]
Question: A person deposits 1/16 of his income as Provident Fund and 1/15 of the remaining as insurance premium. If he spends 5/7 of the balance on domestic needs and deposits an amount of Rs. 50 in the bank, his total income would be
Options:
(A) 150
(B) 200
(C) 250
(D) 300
(E) 350


[User]
Question: What amount does Kiran get if he invests Rs. 18000 at 15% p.a. simple interest for four years?
Options:
(A) 228777
(B) 26788
(C) 26088
(D) 28800
(E) 67881
Ans: (D)
CoT: Simple interest = (18000 * 4 * 15)/100 = Rs. 10800
Amount = P + I = 18000 + 10800 = Rs. 28800
----
Question: How much is 80% of 40 is greater than 4/5 of 25?
Options:
(A) 22
(B) 67
(C) 88
(D) 12
(E) 66
Ans: (D)
CoT: (80/100) * 40 – (4/5) * 25
32 - 20 = 12
----
Question: In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of:
Options:
(A) Rs. 3100
(B) Rs. 6240
(C) Rs. 6500
(D) Rs. 9600
(E) Rs. 8600
Ans: (B)

[Assistant]
CoT: To get Rs. 10, Investment is 96
To get Rs. 650, investment is (96/10)*650 = 6240
----


[User]
Rationale: 1 to 11 = 11 * 44 = 484
1 to 5 = 5 * 49 = 245
5 to 11 = 7 * 52 = 364
5th = 245 + 364 – 484 = 125
The answer: (A)
Question: The average of 11 results is 44, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result?
Options:
(A) 125
(B) 126
(C) 127
(D) 128
(E) 129

Reasoning: 6C1 + 6C2+ 6C3+6C4+6C5+6C6 = 63.
Ans: (E)
Question: Preethi has 6 flavors of ice cream in his parlor. How many options are there for Dorathy to pick a one-flavor, two-flavor, three-flavor, four-flavor, five flavor or six flavor order?
Options:
(A) 26
(B) 36
(C) 64
(D) 67
(E) 63

Rationale: 100*(80/100)*(90/100)*(75/100) = 54
100 - 54 = 46
The answer: (E)
Question: A single discount equivalent to the discount series of 20%, 10% and 25% is?
Options:
(A) 31.9
(B) 31.7
(C) 31.6
(D) 31.5
(E) 46

Reasoning: 1/2 * 20(9 + 6) = 150 cm2
Ans: (B)
Question: Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
Options:
(A) 120 sq m
(B) 150 sq m
(C) 110 sq m
(D) 300 sq m
(E) 330 sq m

Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. When four marbles are picked at random, then the probability that none is blue is = ¹²C₄/¹⁵C₄ = (12 * 11 * 10 * 9)/(15 * 14 * 13 * 12) = 33/91
The answer: (B)
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If four marbles are picked at random, what is the probability that none is blue?
Options:
(A) 17/91
(B) 33/91
(C) 51/91
(D) 65/91
(E) None of these

Rationale: Here, l = 7 and m = 28
Therefore, first number = l/m x 100% of second number = 7/28 x 100% of second number = 25% of second number
The answer: (B)

[Assistant]
Question: If the given two numbers are respectively 7% and 28% of a third number, then what percentage is the first of the second ?
Options:
(A) 20%
(B) 25%
(C) 18%
(D) 30%
(E) none of these


[User] Imagine a question and stream-of-consciousness explanation for which this is the answer: (D)

[Assistant]
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?
Options:
(A) 7 kmph
(B) 6 kmph
(C) 5 kmph
(D) 8 kmph
(E) 2 kmph
Stream-of-consciousness: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph


[User]
Given the following reasoning and answer, what was the question? All others have two vowels each
 The answer: (B)

[Assistant]
The question Four of the following five are alike in a certain way and so form a group. which one does not belong to that group?
Options:
(A) Tooth
(B) Chin
(C) Nose
(D) Eye
(E) Hand


[User] Imagine a question and stream-of-consciousness explanation for which this is the answer: (C)

[Assistant]
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
Options:
(A) 45%
(B) 49%
(C) 57%
(D) 59%
(E) 61%
Stream-of-consciousness: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%


[User]
Reasoning: |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.
Ans: (E)
Question: If n is an integer, then the least possible value of |35 - 6n| is?
Options:
(A) 2
(B) 3
(C) 5
(D) 0
(E) 1

Rationale: Number of ways of choosing 4 stocks = 8C4
Number of ways of ranking the chosen stocks = 4!
Hence total ways of chosing and ranking = 8C4 * 4! = 1680
The answer: (B)
Question: 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?
Options:
(A) 1200
(B) 1680
(C) 2102
(D) 4020
(E) 1840

Reasoning: 20/ (2 * 2) = 5 days
Ans: (C)
Question: Some persons can do a piece of work in 20 days. Two times the number of these people will do half of that work in?
Options:
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

Rationale: The integer should be divisible by: 12, 13, 14, 15 and 16, that is 3*2^2, 13, 2*7, 3*5 and 2^4. The least common multiple of these integers is the product of 13, 7, 5, 3 and 2^4. Then, R/13 is (13 * 7 * 5 * 3 * 2^4)/13 = 7*5*3*16 = 1680.
The answer: (C)
Question: If R is the least positive integer that is divisible by every integer from 12 to 16 inclusive, then R/13 is =
Options:
(A)  40320
(B)  21840
(C)  1680
(D)  840
(E)  240

Reasoning: Each crate requires 3 apples and totally there are 10 crates so required apples = 10 * 3 = 30
Ans: (A)
Question: If 10 crates have 97 apples each and how many apples more is required in order to make 100 apples in each crate?
Options:
(A) 30
(B) 10
(C) 15
(D) 20
(E) 0

Reasoning: In this addition series, 1 is added to the first number; 2 is added to the second number; 3 is added to the third number; 4 is added to the fourth number; and go on.
Ans: (A)

[Assistant]
Question: Look at this series: 201, 202, 204, 207, ... What number should come next?
Options:
(A) 211
(B) 205
(C) 224
(D) 267
(E) 269


[User]
Ques: 3 candidates in an election and received 6136, 7636 and 11628 votes respectively. What % of the total votes did the winning candidate got in that election?
Options:
(A) 46%
(B) 49%
(C) 57%
(D) 59%
(E) 61%
Ans: (A)
CoT: Total number of votes polled = (6136 + 7636 + 11628) = 25400
So, Required percentage = 11628/25400 * 100 = 46%

Ques: The average age of A, B and C is 28 years. If the average age of A and C is 29 years, what is the age of B in years ?
Options:
(A) 19
(B) 26
(C) 20
(D) 32
(E) 21
Ans: (B)
CoT: Age of B = Age of (A + B + C) â€“ Age of (A + C) = 28 Ã— 3 â€“ 29 Ã— 2 = 84 â€“ 58 = 26 years

Ques: How much 90% of 40 is greater than 80% of 30?
Options:
(A) 12
(B) 14
(C) 16
(D) 17
(E) 18
Ans: (A)
CoT: (90/100) * 40 – (80/100) * 30
36 - 24 = 12

Ques: A bus travels k miles in n hours. How many miles will it travel in x hours at the same rate?
Options:
(A) knx
(B) k⁄n
(C) x
(D) kx⁄n
(E) kn⁄x
Ans: (D)

[Assistant]
CoT: Given Speed = k/n
To Find distance in x hours with same speed
Distance = speed * time
Distance = k/n*x = kx/n


[User] Creatively image a question and justification for this answer: (B)

[Assistant]
The question is: The average of 11 results is 53, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
(A) A) 46
(B) B) 23
(C) C) 66
(D) D) 76
(E) E) 74
Step-by-step reasoning process: 1 to 11 = 11 * 53 = 583
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 583 = 23


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: Anything power 0 is always 1 and given that Y is even and negative, then
1 + (-2) will be negative with odd power values for Y.
 The question and answer:

[Assistant]
If x is a positive odd integer and y is a negative even integer, which of the following must be true?
Options:
(A) x^3 + y is a positive odd integer
(B) x^2 + y^2 is a negative odd integer
(C) x^0 + y^11 is a negative odd integer
(D) x + y is a positive odd integer
(E) x + y is a negative odd integer
The answer is (C)


[User]
Answer: (A)
Question: A plane flies 500 miles at a speed of r mph. If the plane flies at a speed of r + 250 miles per hour, it would fly the same distance in 1 hour less. What is the value of r?
Options:
(A) 250 mph
(B) 200 mph
(C) 205 mph
(D) 300 mph
(E) 425 mph
[CoT]: [Equation: 500/r = 500/(r+50) + 1
Plug options into the equation
A fits: 500/250 = 500/(250+250) + 1]

Answer: (B)
Question: A pipe can fill a cistern in 18 minutes whereas the cistern when fill can be emptied by a leak in 36 minutes. When both pipes are opened, find when the cistern will be full?
Options:
(A) 17
(B) 36
(C) 70
(D) 13
(E) 12
[CoT]: [1/18 - 1/36 = 1/36
36 minutes]

Answer: (B)
Question: In b is a positive integer smaller than 200 and (14b)/60 is an integer, then b has how many different positive prime factors?
Options:
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
[CoT]: [7b/30 tells us that b is a factor of 30, which has 2, 3, and 5 as its prime factors. Each of them is distinct. Moreover, all multiples of 30 less than 200 can be derived by multiplying these prime factors alone. Thus, number of different prime factors is 3.]

Answer: (C)
Question:

[Assistant]
A 600 meter long train crosses a signal post in 60 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Options:
(A) 4 min
(B) 2 min
(C) 6 min
(D) 9 min
(E) 5 min
[CoT]: [S = 600/60 = 10 mps
S = 3600/10 = 360 sec = 6 min]


[User]
Stream of consciousness rationale: {Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}
100 = 85 + 75 - {Both correctly} + 15
{Both correctly} = 75.
The question and answer pair are described below.

[Assistant]
Q: 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?
Options:
(A) 60 %
(B) 65 %
(C) 70%
(D) 75%
(E) 80%
A: (D)


[User]
[Ans] (D)
[Question] A can do a piece of work in 6 hours; B and C together can do it in 4 hours, which A and C together can do it in 3 hours. How long will B alone take to do it?
Options:
(A) 8hours
(B) 6hours
(C) 14hours
(D) 12hours
(E) 5hours
[CoT] A's 1 hour work = 1/6;
(B + C)'s 1 hour work = 1/4;
(A + C)'s 1 hour work = 1/3
(A + B + C)'s 1 hour work = (1/4 + 1/6) = 5/12
B's 1 hour work = (5/12 - 1/3) = 1/12
B alone will take 12 hours to do the work.

[Ans] (C)
[Question] The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
Options:
(A) 11
(B) 12
(C) 30
(D) 98
(E) 15
[CoT] 20 + 24 + 8 * 2 = 60/2 = 30

[Ans] (A)
[Question]

[Assistant]
The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
Options:
(A) 15
(B) 66
(C) 77
(D) 52
(E) 42
[CoT] 90 * 10/60 = 15 kmph


[User] Creatively image a question and justification for this answer: (A)

[Assistant]
The question is: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
Options:
(A) 39
(B) 88
(C) 3
(D) 7
(E) 62
Step-by-step reasoning process: Let the average after 7th inning = x
Then average after 16th inning = x - 3
\inline \fn_jvn \therefore 16(x-3)+87 = 17x
\inline \fn_jvn \therefore x = 87 - 48 = 39


[User]
Reasoning: The total of seven numbers = 7X20 = 140
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (140 - 99 ) = 41
Ans: (D)
Question: 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?
Options:
(A) 27
(B) 29
(C) 31
(D) 41
(E) 35

Rationale: 20 + 24 + 8 * 2 = 60/2 = 30
The answer: (C)
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
Options:
(A) 11
(B) 12
(C) 30
(D) 98
(E) 15

Reasoning: Work done by A in 2 days = 2/10 = 1/5
Remaining work = 4/5
Work done by both A and B in one day = 1/10 + 1/15 = 5/30 = 1/6
Remaining work = 4/5 * 6/1 = 24/5 = 4 4/5 days.
Ans: (C)
Question: A and B can do a work in 10 days and 15 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?
Options:
(A) 6 days
(B) 2 days
(C) 4 4/5 days
(D) 3 days
(E) 9 days

Rationale: 1/50 + 1/75 = 5/150
30/1 = 30 days
The answer: (A)
Question: Ravi can do a piece of work in 50 days while Prakash can do it in 75 days. In how many days will they finish it together?
Options:
(A) 30 days
(B) 35 days
(C) 25 days
(D) 27 days
(E) 29 days

Reasoning: In one week, Giri jogs 3 + 4 + 5 + 6 + 7 + 8 + 9 = 42 miles
In two weeks, Giri jogs 84 miles.
Ans: (C)
Question: Every Sunday, Giri jogs 3 miles. For the rest of the week, each day he jogs 1 mile more than the previous day. How many miles does giri jog in 2 weeks ?
Options:
(A) 42
(B) 63
(C) 84
(D) 98
(E) 108

Reasoning: Distance covered by the car = 80 × 10 = 800 km
\ Speed = 800⁄8 = 100 km/hr
\ Speed gain = 100 – 80 = 20 km/hr
Ans: (E)

[Assistant]
Question: A car finishes a journey in ten hours at the speed of 80 km/hr. If the same distance is to be covered in eight hours how much more speed does the car have to gain?
Options:
(A) 8 km/hr
(B) 10 km/hr
(C) 12 km/hr
(D) 16 km/hr
(E) None of these


[User]
Question: A train 510 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
(A) 40
(B) 52
(C) 26
(D) 21
(E) 14
Ans: (B)
CoT: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 510 + 140 = 650 m
Required time = 650 * 2/25 = 52 sec
----
Question: A man walks at a speed of 3 km/hr and runs at a speed of 6 km/hr. How much time will the man require to cover a distance of 12 km, if he completes half of the distance, i.e., (6) km on foot and the other half by running?
Options:
(A) 2.6
(B) 2.2
(C) 2.5
(D) 2
(E) 3
Ans: (E)
CoT: Required time = (6)/3 + (6)/6 = 3 hours.
----
Question: If 10 litres of an oil of Rs.54 per litres be mixed with 5 litres of another oil of Rs.66 per litre then what is the rate of mixed oil per litre?
Options:
(A) Rs.49.17
(B) Rs.58
(C) Rs.54.17
(D) Rs.55.33
(E) None of the above
Ans: (B)

[Assistant]
CoT: 54*10 = 540
66*5 = 330
870/15 = 58
----


[User]
Question: Last year, Company Z made q dollars in profit. Half of the profit went to the company’s founder. The rest was split evenly among his two other partners. In terms of q, how much did each of the other partners receive?
Options:
(A) q/4
(B) q/5
(C) q/6
(D) q/7
(E) q/8
Ans: (A)
CoT: Profit = q
Profit to company founder = q/2
Profit to other partners = q/2
Number of other partners = 2
Profit to each partner = (q/2)/2 = q/4
----
Question: On average, the bottle-nosed dolphin comes up for air once every three minutes; the beluga whale, a close relative, comes up for air on average once every six minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period?
Options:
(A) 25%
(B) 50%
(C) 75%
(D) 100%
(E) 150%
Ans: (E)
CoT: Dolphin once in 3 min;
Beluga once in 6 min;
So, dolphin comes up 2 times frequently than beluga, which is 150% (6-3)/2*100.
----
Question: A train 300 m long is running at a speed of 99 km/hr. In what time will it pass a bridge 195 m long?
Options:
(A) 17
(B) 18
(C) 19
(D) 20
(E) 21
Ans: (B)

[Assistant]
CoT: Speed = 99 * 5/18 = 55/2 m/sec
Total distance covered = 300 + 195 = 495 m
Required time = 495 * 2/55 = 18 sec
----


[User]
[Ques]: 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?
Options:
(A) 4500 M3
(B) 27000 M3
(C) 3000 M3
(D) 2700 M3
(E) 3700 M3
*Ans*: (A)
--CoT--: (3000 * 2 * 5)/60 = 4500 M3

[Ques]: 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?
Options:
(A) 22
(B) 77
(C) 26
(D) 41
(E) 66
*Ans*: (D)
--CoT--: (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
Remaining work = (1 - 7/48) = 41/48
Work done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48
Number of boys required = 41/48 * 41 = 41.

[Ques]: A man rows his boat 75 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
(A) 1 kmph
(B) 6 kmph
(C) 5 kmph
(D) 8 kmph
(E) 7 kmph
*Ans*: (B)
--CoT--: Speed downstream = d/t = 75/(2 1/2) = 30 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (30 - 18)/2 = 6 kmph

[Ques]: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 16. What is the middle number?
Options:
(A) 27
(B) 29
(C) 36
(D) 34
(E) 35
*Ans*: (C)

[Assistant]
--CoT--: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 16 = 90
So, the middle number is (126 - 90 ) = 36


[User] Come up with a question and reasoning that would justify this answer: (A)

[Assistant]
The question is: A man buys two articles for Rs.1980 each and he gains 10% on the first and loses 10% on the next. Find his total gain or loss percent?
Options:
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
Step-by-step reasoning process: (30*30)/100 = 9%loss


[User]
Reasoning: (x*3*1)/100 + [(4000 - x)*5*1]/100 = 144
3x/100 + 200 â€“ 5x/100 = 144
2x/100 = 56 Ã¨ x = 2800
Ans: (A)
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%?
Options:
(A) 2800
(B) 2500
(C) 3000
(D) 3500
(E) 4000

Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
The answer: (E)
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
Options:
(A) 3451
(B) 3467
(C) 3891
(D) 4601
(E) 5184

Reasoning: 5C1 * 4C1 * 3C1 = 5*4*3 = 60.
Ans: (C)
Question: An analyst will recommend a combination of 1 industrial stocks, 1 transportation stocks, and 1 utility stocks. If the analyst can choose from 5 industrial stocks, 4 transportation stocks, and 3 utility stocks, how many different combinations of 3 stocks are possible?
Options:
(A) 12
(B) 19
(C) 60
(D) 180
(E) 720

Rationale: (65/100) * 40 – (4/5) * 25
26 - 20 = 6
The answer: (E)
Question: How much is 65% of 40 is greater than 4/5 of 25?
Options:
(A) 29
(B) 776
(C) 66
(D) 12
(E) 6

Reasoning: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27
Ans: (A)
Question: 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?
Options:
(A) 27
(B) 30
(C) 31
(D) 33
(E) 34

Reasoning: 200/30 * 18/5 = 24 km/hr
Ans: (B)

[Assistant]
Question: A boy runs 200 metres in 30 seconds. What is his speed ?
Options:
(A) 20 km/hr
(B) 24 km/hr
(C) 30 km/hr
(D) 32 km/hr
(E) 34 km/hr


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1. x(2/75 + 1/45) + (30 - x). 2/75 = 1 11x/225 + (60 - 2x)/75 = 1 11x + 180 - 6x = 225. x = 9.
 The question and answer:

[Assistant]
Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
Options:
(A) 9 minutes
(B) 7
(C) 6
(D) 5
(E) 4
The answer is (A)


[User]
Question: There are 15 balls in a jar. You take out 3 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/3. How many blue balls were there in the beginning?
Options:
(A) 12.
(B) 9.
(C) 8.
(D) 7.
(E) 6.
Ans: (D)
CoT: 7 = 3 blue balls + 12 / 3
----
Question: 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?
Options:
(A) 40
(B) 32
(C) 26
(D) 21
(E) 14
Ans: (B)
CoT: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 260 + 140 = 400 m
Required time = 400 * 2/25 = 32 sec
----
Question: What percent is 120 of 90?
Options:
(A) 133 1/3 %
(B) 134 1/3 %
(C) 135 1/3 %
(D) 140 1/3 %
(E) 143 1/3 %
Ans: (A)

[Assistant]
CoT: 120/90 = 4/3
4/3 × 100 = 400/3 = 133 1/3 %
----


[User]
Ques: The average of five numbers is 9. The average of first two numbers is 7 and the average of last two numbers is 12. What is the middle number?
Options:
(A) 7
(B) 8
(C) 5
(D) 10
(E) 6
Ans: (A)
CoT: The total of five numbers = 5x9 = 45
The total of first 2 and last 2 numbers is = 2 X 7+2 X 12 = 38
So, the middle number is (45 - 38 ) = 7

Ques: One fourth of one third of two fifth of a number is 15. What will be the 40% of that number is?
Options:
(A) 120
(B) 130
(C) 150
(D) 180
(E) 250
Ans: (D)
CoT: (1/4) * (1/3) * (2/5) * x = 15 then x = 15 * 30 = 450
40% of 450 = 180

Ques: 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?
Options:
(A) 1,008
(B) 1,296
(C) 1,512
(D) 2*1008
(E) 2,268
Ans: (D)
CoT: Place D and H first: 8 options for D, 7 options for H
We 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
Total = 8*7*3!*3! = 2*1008

Ques: The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?
Options:
(A)  1/8
(B)  1/2
(C)  3/4
(D)  7/8
(E)  15/16
Ans: (D)

[Assistant] CoT: P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8.


[User]
What was the question for this implicit rationale, and corresponding answer?
? = 285 + 1895 – 655 – 645 or, ? = 880
 The answer: (C)

[Assistant]
The question: What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 657.48 = 643.095 + ?
Options:
(A) 870
(B) 790
(C) 880
(D) 770
(E) 890


[User]
Ques: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
(A) 118
(B) 150
(C) 277
(D) 258
(E) 191
Ans: (B)
CoT: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9 = 150 m

Ques: 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?
Options:
(A) 288
(B) 200
(C) 279
(D) 992
(E) 208
Ans: (D)
CoT: (800*3*3)/100 = 72
920 + 72 = 992

Ques: A car finishes a journey in nine hours at the speed of 80 km/hr. If the same distance is to be covered in six hours how much more speed does the car have to gain?
Options:
(A) 8 km/hr
(B) 40 km/hr
(C) 12 km/hr
(D) 16 km/hr
(E) None of these
Ans: (B)
CoT: Distance covered by the car = 80 × 9 = 720 km
\ Speed = 720⁄6 = 120 km/hr
\ Speed gain = 120 – 80 = 40 km/hr

Ques: An equity analyst needs to select 5 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 10, in how many ways can she choose and rank her top 5 picks?
Options:
(A) 21548
(B) 31502
(C) 21250
(D) 30240
(E) 84045
Ans: (D)

[Assistant]
CoT: Number of ways of choosing 5 stocks = 10C5
Number of ways of ranking the chosen stocks = 5!
Hence total ways of chosing and ranking = 10C5 * 5! = 30240


[User] Creatively image a question and justification for this answer: (B)

[Assistant]
The question is: What is the sum of all the prime numbers greater than 30 but less than 50?
Options:
(A) 126
(B) 199
(C) 198
(D) 188
(E) 122
Step-by-step reasoning process: Required sum = (31 + 37 + 41 + 43 + 47) = 199
Note: 1 is not a prime number


[User] Come up with a question and reasoning that would justify this answer: (C)

[Assistant]
The question is: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
Options:
(A) 45%
(B) 54%
(C) 57%
(D) 60%
(E) 65%
Step-by-step reasoning process: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%


[User]
Answer: (E)
Question: A 14 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
(A) 12
(B) 20
(C) 88
(D) 77
(E) 4
[CoT]: [1: 2/5 = 5: 2
2/7 * 14 = 4]

Answer: (E)
Question: 110 is increased by 50%. Find the final number.
Options:
(A) 100
(B) 110
(C) 150
(D) 155
(E) 165
[CoT]: [Final number = Initial number + 50%(original number) = 110 + 50%(110) = 110 + 55 = 165.]

Answer: (D)
Question: An analyst will recommend a combination of 2 industrial stocks, 2 transportation stocks, and 1 utility stocks. If the analyst can choose from 6 industrial stocks, 5 transportation stocks, and 3 utility stocks, how many different combinations of 5 stocks are possible?
Options:
(A) 12
(B) 460
(C) 60
(D) 450
(E) 720
[CoT]: [6C2 * 5C2 * 3C1 = 15*10*3 = 450.]

Answer: (B)
Question:

[Assistant]
The average of first 10 odd numbers is?
Options:
(A) 44
(B) 10
(C) 99
(D) 77
(E) 62
[CoT]: [Sum of 10 odd no. = 100
Average = 100/10 = 10]


[User]
Consider the question. If 20m − n = p, then which of the following represents the average (arithmetic mean) of m, n, and p, in terms of m?
Options:
(A) 2m −1
(B) 4m
(C) 6m
(D) 7m
(E) 6m/5
 What is the step-by-step reasoning process to arrive at the answer: (D)?

[Assistant]
20m - n = p
Add n to both sides:
20m = n + p
Add m to both sides:
21m = n + p + m
Now, divide both sides by 3
7m = (n + p + m)/3 = the average of n, p, and m


[User]
(Ans). (C)
(Question). 10 books are placed at random in a shelf. The probability that a pair of books will always be together is ?
Options:
(A) 1/8
(B) 1/4
(C) 1/5
(D) 1/9
(E) 1/1
(CoT). 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5

(Ans). (E)
(Question). If 10 crates have 94 apples each and how many apples more is required in order to make 100 apples in each crate?
Options:
(A) 5
(B) 10
(C) 15
(D) 20
(E) 60
(CoT). Each crate requires 6 apples and totally there are 10 crates so required apples = 10 * 6 = 60

(Ans). (B)
(Question). A man rows his boat 75 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
(A) 1 kmph
(B) 6 kmph
(C) 5 kmph
(D) 8 kmph
(E) 7 kmph
(CoT). Speed downstream = d/t = 75/(2 1/2) = 30 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (30 - 18)/2 = 6 kmph

(Ans). (E)
(Question).

[Assistant]
In how many different number of ways 7 men and 3 women can sit on a shopa which can accommodate persons?
Options:
(A) 200
(B) 230
(C) 240
(D) 250
(E) 5040
(CoT). 10p4 = 10 X 9 X 8 X 7 = 5040


[User] (12/170)/(4/50) = 15/17 = 88% it means that 12/170 represents only 88%. Therefore a decrease of 12%.is the reasoning for what question and answer pair?

[Assistant]
Q: A pharmaceutical company received $4 million in royalties on the first $50 million in sales of and then $12 million in royalties on the next $170 million in sales. By approximately what percentage did the ratio of royalties to sales decrease from the first $50 million in sales to the next $170 million in sales?
Options:
(A) 12%
(B) 15%
(C) 45%
(D) 52%
(E) 56%
A: (A)


[User]
## Solution
Answer = A. 20 miles
Relational speed = 110 - 100 = 10 miles per hour
In 6 hours, difference = 10 * 6 = 60 miles
Fast train trailing 40 miles, so effective difference = 60 - 40 = 20 miles
## What the question and answer could be
Two trains are traveling on parallel tracks in the same direction. The faster train travels at 110 miles per hour, while the slower train travels at 100 miles per hour. At 1 o’clock the faster train is 40 miles behind the slower one. How far apart are the two trains at 7 o'clock?
Options:
(A) 20 miles
(B) 80 miles
(C) 90 miles
(D) 120 miles
(E) 400 miles
(A)

## Solution
P(B|A) = P(A âˆª B)/P(A)
P(B|A) = (12/15)/(2/15) = 6.
## What the question and answer could be
If P(A) = 2/15, P(B) = 4/15, and P(A âˆª B) = 12/15 Find P(B|A)
Options:
(A) 1/2
(B) 2/3
(C) 3/2
(D) 4/5
(E) 6
(E)

## Solution
Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A ∩ B) = P(A) P(B)
The probability that the pitcher throws a strike at least once in 2 guesses is 1- (3/5)^2 = 1 - 9/25 = 16/25 > 50%.
## What the question and answer could be
During a particular baseball game, the probability of a team's pitcher throwing a strike on each throw is 2/5. What is the least number of times that the pitcher should pitch the ball that will increase the probability of getting a strike at least once to more than 50%.
Options:
(A) 3
(B) 2
(C) 1
(D) 4
(E) 5
(B)

## Solution
25/100*1/5*(total) = 10
1/20*(total) = 10
(total) = 10*20 = 200
## What the question and answer could be

[Assistant]
Twenty five percent of Country Y's yearly exports come from fruit exports. One-fifth of all fruit exports from Country Y are orange exports. If country Y generates $10 million from its orange exports, how much money does it generate from its yearly total of exports?
Options:
(A) $2125m
(B) $25m
(C) $200m
(D) $300m
(E) $153m
(C)


[User]
Rationale: A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 3 days = 3 (1/18) = 1/6.
The answer: (C)
Question: Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 3 days?
Options:
(A) 1/9
(B) 1/7
(C) 1/6
(D) 1/2
(E) 1/1

Reasoning: The total of nine numbers = 9X15 = 135
The total of first 4 and last 4 numbers is = 4 X 11+4 X 14 = 100
So, the middle number is (135 - 100 ) = 35
Ans: (C)
Question: The average of nine numbers is 15. The average of first four numbers is 11 and the average of last four numbers is 14. What is the middle number?
Options:
(A) 19
(B) 20
(C) 35
(D) 31
(E) 27

Rationale: Number of pages typed by Ronald in 1 hour = 32/6 = 16/3
Number of pages typed by Elan in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3
Time taken by both to type 110 pages = (110 * 3/40) = 8 1/4 = 8 hrs 15 min
The answer: (C)
Question: 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?
Options:
(A) 8 hrs 85 min
(B) 8 hrs 18 min
(C) 8 hrs 15 min
(D) 6 hrs 15 min
(E) 3 hrs 15 min

Reasoning: 560 = 2*2*2*2*7*5
Required smallest number = 7 * 5 = 35
35 is the smallest number which should be multiplied with 560 to make it a perfect squar
Ans: (E)
Question: Find the smallest number which should be multiplied with 560 to make it a perfect square.
Options:
(A) 60
(B) 55
(C) 45
(D) 25
(E) 35

Rationale: (30 * 30)/100 = 9% decrease
The answer: (D)
Question: The salary of a worker is first increased by 30% and afterwards reduced by 30%. What is net change in his salary?
Options:
(A) 90% increase
(B) 45% increase
(C) 9% decrease
(D) Same as before
(E) NONE

Rationale: 90 * 10/60 = 15 kmph
The answer: (A)

[Assistant]
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
Options:
(A) 15
(B) 66
(C) 77
(D) 52
(E) 42


[User]
Rationale: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 25 + 55 - {both} + 40
{both} = 20%.
The answer: (D)
Question: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 55% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
Options:
(A) 60%
(B) 50%
(C) 25%
(D) 20%
(E) 10%

Rationale: 100 * 10 * 10 = 10000
The answer: (C)
Question: In filling a room with gas 100 m * 10 m * 10 m the volumes of gas will be?
Options:
(A) 100 cu.m
(B) 1000 cu.m
(C) 10000 cu.m
(D) 100000 cu.m
(E) 10000000 cu.m

Rationale: P = (P*3*R)/100
R = 33 1/3%
The answer: (B)

[Assistant]
Question: In what time a sum of money double itself at 3% per annum simple interest?
Options:
(A) 33 1/7%
(B) 33 1/3%
(C) 33 1/2%
(D) 33 7/3%
(E) 33 5/3%


[User]
Reasoning: Total cost involved for each 75 $ shipment: 3+2 = 5 $. Thus, for two such orders = 10$
Total cost involved for a 150$ shipment: 3+3 = 6$. Thus, for two such orders = 12$
The difference = 2$.
Ans: (B)
Question: For every order, a certain mail-order company charges a shipping fee of $3 plus an additional $2 if the value of the order is over $50 but not over $100 or an additional $3 if the value of the order is over $100. How much greater are the total shipping fees for 2 orders of $75 each than the total shipping fee for 2 order of $150 ?
Options:
(A)  $1
(B)  $2
(C)  $3
(D)  $4
(E)  $5

Reasoning: (A + B) - (B + C) = 5000
A - C = 5000
Ans: (D)
Question: The total population of city A and city B is 5000 more than the total population of city B and city C. How much lesser is the population in city C as compared to city A?
Options:
(A) 8500
(B) 3500
(C) 4500
(D) 5000
(E) 1500

Reasoning: First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 10 positive even integers minus the sum of first 10 positive odd integers will be 10.
Ans: (A)
Question: If X is the sum of first 10 positive even integers and Y is the sum of first 10 positive odd integers, what is the value of x-y?
Please try to explain your answers
Options:
(A) 10
(B) 25
(C) 50
(D) 75
(E) 100

Reasoning: (80/100) * 40 – (10/100) * 15
32 - 15 = 17
Ans: (E)

[Assistant]
Question: How much 80% of 40 is greater than 10% of 15?
Options:
(A) 18
(B) 99
(C) 19
(D) 18
(E) 17


[User]
Question. A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 10 as remainder. Find the no. is?
Options:
(A) 220010
(B) 145778
(C) 220110
(D) 235467
(E) 220001
Answer. (A)
What step-by-step reasoning justifies that answer?

[Assistant] Reasoning: (555 + 445) * 2 * 110 + 10 = 220000 + 10 = 220010


[User] Come up with a question and reasoning that would justify this answer: (A)

[Assistant]
The question is: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was.
Options:
(A) 15000
(B) 2655
(C) 16888
(D) 6677
(E) 1871
Step-by-step reasoning process: Principal = Rs. (100 x 5400)/(12*3) = Rs. 15000.


[User]
[Ques]: Express 30 mps in kmph?
Options:
(A) 122
(B) 108
(C) 110
(D) 150
(E) 100
*Ans*: (B)
--CoT--: 30 * 18/5 = 108 kmph

[Ques]: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
Options:
(A) 4 min
(B) 6 min
(C) 8 min
(D) 2 min
(E) 9 min
*Ans*: (A)
--CoT--: S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min

[Ques]: The population of a bacteria colony doubles every day. If it was started 3 days ago with 3 bacteria and each bacteria lives for 12 days, how large is the colony today?
Options:
(A) 512
(B) 1024
(C) 768
(D) 2048
(E) 4096
*Ans*: (B)
--CoT--: 9 days ago- 2
8 days ago- 4
7 days ago- 8
6 days ago- 16
5 days ago- 32
4 days ago- 64
3 days ago- 128
2 days ago- 256
Yesterday- 512
Today- 1024

[Ques]: Adam sat with his friends in the Chinnaswamy stadium at Madurai to watch the 100 metres running race organized by the Asian athletics Association. Five rounds were run. After every round half the teams were eliminated. Finally, one team wins the game. How many teams participated in the race?
Options:
(A) 32
(B) 77
(C) 279
(D) 27
(E) 91
*Ans*: (A)

[Assistant] --CoT--: Total five rounds were run. So in the final round 2 teams must have participated. In the penultimate round 4 teams, and 3rd round 8, 2nd round 16 and in the first round 32 teams must have participated as in each round half of the teams got eliminated.


[User]
## Solution
Answer = D. 140 miles
Relational speed = 150 - 100 = 50 miles per hour
In 3 hours, difference = 50 * 3 = 150 miles
Fast train trailing 10 miles, so effective difference = 150 - 10 = 140 miles
## What the question and answer could be
Two trains are traveling on parallel tracks in the same direction. The faster train travels at 150 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 10 miles behind the slower one. How far apart are the two trains at 5 o'clock?
Options:
(A) 60 miles
(B) 80 miles
(C) 90 miles
(D) 140 miles
(E) 400 miles
(D)

## Solution
T = 160/32 = 5 h
T = 5 - 3 = 2
Time Ratio = 5:2
Speed Ratio = 2:5
## What the question and answer could be
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?
Options:
(A) 3:5
(B) 4:5
(C) 2:5
(D) 2:4
(E) 2:7
(C)

## Solution
550 = 2*222 + (22*4) + 9*2
K weight of 600 = 2 +4+9 = 15
## What the question and answer could be
K-numbers are positive integers with only 2's as their digits. For example, 2, 22, and 222 are K-numbers. The K-weight of a number n is the minimum number of K-numbers that must be added together to equal n. For example, the K-weight of 50 is 5, because 50 = 22 + 22 + 2 + 2 + 2. What is the K-weight of 550?
Options:
(A) 10
(B) 11
(C) 12
(D) 13
(E) 15
(E)

## Solution
D = 72 * 5/18 = 50 = 1000 â€“ 250 = 750m
## What the question and answer could be

[Assistant]
A train 250 m long running at 72 kmph crosses a platform in 50 sec. What is the length of the platform?
Options:
(A) 150m
(B) 200m
(C) 250m
(D) 750m
(E) 300 m
(D)


[User] Imagine a question and stream-of-consciousness explanation for which this is the answer: (A)

[Assistant]
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
Options:
(A) 150 meter
(B) 250 meter
(C) 200 meter
(D) 480 meter
(E) 153 meter
Stream-of-consciousness: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter


[User]
Q: There are different 15 circles. What is the number of the greatest possible points with which the circles intersect?
Options:
(A) 390
(B) 100
(C) 110
(D) 180
(E) 210
A: (E)
Explain how we arrive at this answer:

[Assistant] Explanation: Maximum points of intersection between n different circles = n*(n - 1) = 15*14 = 210


[User]
Given the stream of consciousness rationale, provide a reasonable question and answer. Rationale: Total number of letters = 8
Using these letters the number of 8 letters words formed is ⁸P₈ = 8!.
 The question and answer:

[Assistant]
Using all the letters of the word "THURSDAY", how many different words can be formed?
Options:
(A) 8
(B) 8!
(C) 7!
(D) 7
(E) 5
The answer is (B)


[User]
Question: What is the probability that Company R's advertisement will be one of the first two be shown during the first commercial break?
Options:
(A)  1/ 225
(B)  1 / 30
(C)  1 /15
(D)  2 / 15
(E)  4 /15
Ans: (D)
CoT: R 1/15 + (14/15) * 1/14 = 2/15
----
Question: There are 13person among whom 2are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1person sit between the brothers, is equal to?
Options:
(A) 4!*2!
(B) 7!*2!
(C) 6!*1!
(D) 10!*2!
(E) 5!*1!
Ans: (D)
CoT: Total number of ways = 10!*2!.
----
Question: K-numbers are positive integers with only 2's as their digits. For example, 2, 22, and 222 are K-numbers. The K-weight of a number n is the minimum number of K-numbers that must be added together to equal n. For example, the K-weight of 50 is 5, because 50 = 22 + 22 + 2 + 2 + 2. What is the K-weight of 750?
Options:
(A) 10
(B) 11
(C) 12
(D) 13
(E) 15
Ans: (E)

[Assistant]
CoT: 750 = 3*222 + (22*3) + 9*2
K weight of 600 = 3 +3+9 = 15
----


[User]
Ques: What will be the remainder when 17^200 is divided by 18
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Ans: (A)
CoT: 17^200 % 18
(17-18)^200 % 18
(-1)^200 % 18
1 % 18 = 1

Ques: What will come in place of the x in the following Number series? 8, 10, 14, 22, 38, x
Options:
(A) 66
(B) 68
(C) 70
(D) 72
(E) 74
Ans: (C)
CoT: 8
8 x 2 - 6 = 10
10 x 2 - 6 = 14
14 x 2 - 6 = 22
22 x 2 - 6 = 38
38 x 2 - 6 = 70

Ques: For some integer x, x^2 - 5 is divisible by all of the following EXCEPT
Options:
(A) 41
(B) 38
(C) 29
(D) 31
(E) 30
Ans: (E)
CoT: Hint: x^2-5 (x is an integer) is never multiple of 3 (try to prove this), hence 30 is out.

Ques: At what rate percent on simple interest will a sum of money double itself in 30 years?
Options:
(A) 3 1/3%
(B) 3 1/6%
(C) 3 1/5%
(D) 3 5/3%
(E) 7 1/3%
Ans: (A)

[Assistant]
CoT: P = (P*30*R)/100
R = 3 1/3%


[User]
Reasoning: Here both numbers are less than 100. So they are deficient of - 4 and - 1 compared with 100. So
Ans: (E)
Question: Find 96 ×× 98
Options:
(A) 93/198
(B) 93/12
(C) 93/13
(D) 93/10
(E) 93/8

Rationale: 8^10 = (2^3)^10 = 2^30
The answer: (E)
Question: What is the greatest positive integer x such that 2^x is a factor of 8^10?
Options:
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30

Reasoning: A prime factors are 3 and 11. 33<sqrt(99)? no
B prime factors are 2 and 7. 14<sqrt(98)? no
C prime number. its sqrt is never greater than itself
D A prime factors are 2 and 6. 6<sqrt(96)? yes
E prime factors are 5 and 19. 45<sqrt(95)? no
Ans: (D)
Question: A number is said to be prime saturated if the product of all the different positive prime factors of n is less than the square root of n. What is the greatest two digit prime saturated integer ?
Options:
(A) 99
(B) 98
(C) 97
(D) 96
(E) 95

Rationale: 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/7
15 women's 1 day work = (1/7 - 10/100) = 3/70
1 woman's 1 day work = 1/350
1 woman alone can complete the work in 350 days.
The answer: (E)
Question: 10 men and 15 women together can complete a work in 7 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?
Options:
(A) 127 days
(B) 667 days
(C) 177 days
(D) 187 days
(E) 350 days

Reasoning: D = 25 * 60 + 1000 = 2500 m
T = 2500/60 * 18/5 = 150 se
Ans: (C)
Question: A train of 25 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.0 km long?
Options:
(A) 2 mins 14 sec
(B) 2 mins 34 sec
(C) 150 sec
(D) 164 sec
(E) 2 mins 44 sec

Reasoning: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 25 + 55 - {both} + 40
{both} = 20%.
Ans: (D)

[Assistant]
Question: Walking across campus, a student interviewed a group of students. 25% of the students took a finance class last semester, 55% took a marketing class last semester, and 40% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
Options:
(A) 60%
(B) 50%
(C) 25%
(D) 20%
(E) 10%


[User]
Consider the question. In a particular year, the month of january had exactly 4 thursdays, and 4 sundays. On which day of the week did january 1st occur in the year.
Options:
(A) 33
(B) Monday
(C) 299
(D) 299
(E) 277
 What is the step-by-step reasoning process to arrive at the answer: (B)?

[Assistant] Ans: If a month has 31 days, and it starts with sunday, Then Sundays, Mondays, tuesdays are 5 for that month. If this month starts with monday, then mondays, tuesdays, and wednesdays are 5 and remaining days are 4 each. so this month start with Monday.


[User]
Probability that trouser is not grey = 2/3
Probability that shirt is not grey = 3/4
∴ Required probability = 2/3 x 3/4 = 1/2is the reasoning for what question and answer pair?

[Assistant]
Q: 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?
Options:
(A) 1/2
(B) 2/3
(C) 3/5
(D) 2/7
(E) 3/8
A: (A)


[User]
Question: If x is an even integer and y is an odd integer, which of the following is an even integer?
Options:
(A) x+y
(B) x+2y
(C) 3x+y
(D) x+y^2
(E) x+y+2
Ans: (B)
CoT: Plug in an even integer for x; in this case 2
Plug in an odd integer for y; in this case 1
2+1 = 3 Odd
2+(2*1) = 4 Even
(3*2)+1 = 6 + 1 = 7 Odd
2+(1^2) = 2 + 1 = 3 Odd
2+1+2 = 5 Odd
----
Question: A man rows his boat 120 km downstream and 92 km upstream, taking 4 hours each time. Find the speed of the stream?
Options:
(A) 6 kmph
(B) 4 kmph
(C) 2 kmph
(D) 8 kmph
(E) 1 kmph
Ans: (B)
CoT: Speed downstream = d/t = 120/(4) = 30 kmph
Speed upstream = d/t = 92/(4) = 23 kmph
The speed of the stream = (30 - 23)/2 = 4 kmph
----
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. Find the length of the train.
Options:
(A) 110 meter
(B) 120 meter
(C) 100 meter
(D) 90 meter
(E) 105 meter
Ans: (C)

[Assistant]
CoT: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 6 = 100 meter
----


[User]
Reasoning: Total number of persons in the committee = 5 + 6 = 11
Number of ways of selecting group of eight persons = ¹¹C₈ = ¹¹C₃ = (11 * 10 * 9)/(3 * 2) = 165 ways.
Ans: (A)
Question: A committee has 5 men and 6 women. What are the number of ways of selecting a group of eight persons?
Options:
(A) 165
(B) 185
(C) 205
(D) 225
(E) 245

Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 6 = 100 m
The answer: (E)
Question: A train running at the speed of 60 km/hr crosses a pole in 6 sec. What is the length of the train?
Options:
(A) 118
(B) 150
(C) 277
(D) 258
(E) 100

Reasoning: S = (90 + 60)/2 = 75 kmph
Ans: (B)
Question: The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
Options:
(A) 228
(B) 75
(C) 299
(D) 267
(E) 312

Rationale: Using the elimination method the option that fits this description is 26
6-2 = 4 (unit's digit that exceeds its ten's digit by 3)
26*8 = 208 (the product of the given number and the sum of its digits is equal to 175)
The answer: (D)
Question: Which of the options is a two-digit number, which has a unit's digit that exceeds its ten's digit by 4 and the product of the given number and the sum of its digits is equal to 208.
Options:
(A) 15
(B) 37
(C) 55
(D) 26
(E) 73

Reasoning: Assuming that the technician makes a round-trip of 40 miles (each way is 20 miles), then the technician would have completed 20 miles + 2 miles (10% of the remaining 20 miles). Therefore, the total is 22 miles. 22miles/40 miles is 55% of the entire trip.
Ans: (E)
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 10 percent of the drive from the center, what percent of the round-trip has the technician completed?
Options:
(A) 5%
(B) 10%
(C) 25%
(D) 40%
(E) 55%

Reasoning: Distance covered in first two hours = 10 Ã— 2 = 20 km
Distance covered in next two hours = 12 Ã— 2 = 24 km
Distance covered in next two hours = 14 Ã— 2 = 48 km
Distance covered in first six hours
20 + 24 + 48 = 92 km
Remaining distance = 8 km
92 + 8 = 100 km
Ans: (B)

[Assistant]
Question: A woman begins bicycling with a pace of 10 kmph and she increases her pace every two hours by 2 kmph. She rests from bicycling 2 hours after her pace reaches her maximum speed of 14 kmph. She does a cool-down for the final 8 km at a pace of 2 kmph. How far in km did she bicycle?
Options:
(A) 96 km
(B) 100 km
(C) 106 km
(D) 116 km
(E) 126 km


[User]
Rationale: Each crate requires 2 apples and totally there are 10 crates so required apples = 10 * 2 = 20
The answer: (D)
Question: If 10 crates have 98 apples each and how many apples more is required in order to make 100 apples in each crate?
Options:
(A) 5
(B) 10
(C) 15
(D) 20
(E) 0

Reasoning: Answer = A. 60 miles
Relational speed = 130 - 100 = 30 miles per hour
In 3 hours, difference = 30 * 3 = 90 miles
Fast train trailing 30 miles, so effective difference = 90 - 30 = 60 miles
Ans: (A)
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 130 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 30 miles behind the slower one. How far apart are the two trains at 5 o'clock?
Options:
(A) 60 miles
(B) 80 miles
(C) 90 miles
(D) 120 miles
(E) 400 miles

Rationale: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8.
The answer: (C)
Question: The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?
Options:
(A) 3
(B) 4
(C) 8
(D) 9
(E) 12

Reasoning: (A + B) - (B + C) = 5000
A - C = 5000
Ans: (D)
Question: The total population of city A and city B is 5000 more than the total population of city B and city C. How much lesser is the population in city C as compared to city A?
Options:
(A) 8500
(B) 3500
(C) 4500
(D) 5000
(E) 1500

Rationale: S = 400/16 * 18/5 = 90 kmph
The answer: (E)
Question: A train 400 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
Options:
(A) 22 kmph
(B) 77 kmph
(C) 54 kmph
(D) 71 kmph
(E) 90 kmph

Rationale: Volume of prism = Area of base * height = 1/2* (square root of 2) * (square root of 2)*3 = 3
The answer: (D)

[Assistant]
Question: Right triangle ABC is the base of the prism in the figure above. If AB=AC=√2 and the height of the prism is 3, what is the volume of the prism?
Options:
(A) 1
(B) 3/2
(C) 2
(D) 3
(E) 6


[User]
Average of the first 'n' natural numbers = (n + 1)/2
We get (9 + 1)/2 = 5
Find the average of the first 9 natural numbers?
Options:
(A) 8
(B) 5
(C) 10
(D) 11
(E) 12
(B)

1 minute’s work of both the punctures = (1⁄9 + 1⁄6) = 5⁄18
So, both the punctures will make the tyre flat in 18⁄5 = 33⁄5 min.
A tyre has two punctures. The first puncture along would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat?
Options:
(A) 1 1⁄2 minutes
(B) 3 1⁄2 minutes
(C) 3 3⁄5 minutes
(D) 4 1⁄4 minutes
(E) None of these
(C)

(1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2

[Assistant]
What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?
Options:
(A) 1
(B) 2
(C) 5
(D) 6
(E) 8
(B)


[User]
(Ans). (E)
(Question). A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
(A) 40
(B) 87
(C) 26
(D) 21
(E) 44
(CoT). Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 410 + 140 = 550 m
Required time = 550 * 2/25 = 44 sec

(Ans). (A)
(Question). A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train.
Options:
(A) 150 m
(B) 155 m
(C) 180 m
(D) 190 m
(E) 205 m
(CoT). Answer: Option A
Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (distance) = speed * Time
(50/3) * 9 = 150 meter

(Ans). (E)
(Question). The average age of A, B and C is 29 years. If the average age of A and C is 32 years, what is the age of B in years ?
Options:
(A) 19
(B) 35
(C) 20
(D) 32
(E) 23
(CoT). Age of B = Age of (A + B + C) â€“ Age of (A + C) = 29 Ã— 3 â€“ 32 Ã— 2 = 87 â€“ 64 = 23 years

(Ans). (E)
(Question).

[Assistant]
What is the maximum number of pieces of birthday cake of size 5” by 5” that can be cut from a cake 15” by 15”?
Options:
(A) 5
(B) 10
(C) 16
(D) 20
(E) 9
(CoT). The prompt is essentially asking for the maximum number of 5 x 5 squares that can be cut from a larger 15 by 15 square. Since each 'row' and each 'column' of the larger square can be sub-divided into 3 'pieces' each, we have (3)(3) = 9 total smaller squares (at maximum).


[User] Come up with a question and reasoning that would justify this answer: (D)

[Assistant]
The question is: In digging a grave 200 m * 100 m * 3 m the volumes of the dirt to be extracted will be?
Options:
(A) 600 cu.m
(B) 12000 cu.m
(C) 6000 cu.m
(D) 60000 cu.m
(E) 4000 cu.m
Step-by-step reasoning process: 200 * 100 * 3 = 60000


[User]
Number of students = 10
Number of ways 10 students can sit around a circular table = (10 - 1)! = 9!
Number of ways A and D sit together (consider A and D as one entity) = (9 - 1)! = 8! * 2
Number of ways A and D do not sit together = 9! - (8! * 2)
Probability = (9! - (8! * 2))/9! = 1 - 2/9 = 7/9
This justifies what answer for what question? Q & A:

[Assistant]
There are 10 students named alphabetically from A to J. What is the Probability that A and D do not sit together if all 10 sit around a circular table?
Options:
(A) 2/9
(B) 2/5
(C) 7/9
(D) 4/5
(E) 8/9
(C)


[User] Creatively image a question and justification for this answer: (E)

[Assistant]
The question is: 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?
Options:
(A) 1797787
(B) 1597723
(C) 159776
(D) 159728
(E) 157304
Step-by-step reasoning process: Population after n years = P [1 + (R/100)]2
Population after 2 years = 140000 * [1 + 6/100]2 = (160000 x 53/50 x 53/50) = 157304


[User]
Consider the question. 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?
Options:
(A) 226
(B) 992 rs
(C) 665
(D) 771
(E) 211
 What is the step-by-step reasoning process to arrive at the answer: (B)?

[Assistant]
(800*3*3)/100 = 72
920 + 72 = 992


[User] Come up with a question and stream of consciousness reasoning that would justify this answer: (D)

[Assistant]
The question is: How many seconds will a train 100 meters long take to cross a bridge 120 meters long if the speed of the train is 36 kmph?
Options:
(A) 54 sec
(B) 65 sec
(C) 25 sec
(D) 22 sec
(E) 24 sec
Stream of consciousness: D = 100 + 120 = 220
S = 36 * 5/18 = 10 mps
T = 220/10 = 22 sec


[User]
Explain simply why (B) is the correct answer to: 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?
Options:
(A) 22 1/8
(B) 22 1/2
(C) 22 1/1
(D) 22 1/5
(E) 22 1/9. Explanation:

[Assistant]
1/18 + 1/30 = 8/90 = 4/45
45/4 = 11 ¼ *2 = 22 1/2 days


[User]
Answer: (A)
Question: If P(A) = 6/17, P(B) = 5/17, and P(A ∪ B) = 4/17 Find P(B|A)?
Options:
(A) 2/3
(B) 3/5
(C) 2/7
(D) 3/7
(E) 4/9
[CoT]: [P(B|A) = P(A ∪ B)/P(A)
P(B|A) = (4/17)/(6/17) = 4/6 = 2/3.]

Answer: (B)
Question: What is the area of a square with perimeter 8P ?
Options:
(A)  16p^2
(B)  4P^2
(C)  P^2/4
(D)  P/16
(E)  P^2/16
[CoT]: [Each side is 2p
A = (2p)^2 = 4(p^2)]

Answer: (A)
Question: 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 ?
Options:
(A) 5
(B) 7
(C) 23
(D) 4
(E) 2
[CoT]: [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.]

Answer: (C)
Question:

[Assistant]
How much 50% of 56 is greater than 30% of 50?
Options:
(A) 18
(B) 99
(C) 13
(D) 55
(E) 71
[CoT]: [(50/100) * 56 – (30/100) * 50
28 - 15 = 13]


[User]
Explain simply why (A) is the correct answer to: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 1 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
Options:
(A) 40 gallons
(B) 100 gallons
(C) 120 gallons
(D) 180 gallons
(E) 130 gallons. Explanation:

[Assistant]
Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 1 gallons\
Volume of whole = 1 * 40 = 40 gallons.


[User]
Consider the question. There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one liter every hour in A, it gets filled up like 10, 20, 40, 80, 160 in tank B. (At the end of first hour, B has 10 liters, second hour it has 20, third hour it has 40 and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?
Options:
(A) 22
(B) 28
(C) 269
(D) 26
(E) 82
 If the answer is '(D)'; explain the reasoning:

[Assistant] The data related to the first tank A is not necessary. As you can see, the capacity that gets filled in the tank B after each hour is doubled. So If the tank is 1/32nd part is full after 21 hours, it is 1/16th part full after 22 hours, 1/8th part full after 23 hours, 1/4th part full after 24 hours, 1/2 full after 25 hours, completely full after 26 hours.


[User] Come up with a question and reasoning that would justify this answer: (B)

[Assistant]
The question is: Look at this series: 53, 53, 39, 39, 25, 25, ... What number should come next?
Options:
(A) A) 12
(B) B) 11
(C) C) 27
(D) D) 53
(E) E) 86
Step-by-step reasoning process: In this series, each number is repeated, then 14 is subtracted to arrive at the next number.


[User]
(Ans). (A)
(Question). Alice, Benjamin, and Carol each try independently to win a carnival game. If their individual probabilities for success are 1/5, 3/8, and 3/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
Options:
(A) 63/280
(B) 1/280
(C) 3/56
(D) 3/35
(E) 7/40
(CoT). P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 1/5*3/8*4/7 + 1/5*5/8*3/7 + 4/5*3/8*3/7 = 63/280.

(Ans). (D)
(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?
Options:
(A) 1 kmph
(B) 6 kmph
(C) 5 kmph
(D) 8 kmph
(E) 7 kmph
(CoT). Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph

(Ans). (A)
(Question). In how many different ways can the letters of the word â€˜EVERâ€™ be arranged?
Options:
(A) 12
(B) 280
(C) 300
(D) 310
(E) 360
(CoT). Number of ways = 4!/2! = 4X3X2X1/2X1 = 12

(Ans). (A)
(Question).

[Assistant]
A train running at the speed of 30 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
(A) 75
(B) 65
(C) 25
(D) 288
(E) 212
(CoT). Speed = 30*(5/18) m/sec = 25/3 m/sec
Length of Train (Distance) = Speed * Time
(25/3) * 9 = 75 meter


[User]
Given the following reasoning and answer, what was the question? 1/2 * 20(9 + 6) = 150 cm2
 The answer: (B)

[Assistant]
The question Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm?
Options:
(A) 328
(B) 150
(C) 279
(D) 277
(E) 267


[User] Come up with a question and reasoning that would justify this answer: (A)

[Assistant]
The question is: Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?
Options:
(A) 10
(B) 12
(C) 7
(D) 8
(E) 9
Step-by-step reasoning process: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.


[User]
Given the rationale, provide a reasonable question and answer. Step-by-step reasoning process: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
 The question and answer:

[Assistant]
If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
(A) 228
(B) 162
(C) 5528
(D) 256
(E) 191
The answer is (B)


[User]
Population after n years = P [1 + (R/100)]2
Population after 2 years = 110000 * [1 + 6/100]2 = (110000 x 53/50 x 53/50) = 123596
This justifies what answer for what question? Q & A:

[Assistant]
he population of a city is 110,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?
Options:
(A) 123596
(B) 1237723
(C) 123776
(D) 123728
(E) 123718
(A)


[User]
Rationale: 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: (C)
Question: 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%?
Options:
(A) 1
(B) 2
(C) 50
(D) 49
(E) 97

Reasoning: 142 + 110 = 252/14 = 18 (Remainder)
Ans: (C)
Question: A no.when divided by 142 gives a remainder 110, what remainder will be obtainedby dividingthe same no.14?
Options:
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20

Rationale: Let x be the other amount
\ 3x⁄10 + 3600 = 900 ⇒ x = 18000
\ total borrowed sum = 33000
The answer: (B)
Question: Anish borrowed 15000 at the rate of 12% and an other amount at the rate of 15% for two years. The total interest paid by him was 9000. How much did he borrow?
Options:
(A) 32,000
(B) 33,000
(C) 30,000
(D) 35,000
(E) None of these

Reasoning: Area of the outer rectangle = 22 Ã— 16 = 352 m2
Area of the inner rectangle = 18 Ã— 12 = 216 m2
Required area = (352 â€“ 216) = 136 m2
Ans: (C)
Question: The floor of a rectangular room is 18 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is :
Options:
(A) 124 m2
(B) 126 m2
(C) 136 m2
(D) 158 m2
(E) None of these

Rationale: S = (200 + 300)/45 = 500/45 * 18/5 = 40
The answer: (C)
Question: A train 200 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
Options:
(A) 32
(B) 28
(C) 40
(D) 27
(E) 21

Rationale: 46080 /12 = 3840
3840 /10 = 384
384 /8 = 48
The answer: (A)

[Assistant]
Question: What will come in place of the x in the following Number series? 46080, 3840, 384, x
Options:
(A) 48
(B) 3
(C) 4
(D) 5
(E) 6


[User] Imagine a question and stream-of-consciousness explanation for which this is the answer: (C)

[Assistant]
Question: A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
Options:
(A) 22
(B) 88
(C) 15
(D) 66
(E) 81
Stream-of-consciousness: B's 1 day work = (1/12 - 1/20) = 1/30
Now, (A + B)'s 1 day work = (1/20 + 1/60) = 1/15
So, A and B together will complete the work in 15 days.


[User]
Rationale: Rate of H = 7 acres/hr
Remaining land to be harvested = 100 - 30 = 70
Rate of H and K = 70/7 = 10 acres/hr
Rate of K = 10 - 7 = 3
The answer: (D)
Question: A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 30 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective constant rates, harvested the remaining acres of wheat in 7 hours. Harvesting machine K harvested how many acres of wheat per hour?
Options:
(A)  7
(B)  8
(C)  12
(D)  3
(E)  15

Reasoning: D = 130 + 150 = 280
S = 36 * 5/18 = 10 mps
T = 280/10 = 28 sec
Ans: (A)
Question: 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?
Options:
(A) 28 sec
(B) 23 sec
(C) 24 sec
(D) 25 sec
(E) 26 sec

Rationale: D = 80 * 5/18 = 22 = 488 – 200 = 288
The answer: (D)
Question: A train 200 m long running at 80 kmph crosses a platform in 22 sec. What is the length of the platform?
Options:
(A) 338
(B) 277
(C) 350
(D) 288
(E) 271

Reasoning: Other parts are equal to
2x2 + y2 – 3xy.
Ans: (B)
Question: Four of the following five parts numbered (a), (b), (c), (d) and (e) are exactly equal. The number of the part which is not equal to the other four parts is your answer.
Options:
(A) 2x2 – 3xy + y2
(B) (2x + y) (x – y)
(C) (x – y) 2 + x(x – y)
(D) (2x – y) 2 – x(2x – y)
(E) (2x – y) 2 – 2x2 + xy

Rationale: If the number is divisible by 9, it must also be divisible by 3. Only 7 yields such a number.
The answer: (D)
Question: The number N is 5,2H4, where H represents the ten's digit. If N is divisible by 9, what is the value of H?
Options:
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

Rationale: Six members can be selected from ten members in
10C6 = 10C4 ways.
The answer: (B)

[Assistant]
Question: in how many ways can six members be selected from a group of ten members?
Options:
(A) 10C6
(B) 10C4
(C) 10C9
(D) 10C2
(E) 10C1


[User] 3!4! Required probability = 3!4!/6! = 1/5is the reasoning for what question and answer pair?

[Assistant]
Q: If six persons sit in a row, then the probability that three particular persons are always together is -.
Options:
(A) 1/5
(B) 1/7
(C) 1/9
(D) 1/2
(E) 2/7
A: (A)


[User]
[Ques]: If 10 crates have 97 apples each and how many apples more is required in order to make 100 apples in each crate?
Options:
(A) 30
(B) 10
(C) 15
(D) 20
(E) 0
*Ans*: (A)
--CoT--: Each crate requires 3 apples and totally there are 10 crates so required apples = 10 * 3 = 30

[Ques]: The average of first 13 natural numbers is?
Options:
(A) 5.2
(B) 5.5
(C) 7
(D) 9
(E) 10
*Ans*: (C)
--CoT--: Sum of 13 natural no. = 182/2 = 91
Average = 91/13 = 7

[Ques]: If X is the sum of first 100 positive even integers and Y is the sum of first 100 positive odd integers, what is the value of x-y?
Please try to explain your answers
Options:
(A) 0
(B) 25
(C) 50
(D) 75
(E) 100
*Ans*: (E)
--CoT--: First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 100 positive even integers minus the sum of first 100 positive odd integers will be 100.

[Ques]: Which one of the following is not a prime number?
Options:
(A) 31
(B) 61
(C) 71
(D) 73
(E) 91
*Ans*: (D)

[Assistant] --CoT--: 91 is divisible by 7. So, it is not a prime number.


[User] Come up with a question and stream of consciousness reasoning that would justify this answer: (D)

[Assistant]
The question is: The length E of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
Options:
(A) Decreases by 19%
(B) Decreases by 25%
(C) Increases by 6%
(D) Increases by 19%
(E) Increases by 25%
Stream of consciousness: Let the length E of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence


[User]
Reconstruct a question, answer pair from this explanation: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 15 = 250 m

[Assistant]
Q:A train running at the speed of 60 km/hr crosses a pole in 15 sec. What is the length of the train?
Options:
(A) 120 m
(B) 190 m
(C) 115 m
(D) 110 m
(E) 250 m
A:(E)


[User]
[Ques]: A 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?
Options:
(A) 9 days
(B) 8 days
(C) 5 days
(D) 54 days
(E) 2 days
*Ans*: (B)
--CoT--: A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days

[Ques]: Rs. 5000 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/5:1/5:1/10?
Options:
(A) 1000
(B) 992
(C) 772
(D) 552
(E) 312
*Ans*: (A)
--CoT--: 1/5:1/5:1/10 = 2:2:1
1/5*5000 = 1000
2000-1000 = 1000

[Ques]: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
Options:
(A) 277
(B) 270
(C) 288
(D) 266
(E) 121
*Ans*: (B)
--CoT--: I = (500*9*6)/100 = 270

[Ques]: 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?
Options:
(A) 6
(B) 7
(C) 8
(D) 10
(E) 11
*Ans*: (D)

[Assistant] --CoT--: It's a simple geometry problem. Look at the diagram below:


[User]
For this chain-of-thought reasoning and answer, what was the question?
(1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
 A: (B)

[Assistant]
Q: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?
Options:
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5