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[
{
"content": "Two friends plan to walk along a 43-km trail, starting at opposite ends of the trail at the same time. If Friend P's rate is 15% faster than Friend Q's, how many kilometers will Friend P have walked when they pass each other?\n\n['A)21', 'B)21.5', 'C)22', 'D)22.5', 'E)23']",
"role": "user"
}... | aqua-rat |
[
{
"content": "In the coordinate plane, points (x, 1) and (5, y) are on line k. If line k passes through the origin and has slope 1/5, then what are the values of x and y respectively?\n\n['A)4 and 1', 'B)1 and 5', 'C)5 and 1', 'D)3 and 5', 'E)5 and 3']",
"role": "user"
},
{
"content": "Line k passes... | aqua-rat |
[
{
"content": "For all numbers p and q, the operation @ is defined by p@q = p^2 - pq. If xy ≠ 0, then which of the following can be equal to zero?\nI. x@y\nII. (xy)@y\nIII. x@(x + y)\n\n['A)II', 'B)I and II', 'C)I and III', 'D)II and III', 'E)All of the above']",
"role": "user"
},
{
"content": "p@q =... | aqua-rat |
[
{
"content": "Carl is facing very difficult financial times and can only pay the interest on a $10,000 loan he has taken. The bank charges him a quarterly compound rate of 4%. What is the approximate interest he pays annually?\n\n['A)$1600', 'B)$2000', 'C)$2150', 'D)$2500', 'E)$12000']",
"role": "user"
},... | aqua-rat |
[
{
"content": "The speed at which a man can row a boat in still water is 25 kmph. If he rows downstream, where the speed of current is 11 kmph, what time will he take to cover 80 metres?\n\n['A)18 seconds', 'B)27 seconds', 'C)26 seconds', 'D)12 seconds', 'E)8 seconds']",
"role": "user"
},
{
"content"... | aqua-rat |
[
{
"content": "There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 6 possible combinations in which Jim and Ellen are not selected, what is the value of k?\n\n['A)8', 'B)9', 'C)10', 'D)11', 'E)12']",
"role": "user... | aqua-rat |
[
{
"content": "If (x^2 + 4x - 11)/5 ≤ x + 1, then x could be represented by which of the following?\n\n['A)− 3 ≤ x ≤ 4', 'B)− 4 ≤ x ≤ 3', 'C)− 3 ≤ x ≤ 3', 'D)− 4 ≤ x ≤ − 3', 'E)3 ≤ x ≤ 4']",
"role": "user"
},
{
"content": "IMO A is correct answer\nsolving through eqautions\nx^2 +4x-11<= 5x+5\n(x+3)(x... | aqua-rat |
[
{
"content": "Find the smallest number of five digits exactly divisible by 22,33,66 and 44.\n\n['A)10101', 'B)11000', 'C)10110', 'D)10111', 'E)10100']",
"role": "user"
},
{
"content": "Smallest number of five digits is 10000.\nRequired number must be divisible by L.C.M. of 22,33,66,44 i.e 132,\nOn d... | aqua-rat |
[
{
"content": "The entrance fee for a fair is $5 for persons under the age of 18, and 20% more for persons older. Each ride at the fair costs $0.50. If Joe goes with her 6 years old twin brothers, and they each took 3 rides in total. How much money does Joe end up spending at the fair?\n\n['A)16', 'B)20.5', 'C)1... | aqua-rat |
[
{
"content": "If X and Y are digits and 8XY is a 3-digit number that is divisible by 2, which of the following is a possible product of X and Y?\n\n['A)15', 'B)31', 'C)12', 'D)27', 'E)91']",
"role": "user"
},
{
"content": "Key to this question is to remember the fact that a number divisible by 2 mus... | aqua-rat |
[
{
"content": "If Tim had lunch at $50 and he gave 20% tip, how much did he spend?\n\n['A)A)$60.00', 'B)B)$35.42', 'C)C)$60.60', 'D)D)$21.56', 'E)E)$78.45']",
"role": "user"
},
{
"content": "The tip is 20% of what he paid for lunch.\ntip = 20% of 50.00 = (20/100)*50.00 = = $10.00\nTotal spent\n50.00 ... | aqua-rat |
[
{
"content": "Rs. 825 becomes Rs. 956 in 3 years at a certain rate of simple interest.If the rate of interest is increased by 4% ,What amount will Rs. 825 become in 3 years ?\n\n['A)Rs. 1020.80', 'B)Rs. 1025', 'C)Rs. 1055', 'D)Data inadequate', 'E)None of these']",
"role": "user"
},
{
"content": "So... | aqua-rat |
[
{
"content": "q is a positive integer and multiple of 2; p = 4^q, what is the remainder when p is divided by 10?\n\n['A)10', 'B)6', 'C)4', 'D)0', 'E)It Cannot Be Determined']",
"role": "user"
},
{
"content": "It is essential to recognize that the remainder when an integer is divided by 10 is simply ... | aqua-rat |
[
{
"content": "If q is the square of a positive integer, which of the following must be equal to the square of the next positive integer?\n\n['A)√n + 1', 'B)n + 1', 'C)n^2 + 1', 'D)q + 2√q + 1', 'E)n^2 + 2n + 1']",
"role": "user"
},
{
"content": "If q is the square of a positive integer, which of the... | aqua-rat |
[
{
"content": "Rs. 5600 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/7:1/7:1/14?\n\n['A)300', 'B)992', 'C)1120', 'D)552', 'E)312']",
"role": "user"
},
{
"content": "1/7:1/7:1/14 = 2:2:1\n1/5*5600 = 1120\n2240-1120 = 1120\nAnswer: C",
"role": "assistant"
... | aqua-rat |
[
{
"content": "If a/b=3/4 and 8a+5b=22,then find the value of a.\n\n['A)1/2', 'B)3/2', 'C)5/2', 'D)4/2', 'E)7/2']",
"role": "user"
},
{
"content": "(a/b)=3/4 b=(4/3) a.\nTherefore, 8a+5b=22 = 8a+5*(4/3) a=22 8a+(20/3) a=22\n=44a = 66 = a=(66/44)=3/2\nAnswer is B.",
"role": "assistant"
}
] | aqua-rat |
[
{
"content": "Given that k/l < 1, and both k and l are positive integers, which one of the following must be greater than 1?\n\n['A)k/l^2', 'B)k^2/l', 'C)k^2/l^2', 'D)l/k', 'E)√(k/l)']",
"role": "user"
},
{
"content": "Since k/l is a fraction l must always be > 1\nGiven -\nWhich one of the following... | aqua-rat |
[
{
"content": "Mike took 5 mock tests before appearing for the GMAT. In each mock test he scored 10 points more than the previous mock test. If he scored 760 on the GMAT and his average score for the mocks and the GMAT was 716.67, what was the difference in the score of his last mock and his GMAT score?\n\n['A)2... | aqua-rat |
[
{
"content": "John found that the average of 15 numbers is 40. If 10 is added to each number then the mean of number is?\n\n['A)50', 'B)45', 'C)65', 'D)78', 'E)64']",
"role": "user"
},
{
"content": "(x+x1+...x14)/15 = 40\n50\nOption A",
"role": "assistant"
}
] | aqua-rat |
[
{
"content": "A person is traveling at 20 km/hr and reached his destiny in 2.5 hr then find the distance?\n\n['A)53 km', 'B)55 km', 'C)52 km', 'D)60 km', 'E)50 km']",
"role": "user"
},
{
"content": "T = 2.5 hrs = 5/2 hrs\nD= T*S = 20*5/2 = 50 km\nAnswer is E",
"role": "assistant"
}
] | aqua-rat |
[
{
"content": "The first five numbers in a regular sequence are 4, 10, X, 46, and 94. What is x ?\n\n['A)28', 'B)26', 'C)30', 'D)22', 'E)24']",
"role": "user"
},
{
"content": "it is a good Q to learn to pick up number properties in the given set, even if we do not get a Q on these line in actuals..\n... | aqua-rat |
[
{
"content": "Tim has 350 pounds of cement in 100, 50, and 25 pound bags. He has an equal number of each size bag. How many bags of cement does Tim have?\n\n['A)2', 'B)4', 'C)6', 'D)8', 'E)10']",
"role": "user"
},
{
"content": "Let the number of each sized bag = c\r100c + 50c + 25c = 350\r175c = 350... | aqua-rat |
[
{
"content": "What is the least value of x, So that 2x5475 is divisible by 9\n\n['A)7', 'B)8', 'C)4', 'D)3', 'E)2']",
"role": "user"
},
{
"content": "Explanation:\nThe sum of the digits of the number is divisible by 9.\nThen the number is divisible by 9.\n2 + x + 5 + 4 + 7 + 5 = 23 + x\nLeast value ... | aqua-rat |
[
{
"content": "Square P is inscribed in circle Q. If the perimeter of P is 40, what is the circumference of Q?\n\n['A)11√ 2π', 'B)10√ 2π', 'C)9√ 2π', 'D)8√ 2π', 'E)7√ 2π']",
"role": "user"
},
{
"content": "square forms two right angled triangles.\nAny time we have a right angle triangle inside a circ... | aqua-rat |
[
{
"content": "A debtor reached an agreement with his creditor to repay a loan by making a monthly payment which is double of the amount she paid the previous month. If the debtors first payment was $200, and he is expected to pay back 51200, how many months will it take to fully repay the loan?\n\n['A)9', 'B)10... | aqua-rat |
[
{
"content": "As a bicycle salesperson, James earns a fixed salary of $30 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week.... | aqua-rat |
[
{
"content": "A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio Q of students per class?\n\n['A)Q=3', 'B)Q=4', 'C)6', 'D)8', 'E)12']",
"role": "... | aqua-rat |
[
{
"content": "A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $95,000, what is the average income of the other 40 customers?\nIs there a way to solve this using weighted... | aqua-rat |
[
{
"content": "The slant height of a cone is 35 cm and radius of the base is 14cm, find the curved surface of the cone.\n\n['A)4150', 'B)1780', 'C)1540', 'D)1500', 'E)6100']",
"role": "user"
},
{
"content": "π * 14 * 35= 1540\nAnswer:C",
"role": "assistant"
}
] | aqua-rat |
[
{
"content": "A cheese factory sells its cheese in rectangular blocks. A normal block has a volume of 8 cubic feet. If a small block has half the width, half the depth, and half the length of a normal block, what is the volume of cheese in a small block in cubic feet?\n\n['A)1', 'B)5', 'C)4', 'D)6', 'E)2']",
... | aqua-rat |
[
{
"content": "In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 20 feet between each tree. How many trees can be planted if the road is 148 feet long?\n\n['A)8', 'B)9', 'C)10', 'D)11', 'E)16']",... | aqua-rat |
[
{
"content": "What will be the difference in simple and compound interest on 2000 after three years at the rate of 10 percent per annum?\n\n['A)160', 'B)42', 'C)62', 'D)20', 'E)None of these']",
"role": "user"
},
{
"content": "For 3 years:\nDiff.=Sum×(rate)2(300+rate)/(100)3\n= 2000×10×10×310/100×10... | aqua-rat |
[
{
"content": "A $500 investment and a $1,500 investment have a combined yearly return of 19 percent of the total of the two investments. If the $500 investment has a yearly return of 7 percent, what percent yearly return does the $1,500 investment have?\n\n['A)9%', 'B)10%', 'C)23%', 'D)21%', 'E)22%']",
"rol... | aqua-rat |
[
{
"content": "Find the constant k so that : -x2 - (k + 11)x - 8 = -(x - 2)(x - 4)\n\n['A)11', 'B)12', 'C)17', 'D)14', 'E)15']",
"role": "user"
},
{
"content": "-x2 - (k + 11)x - 8 = -(x - 2)(x - 4) : given\n-x2 - (k + 11)x - 8 = -x2 + 6x - 8\n-(k + 11) = 6 : two polynomials are equal if their corres... | aqua-rat |
[
{
"content": "A positive whole number has factors of 3 and 5. The number MUST be divisible by: I. 15 II. 30 III. 60\n\n['A)I & II', 'B)III', 'C)I & III', 'D)II & III', 'E)II']",
"role": "user"
},
{
"content": "15 , 30 is not divisible by 60.But 60 is divisible by 3,5,15,30\nSo answer is III\nAnswer ... | aqua-rat |
[
{
"content": "Krishan and Nandan jointly started a business. Krishan invested six times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 6000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?\n\n[... | aqua-rat |
[
{
"content": "There are 8 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?\n\n['A)10', 'B)30', 'C)28', 'D)60', 'E)90']",
"role": "user"
},
{
"content": "10 players are there.\ntwo players play... | aqua-rat |
[
{
"content": "A pipe takes a hours to fill the tank. But because of a leakage it took 2 times of its original time. Find the time taken by the leakage to empty the tank\n\n['A)50 min', 'B)60 min', 'C)90 min', 'D)80 min', 'E)120 min']",
"role": "user"
},
{
"content": "pipe a can do a work 60 min.\nle... | aqua-rat |
[
{
"content": "Today is 22 days before Mariah's graduation. If she graduates on a Friday, what day of the week is it today?\n\n['A)Monday', 'B)Friday', 'C)Tuesday', 'D)Thursday', 'E)Sunday']",
"role": "user"
},
{
"content": "Each weekday is repeated every 7 days. 22 divided by 7 is 3, with a remainde... | aqua-rat |
[
{
"content": "Suppose a, b, and c are positive integers with a < b < c such that\n1/a\n+\n1/b\n+\n1/c\n= 1. What is\na + b + c?\n\n['A)1', 'B)4', 'C)9', 'D)11', 'E)no such integers exist']",
"role": "user"
},
{
"content": "First note that we must have 1/a < 1, so a > 1. Since 1/a > 1/b > 1/c, we\nmu... | aqua-rat |
[
{
"content": "The age of man is three times the sum of the ages of his two sons.Four years hence,his age will be double of the sum of the ages of his sons.The father’s present age is :\n\n['A)36 years', 'B)45 years', 'C)50 years', 'D)55 years', 'E)75 years']",
"role": "user"
},
{
"content": "Solut... | aqua-rat |
[
{
"content": "A bottle of coke contains 200gm in place of 1kg of fluid. Find the actual % difference, given a 10% gain on initial fluid?\n\n['A)32.5%', 'B)112.5%', 'C)35%', 'D)40%', 'E)50%']",
"role": "user"
},
{
"content": "fluid price of 200gm = 100+10 = 110\nDifference = 110-20 = 90\n% of differe... | aqua-rat |
[
{
"content": "A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 64 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?\n\n['A)20', 'B)30', 'C)48', 'D)64', 'E)72']",
"role": "user"
},
{
"content... | aqua-rat |
[
{
"content": "5358 x 51 = ?\n\n['A)273258', 'B)273268', 'C)273348', 'D)273358', 'E)None of these']",
"role": "user"
},
{
"content": "Explanation:\n5358 x 51\t= 5358 x (50 + 1)\n= 5358 x 50 + 5358 x 1\n= 267900 + 5358\n= 273258.\nANSWER IS A",
"role": "assistant"
}
] | aqua-rat |
[
{
"content": "3 persons (1 couple and 1 single) are seated at random in a row of 5 chairs. What is the probability that the couple does not sit together?\n\n['A)5/7', 'B)4/5', 'C)2/5', 'D)3/5', 'E)11/8']",
"role": "user"
},
{
"content": "Let's find the probability that a couple sits together (right ... | aqua-rat |
[
{
"content": "In a recent survey at a local deli, it was observed that 3 out of 5 customers bought a bagel and 5 out of 7 customers bought a coffee. Some customers bought both. If 8 customers are selected, what are the chances that at least 1 customer bought a coffee and a bagel?\n\n['A)27/343', 'B)3/7', 'C)27/... | aqua-rat |
[
{
"content": "|x+3| – |4-x| = |8+x| How many S solutions will this equation have?\n\n['A)0', 'B)1', 'C)2', 'D)3', 'E)4']",
"role": "user"
},
{
"content": "|x| = x when x >= 0 (x is either positive or 0)\n|x| = -x when x < 0 (note here that you can put the equal to sign here as well x <= 0 because if... | aqua-rat |
[
{
"content": "The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 20%. By approximately what percent would the output now have to be decreased in order to restore the original output?\n\n['A)20%', 'B)24%', 'C)30%', 'D)32%', 'E)... | aqua-rat |
[
{
"content": "In a graduate physics course, 70 percent of the students are male and 30 percent of the students are married. If two-sevenths of the male students are married, what fraction of the male students is single?\n\n['A)2/7', 'B)1/3', 'C)1/2', 'D)2/3', 'E)5/7']",
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{
"content"... | aqua-rat |
[
{
"content": "The cost of painting the whole surface area of a cube at the rate of 13 paise per Sq.cm is Rs. 343.98. Then the volume of the cube is\n\n['A)8500 cm3', 'B)9000 cm3', 'C)9250 cm3', 'D)9261 cm3', 'E)None']",
"role": "user"
},
{
"content": "Solution\nSurface area\t= (34398 / 13)\n‹=›2646c... | aqua-rat |
[
{
"content": "A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $50 to incur a loss 20%?\n\n['A)25', 'B)36', 'C)40', 'D)50', 'E)48']",
"role": "user"
},
{
"content": "Production cost per article: $60*(100%-20%) / 20 = $2.40\nRequired production costs for a loss of 2... | aqua-rat |
[
{
"content": "A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio:\n\n['A)3:5', 'B)2:1', 'C)16:15', 'D)4:5', 'E)None of these']",
"role": "user"
},
{
"content": "Explanation:\nFor an income of Re... | aqua-rat |
[
{
"content": "A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?\n\n['A)Rs. 45', 'B)Rs. 50', 'C)Rs. 55', 'D)Rs. 60', 'E)Rs. 65']",
"role": "user"
},
... | aqua-rat |
[
{
"content": "A train 500 m long can cross an electric pole in 20 sec and then find the speed of the train?\n\n['A)95 Kmph', 'B)90 Kmph', 'C)92 Kmph', 'D)95 Kmph', 'E)98 Kmph']",
"role": "user"
},
{
"content": "Length = Speed * time\nSpeed = L/T\nS = 500/20\nS = 25 M/Sec\nSpeed= 25*18/5 (To convert ... | aqua-rat |
[
{
"content": "The smallest number when increased by \" 1 \" is exactly divisible by 6,9,15,35,45 is:\n\n['A)631', 'B)630', 'C)359', 'D)629', 'E)600']",
"role": "user"
},
{
"content": "LCM = 630\n630 - 1 = 629\nANSWER:D",
"role": "assistant"
}
] | aqua-rat |
[
{
"content": "How many keystrokes are needed to type the numbers from 1 to 500?\n\n['A)1156', 'B)1392', 'C)1480', 'D)1562', 'E)1788']",
"role": "user"
},
{
"content": "There are 9 one-digit numbers from 1 to 9.\nThere are 90 two-digit numbers from 10 to 99.\nThere are 401 three-digit numbers from 10... | aqua-rat |
[
{
"content": "In a two-digit number, the digit in the unit's place is four times the digit in ten's place and the sum of the digits is equal to 10. What is the number?\n\n['A)82', 'B)41', 'C)14', 'D)56', 'E)28']",
"role": "user"
},
{
"content": "Let the ten's digit be x. then, unit's digit = 4x\nthe... | aqua-rat |
[
{
"content": "The edge of a cube is 7a cm. Find its surface?\n\n['A)24a8', 'B)24a4', 'C)24a1', 'D)24a2', 'E)294a2']",
"role": "user"
},
{
"content": "6a2 = 6 * 7a * 7a = 294a2\nAnswer:E",
"role": "assistant"
}
] | aqua-rat |
[
{
"content": "A shop sells chocolates It is used to sell chocolates for Rs.2 each but there were no sales at that price.When it reduced the price all the chocolates sold out enabling the shopkeeper to realize Rs 164.90 from the chocolates alone If the new price was not less than half the original price quoted H... | aqua-rat |
[
{
"content": "A board 7ft. 9 inches long is divided into 3 equal parts . What is the length of each part?\n\n['A)31 inches', 'B)32 inches', 'C)33 inches', 'D)34 inches', 'E)35 inches']",
"role": "user"
},
{
"content": "7 ft 9 in is 84 + 9 = 93 inches. so 93/3 = 31 inches or 2 ft. 7 inch.\nANSWER:A",... | aqua-rat |
[
{
"content": "Find the number of zeroes in the expression 15*32*25*22*40*75*98*112*125\n\n['A)12', 'B)9', 'C)14', 'D)7', 'E)6']",
"role": "user"
},
{
"content": "(3*5)*(2*2*2*2*2)*(5*5)*(2*11)*(2*2*2*2*5)*(5*5*3)*(2*7*7)*(2*2*2*2*7)*(5*5*5)\nthere are 9 (5*2) pairs which gives zero\nso.no of zeros 9... | aqua-rat |
[
{
"content": "The diagonals of a rhombus are 18 cm and 22 cm. Find its area?\n\n['A)277', 'B)266', 'C)198', 'D)288', 'E)212']",
"role": "user"
},
{
"content": "1/2 * 18 * 22 = 198\nAnswer: C",
"role": "assistant"
}
] | aqua-rat |
[
{
"content": "If rupee one produces rupees nine over a period of 40 years, find the rate of simple interest?\n\n['A)22 1/8 %', 'B)22 3/2 %', 'C)28 1/2 %', 'D)22 1/2 %', 'E)32 1/2 %']",
"role": "user"
},
{
"content": "9 = (1*40*R)/100\nR = 22 1/2 %\nAnswer:D",
"role": "assistant"
}
] | aqua-rat |
[
{
"content": "A and B invests Rs.6000 and Rs.12000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?\n\n['A)32:99', 'B)8:21', 'C)32:45', 'D)34:89', 'E)35:21']",
"role": ... | aqua-rat |
[
{
"content": "A train covers a distance of 10km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?\n\n['A)m', 'B)m', 'C)m', 'D)m', 'E)m']",
"role": "user"
},
{
"content": "Speed = (10/10 * 60) km/hr\n= (60 * 5/18) m/sec = 50/3 m/sec.\nLength of the train = 50/3 *... | aqua-rat |
[
{
"content": "The rental charge for a car is 34 cents for the first 1/4 mile driven and 6 cents for every 1/5 mile driven over the initial 1/4 mile. If a man paid $1.24 in rental charges, how many miles did he drive?\n\n['A)2.5', 'B)3.0', 'C)3.25', 'D)3.75', 'E)4.0']",
"role": "user"
},
{
"content":... | aqua-rat |
[
{
"content": "A question paper consists of three sections 4,5 and 6 questions respectively. Attempting one question from each section is compulsory but a candidate need not attempt all the questions. In how many ways can a candidate attempt the questions?\n\n['A)209', 'B)(4!-1)*(5!-1)*(6!-1)', 'C)119', 'D)29295... | aqua-rat |
[
{
"content": "10 women can complete a work in 9 days and 10 children take 12 days to complete the work. How many days will 6 women and 7 children take to complete the work?\n\n['A)4', 'B)5', 'C)7', 'D)8', 'E)2']",
"role": "user"
},
{
"content": "1 women's 1 day work = 1/90\n1 child's 1 day work = 1/... | aqua-rat |
[
{
"content": "Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 54. Find the third number?\n\n['A)A)37', 'B)B)85', 'C)C)48', 'D)D)43', 'E)E)54']",
"role": "user"
},
{
"content": "Let the numbers be 5x, 6x, 7x.\nLargest number... | aqua-rat |
[
{
"content": "At the end of a business conference the nine people present all shake hands with each other once. How many handshakes will there be altogether ?\n\n['A)20', 'B)45', 'C)36', 'D)90', 'E)95']",
"role": "user"
},
{
"content": "number of handshakes = 9C2= 9*8/2 = 36\nANSWER:C",
"role": ... | aqua-rat |
[
{
"content": "Sum of the squares of three numbers is 351 and the sum of their products taken two at a time is 245. Find the sum?\n\n['A)20', 'B)22', 'C)25', 'D)26', 'E)29']",
"role": "user"
},
{
"content": "(a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 351 + 2* 245\na + b + c = √841 = 29\nE",
"... | aqua-rat |
[
{
"content": "What is the are of an equilateral triangle of side 16 cm?\n\n['A)64√6 cm2', 'B)64√3 cm2', 'C)64√9 cm2', 'D)34√3 cm2', 'E)24√3 cm2']",
"role": "user"
},
{
"content": "Area of an equilateral triangle = √3/4 S2\nIf S = 16, Area of triangle = √3/4 * 16 * 16\n= 64√3 cm2;\nAnswer: D",
"r... | aqua-rat |
[
{
"content": "Each of the following equations W has at least one solution EXCEPT\n\n['A)W=–2^n = (–2)^-n', 'B)2^-n = (–2)^n', 'C)2^n = (–2)^-n', 'D)(–2)^n = –2^n', 'E)(–2)^-n = –2^-n']",
"role": "user"
},
{
"content": "While it is possible to reason out which of these choices must not work, we may n... | aqua-rat |
[
{
"content": "If the population of a certain country increases at the rate of one person every 40 seconds, by how many persons does the population increase in 1 hour?\n\n['A)90', 'B)120', 'C)150', 'D)180', 'E)160']",
"role": "user"
},
{
"content": "Answer = 1.5 * 60 = 90\nAnswer is A",
"role": "... | aqua-rat |
[
{
"content": "A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?\n\n['A)288', 'B)180', 'C)288', 'D)277', 'E)265']",
"role": "user"
},
{
"content": "Length of the train be ‘X’\nX + 120/15 = X + 180/18\n6X + ... | aqua-rat |
[
{
"content": "Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?\n\n['A)272 sq.cm', 'B)267 sq.cm', 'C)286 sq.cm', 'D)251 sq.cm', 'E)600 sq.cm']",
"role": "user"
},
{
"content": "Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at righ... | aqua-rat |
[
{
"content": "How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?\n\n['A)12.8 sec', 'B)12.1 sec', 'C)12.2 sec', 'D)12.6 sec', 'E)11.1 sec']",
"role": "user"
},
{
"content": "Speed = 72 * 5/18 = 20 m/sec\nTotal distance covered = 110 + 132 = 242 m.\... | aqua-rat |
[
{
"content": "The consumption of diesel per hour of a bus varies directly as square of its speed. When the bus is travelling at 60 kmph its consumption is 1 litre per hour. if each litre costs $60 and other expenses per hous is $ 60, then what would be the minimum expenditure required to cover a distance of 600... | aqua-rat |
[
{
"content": "From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. What is the probability of having 0 woman in committee ?\n\n['A)7/36', 'B)9/144', 'C)1/36', 'D)1/18', 'E)5/18']",
"role": "user"
},
{
"content": "We... | aqua-rat |
[
{
"content": "A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good.?\n\n['A)20/69', 'B)20/63', 'C)20/65', 'D)20/61', 'E)20/62']",
"role": "user"
},
{
"content": "Required probability = (10 * 4)/126 = 20/63.... | aqua-rat |
[
{
"content": "A train passes a station platform in 32 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?\n\n['A)228', 'B)240', 'C)887', 'D)166', 'E)180']",
"role": "user"
},
{
"content": "Speed = 54 * 5/18 = 15 m/sec.\nLength ... | aqua-rat |
[
{
"content": "If |w|=−w, which of the following must be true?\n\n['A)x≥0', 'B)w≤0', 'C)x2>x', 'D)x3<0', 'E)2x<x']",
"role": "user"
},
{
"content": "|w| =-w means absolute value of w is equal to negative of w. Since absolute value cannot be negative hence negative of w should result in a non negative... | aqua-rat |
[
{
"content": "Two numbers are less than third number by 30% and 37% respectively. How much percent is the second number less than by the first\n\n['A)8%', 'B)9%', 'C)10%', 'D)11%', 'E)12%']",
"role": "user"
},
{
"content": "Explanation:\nLet the third number is x.\nthen first number = (100-30)% of x... | aqua-rat |
[
{
"content": "How many numbers from 39 to 79 are exactly divisible by 11?\n\n['A)5', 'B)7', 'C)4', 'D)11', 'E)12']",
"role": "user"
},
{
"content": "39/11 = 1 and 79/11 = 7 ==> 7 - 3 = 4 Numbers\nAnswer : C",
"role": "assistant"
}
] | aqua-rat |
[
{
"content": "It is found that the volume of a cube is numerically equal to its surface area. Then the measure of its edge in meters is:\n\n['A)4', 'B)6', 'C)8', 'D)9', 'E)cannot be determined']",
"role": "user"
},
{
"content": "if edge of cube = a\nvolume of cube = a^3\nsurface area = 6(a^2)\nthen\... | aqua-rat |
[
{
"content": "if there are 30 cans out of them one is poisned if a person tastes very little he will die within 14 hours so if there are mice to test and 24 hours to test, how many mices are required to find the poisned can?\n\n['A)3', 'B)2', 'C)6', 'D)1', 'E)7']",
"role": "user"
},
{
"content": "as... | aqua-rat |
[
{
"content": "How long does a train 165 meters long running at the rate of 72 kmph take to cross a bridge 660 meters in length?\n\n['A)28', 'B)41.25', 'C)55', 'D)18', 'E)12']",
"role": "user"
},
{
"content": "T = (660 + 165)/72 * 18/5\nT = 41.25\nAnswer: B",
"role": "assistant"
}
] | aqua-rat |
[
{
"content": "A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 15%. What was its profit on the items sold in February?\n\n[... | aqua-rat |
[
{
"content": "Half of 2 percent written as decimal is\n\n['A)0.01', 'B)0.5', 'C)0.05', 'D)0.005', 'E)None of these']",
"role": "user"
},
{
"content": "Explanation:\nIt will be 1/2(2%) = 1/2(2/100) = 2/200 = 0.01\nOption A",
"role": "assistant"
}
] | aqua-rat |
[
{
"content": "If books bought at prices ranging from Rs. 98 to Rs. 195 are sold at prices ranging from Rs. 120 to Rs 215, what is the greatest possible profit that might be made in selling 13 books ?\n\n['A)Rs. 1650', 'B)Rs. 3000', 'C)Rs. 1521', 'D)Rs. 1400', 'E)Rs. 1560']",
"role": "user"
},
{
"con... | aqua-rat |
[
{
"content": "Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 60kmph, find the rate at which the train B runs.\n\n['A)40', 'B)90', 'C)120', 'D)80', 'E)100']",
"rol... | aqua-rat |
[
{
"content": "I bought three toys for my triplet boys (one for each). I placed the toys in the dark store. One by one each boy went to the store and pick the toy. What is the probability that no boy will choose his own toy?\n\n['A)1/3', 'B)2/3', 'C)3/3', 'D)4/3', 'E)5/3']",
"role": "user"
},
{
"cont... | aqua-rat |
[
{
"content": "A man, a woman and a boy can complete a job in 3 days, 4 days and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4th of a day?\n\n['A)10', 'B)41', 'C)31', 'D)21', 'E)22']",
"role": "user"
},
{
"content": "Explanation:\n1 man’s 1 day’s work = ... | aqua-rat |
[
{
"content": "At present, the ratio between the ages of Amit and Dhiraj is 5 : 4. After 6 years, Amit’s age will be 26 years. What is the age of Dhiraj at present?\n\n['A)16', 'B)77', 'C)566', 'D)197', 'E)161']",
"role": "user"
},
{
"content": "Explanation:\nLet the present ages of Amit and Dhiraj b... | aqua-rat |
[
{
"content": "A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?\n\n['A)9:6', 'B)9:8', 'C)9:1', 'D)9:9', 'E)9:5']",
"role": "user"
},
{
"content": "(3*6 + 6*6): (4*12)\n54:48 => 9:8.Answer:B... | aqua-rat |
[
{
"content": "If x-y=10, which of the following must be true?\nI. Both x and y are positive\nII. If x is negative, y must be negative\nIII.If x is positive, y must be positive\n\n['A)I only', 'B)II only', 'C)III only', 'D)I and II', 'E)II and III']",
"role": "user"
},
{
"content": "The best way to a... | aqua-rat |
[
{
"content": "If each side of a square is increased by 25%, find the percentage change in its area?\n\n['A)65.25', 'B)56.25', 'C)65', 'D)56', 'E)25']",
"role": "user"
},
{
"content": "let each side of the square be a , then area = a x a\nNew side = 125a / 100 = 5a / 4\nNew area =(5a x 5a) / (4 x 4) ... | aqua-rat |
[
{
"content": "If the sum and difference of two numbers are 20 and 8 respectively, then the difference of their square is:\n\n['A)12', 'B)28', 'C)160', 'D)180', 'E)18']",
"role": "user"
},
{
"content": "Let the numbers be x and y.\nThen, x + y = 20 and x - y = 8\nx2 - y2 = (x + y)(x - y) = 20 * 8 = 1... | aqua-rat |
[
{
"content": "If $500 is deposited into a savings account at an annual interest rate of 5% that compounds monthly, what is the value of the investment after 10 years?\n\n['A)$750.00', 'B)$823.50', 'C)$973.25', 'D)$1000.25', 'E)$1100.00']",
"role": "user"
},
{
"content": "ROI = 5% per annum compounde... | aqua-rat |
[
{
"content": "Two jars contain milk and water in the ratio 5: 4 and 2: 1 regpectively. What volume should be taken out from the first jar if volumes have to be taken out from both jars so as to fill up a third 30 l jar with milk to water in the ratio 1: 1 ?\n\n['A)7.5 l', 'B)15 l', 'C)22.5 l', 'D)It is impossib... | aqua-rat |
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