Cheukting/mathqa huggingface dataset:
Question (general): a waitress ' s income consists of her salary and tips . during one week , her tips were 11 / 4 of her salary . what fraction of her income for the week came from tips ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 3 , d ) 4 / 9 , e ) 11 / 15
Rationale: "her tips were 11 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 11 / 4 ) ( $ 4 ) = $ 11 so , her total income = $ 4 + $ 11 = $ 15 what fraction of her income for the week came from tips $ 11 / $ 15 = 11 / 15 = e"
Answer: e
Question (other): on a certain farm the ratio of horses to cows is 5 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 17 : 7 . after the transaction , how many more horses than cows would the farm own ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: originally , there were 5 k horses and k cows . 7 ( 5 k - 15 ) = 17 ( k + 15 ) 35 k - 17 k = 255 + 105 18 k = 360 k = 20 the difference between horses and cows is ( 5 k - 15 ) - ( k + 15 ) = 4 k - 30 = 50 the answer is c .
Answer: c
Question (physics): in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 50 questions and secures 130 marks , the no of questions he attempts correctly is :
Options: a ) a ) 36 , b ) b ) 38 , c ) c ) 90 , d ) d ) 88 , e ) e ) 37
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 50 – x ) = 130 = > 5 x = 180 = > x = 36 answer : a"
Answer: a
Question (gain): the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 684 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1634 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 684 × 100 ) / ( 6 × 12 ) = rs . 950 bg = bd – td = > 684 = bd - 950 = > bd = 684 + 950 = 1634 answer : option d"
Answer: d
Question (gain): a sum of money at simple interest amounts to $ 780 in 3 years and to $ 930 in 4 years . the sum is :
Options: a ) $ 153 , b ) $ 698 , c ) $ 330 , d ) $ 549 , e ) $ 675
Rationale: "c $ 330 s . i . for 1 year = $ ( 930 - 780 ) = $ 150 . s . i . for 3 years = $ ( 150 x 3 ) = $ 450 . principal = $ ( 780 - 450 ) = $ 330 ."
Answer: c
Question (gain): what is 15 percent of 44 ?
Options: a ) 6.6 , b ) 7.8 , c ) 8.9 , d ) 9.4 , e ) 10.2
Rationale: "( 15 / 100 ) * 44 = 6.6 the answer is a ."
Answer: a
Question (general): the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 5.20 and the price of commodity y was $ 7.30 . in which year will the price of commodity x be 90 cents more than the price of commodity y ?
Options: a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014
Rationale: "the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 90 cents more than commodity y . $ 3.00 / 25 cents = 12 years the answer is 2001 + 12 years = 2013 . the answer is d ."
Answer: d
Question (general): 1 , 1 , 3 , 9 , 5 , 25 , 7 , 49 _ , 81
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "as seq is 1 , 1 , 3 , 9 , 5 , 25 , 7 , 49 9 , 81 two series are there . 1 , 3,5 , 7,9 . . . odd numbers and 1 , 9,25 , 49,81 . . square of odd numbers answer : d"
Answer: d
Question (gain): a shopkeeper cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 20 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 10 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage .
Options: a ) 20 % , b ) 32 % , c ) 23.365 % , d ) 22.109 % , e ) 2 %
Rationale: anyways , one can infer that he ' steals ' 20 % from suppliers and then charges 10 % extra to customers so basically 1.2 * 1.1 = 1.32 given that 1 is start point , we get 32 % more hence answer is b
Answer: b
Question (general): of 3 numbers , the third is 4 times the second and the second is two times the first . if their average is 165 , the smallest of the 3 numbers is :
Options: a ) 18 , b ) 19 , c ) 45 , d ) 21 , e ) 22
Rationale: explanation : let first number be x . so , 2 nd no . = 2 x & 3 rd no . = 8 x . so , x + 2 x + 8 x = 165 × 3 = 495 11 x = 495 / 11 x = 495 / 11 hence , smallest number x = 45 answer : c
Answer: c
Question (general): two mixers and one t . v . cost rs . 7000 , while two t . v . s and a mixer cost rs , 9800 . the value of one t . v . is :
Options: a ) rs . 4000 , b ) rs . 4500 , c ) rs . 4300 , d ) rs . 4200 , e ) none of these
Rationale: explanation : let c . p . of a mixer be rs . x and that of a t . v . be rs . y . then , 2 x + y = 7000 and 2 y + x = 9800 . multiplying 2 nd equatien by 2 and subtracting first from it , we get 3 y = 19600 - 7000 = 12600 or y = 4200 c . p . of a t . v . = rs . 4200 answer : d
Answer: d
Question (physics): a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 550 - mile journey ? assume that the train makes no intermediate stops .
Options: a ) 8 , b ) 8.5 , c ) 9 , d ) 9.5 , e ) 10
Rationale: "a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 550 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 7 70 280 8 80 360 9 90 450 10 100 550 it takes a total of nine hours to cover the 550 mile distance . answer : e"
Answer: e
Question (general): ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of ( a - b ) / 2 ?
Options: a ) 1 , b ) 10 , c ) 19 , d ) 5 , e ) 2
Rationale: "answer is 10 yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 ( a - b ) / 2 = 110 - 100 = 10 / 2 = 5 ans : d"
Answer: d
Question (general): in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 7.8 , 9.0 , 6.0 , and 8.5 , what was the point value of the dive ?
Options: a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 76.16 , e ) 81.6
Rationale: degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.0 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 7.8 + 8.5 ) = 23.8 point of value of the dive = 23.8 * 3.2 = 76.16 answer d
Answer: d
Question (gain): the workforce of company x is 60 % female . the company hired 28 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 336 , d ) 360 , e ) 420
Rationale: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 28 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 28 ) 0.05 x = 15.4 x = 308 - this is quantity of employees before adding 28 men so after adding it will be 336 answer is c"
Answer: c
Question (general): the average of first 25 prime numbers is ?
Options: a ) 9.9 , b ) 8.8 , c ) 5.6 , d ) 11.9 , e ) 11.11
Rationale: "explanation : average = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 / 9 = 100 / 9 = 11.11 ( approx ) answer is e"
Answer: e
Question (physics): 14 men can complete a piece of work in 22 days . in how many days can 18 men complete that piece of work ?
Options: a ) 23 days , b ) 26 days , c ) 17 days , d ) 29 days , e ) 20 days
Rationale: "c 17 days 14 * 22 = 18 * x = > x = 17 days"
Answer: c
Question (gain): what amount does an investor receive if the investor invests $ 7000 at 10 % p . a . compound interest for two years , compounding done annually ?
Options: a ) $ 8080 , b ) $ 8130 , c ) $ 8260 , d ) $ 8320 , e ) $ 8470
Rationale: "a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 7000 = 1.21 * 7000 = 8470 the answer is e ."
Answer: e
Question (general): 15 times a number gives 150 . the number is
Options: a ) 11 , b ) 15 , c ) 13 , d ) 14 , e ) can not be determined
Rationale: explanation : let the number be ' n ' 15 × n = 150 ⇒ n = 10 correct option : b
Answer: b
Question (general): on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 320,000 ?
Options: a ) 30 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 320 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 160,000 = 6 years 160,000 - 320,000 = 6 years total 30 years ."
Answer: a
Question (geometry): what is the total surface area in square meters of a rectangular solid whose length is 10 meters , width is 9 meters , and depth is 6 meters ?
Options: a ) 400 m 2 , b ) 404 m 2 , c ) 408 m 2 , d ) 401 m 2 , e ) 412 m 2
Rationale: "surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 10 * 9 + 9 * 6 + 10 * 6 ) = 2 ( 90 + 54 + 60 ) = 2 * 204 = 408 m 2 answer : c"
Answer: c
Question (physics): 39 persons can repair a road in 12 days , working 10 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 14 , d ) 15 , e ) 26
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 39 : : 12 : x working hours / day 6 : 10 30 x 6 x x = 39 x 10 x 12 x = ( 39 x 10 x 12 ) / ( 30 x 6 ) x = 26 . answer : e"
Answer: e
Question (physics): find the lcm of 0.6 , 9.6 and 0.36 .
Options: a ) 26.3 , b ) 35.6 , c ) 32.9 , d ) 25.5 , e ) 28.8
Rationale: "the given numbers are equivalent to 0.60 , 9.60 and 0.36 . now , find the lcm of 60,960 and 36 . which is equal to 2880 . the required lcm = 28.80 . answer is e"
Answer: e
Question (gain): what is the rate percent when the simple interest on rs . 4000 amount to rs . 320 in 2 years ?
Options: a ) 4 % , b ) 4.1 % , c ) 4.2 % , d ) 4.3 % , e ) 4.5 %
Rationale: "interest for 1 year = 320 / 2 = 160 interest on rs 4000 p / a = 160 interest rate = 160 / 4000 * 100 = 4 % answer : a"
Answer: a
Question (physics): man can row upstream at 30 kmph and downstream at 40 kmph , and then find the speed of the man in still water ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 70 , e ) 45
Rationale: "us = 30 ds = 40 m = ( 30 + 40 ) / 2 = 35 answer : b"
Answer: b
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 4 hours and 10 hours respectively . the ratio of their speeds is
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 12 , d ) 4 : 8 , e ) 5 : 2
Rationale: let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 10 : 4 = 5 : 2 . answer : e
Answer: e
Question (general): for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score q for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean q = 74 . answer : a .
Answer: a
Question (general): the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 47 . what is a possible value for the mean of the distribution ?
Options: a ) 46 , b ) 54 , c ) 48 , d ) 49 , e ) 50
Rationale: the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 47 : { mean } - 3 * { sd } > 47 ; { mean } - 6 > 47 ; { mean } > 53 . answer : b .
Answer: b
Question (gain): a cycle is bought for rs . 900 and sold for rs . 1120 , find the gain percent ?
Options: a ) 11 , b ) 24 , c ) 99 , d ) 77 , e ) 18
Rationale: "900 - - - - 220 100 - - - - ? = > 24 % answer : b"
Answer: b
Question (general): 6.006 / 3.003
Options: a ) 0.002 , b ) 0.02 , c ) 0.2 , d ) 20 , e ) 2
Rationale: "answer is 2 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 6006 / 3003 = 2 answer e"
Answer: e
Question (other): the ratio between the sale price and the cost price of an article is 4 : 3 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 9 , b ) 2 : 5 , c ) 3 : 6 , d ) 2 : 0 , e ) 1 : 3
Rationale: "let c . p . = rs . 3 x and s . p . = rs . 4 x . then , gain = rs . x required ratio = x : 3 x = 1 : 3 answer : e"
Answer: e
Question (physics): two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 27 seconds . what is the length of each train ( in meters ) ?
Options: a ) 50.5 , b ) 88.5 , c ) 37.5 , d ) 55.5 , e ) 23.5
Rationale: "the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 27 seconds , the relative difference in distance traveled is 27 * 25 / 9 = 75 meters this distance is twice the length of each train . the length of each train is 75 / 2 = 37.5 meters the answer is c ."
Answer: c
Question (general): the average of 35 numbers is 25 . if each number is multiplied by 5 , find the new average ?
Options: a ) 125 , b ) 189 , c ) 297 , d ) 267 , e ) 298
Rationale: "sum of the 35 numbers = 35 * 25 = 875 if each number is multiplied by 5 , the sum also gets multiplied by 5 and the average also gets multiplied by 5 . thus , the new average = 25 * 5 = 125 . answer : a"
Answer: a
Question (general): the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 50 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 20 , b ) 27 , c ) 25 , d ) 99 , e ) 21
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 50 ) = 90 ( x - 5 ) 200 = 10 x = > x = 20 . answer : a"
Answer: a
Question (general): if n = 5 ^ 11 – 5 , what is the units digit of n ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 6 , e ) 8
Rationale: always divide the power ( incase 11 ) by 4 and use the remainder as the new power . the question now becomes 5 ^ 3 - 5 . now 5 ^ 3 has last digit 5 . we subtract 5 from 5 = 0 is the answer . option a
Answer: a
Question (general): p , q and r have rs . 4000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) rs . 3000 , b ) rs . 1600 , c ) rs . 2400 , d ) rs . 4000 , e ) none of these
Rationale: "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 4000 - r ) = > 3 r = 8000 - 2 r = > 5 r = 8000 = > r = 1600 . answer : b"
Answer: b
Question (general): 8500 + ( 1600 ÷ ? ) of 1 / 5 = 8501
Options: a ) 310 , b ) 312 , c ) 320 , d ) 325 , e ) 345
Rationale: "explanation : = > 8500 + ( 1600 / ? ) × 1 / 5 = 8501 = > 1600 / ? × 1 / 5 = 8501 - 8500 = 1 = > ? = 1600 / 5 = 320 answer : option c"
Answer: c
Question (general): 8.008 / 4.004
Options: a ) 2 , b ) 0.02 , c ) 0.2 , d ) 20 , e ) 2
Rationale: "answer is 2 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 8008 / 4004 = 2 answer a"
Answer: a
Question (general): two friends a , b decided to share a lot of apples . each of them had half of the total plus half an apple in order . after each of them took their share 4 time , no apples were left . how many apples were there ?
Options: a ) 250 , b ) 255 , c ) 254 , d ) 253 , e ) 251
Rationale: whenever the rate of reduction is ' half of the total and half of it ' , the answer is always ( 2 ^ n ) - 1 , where ' n ' is the number of times the process is repeated . here , the process is repeated 8 times . so answer is ( 2 ^ 8 ) - 1 = 255 answer : e
Answer: e
Question (gain): find the simple interest on $ 10000 at 9 % per annum for 12 months ?
Options: a ) $ 410 , b ) $ 500 , c ) $ 650 , d ) $ 710 , e ) $ 900
Rationale: p = $ 10000 r = 9 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 9 * 1 / 100 = $ 900 answer is e
Answer: e
Question (general): when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 5 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 15 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "n = 3 p + 1 = 5 q + 3 n + 2 = 3 p + 3 = 5 q + 5 n + 2 is a multiple of 3 and 5 , so it is a multiple of 15 . the answer is a ."
Answer: a
Question (general): how many multiples of 4 are there between 64 and 256 ?
Options: a ) 47 , b ) 49 , c ) 42 , d ) 41 , e ) 40
Rationale: "it should be mentioned whether 64 and 256 are inclusive . if 64 and 256 are inclusive , then the answer is ( 256 - 64 ) / 4 + 1 = 49 . if 64 and 256 are not inclusive , then the answer is ( 252 - 68 ) / 4 + 1 = 47 . since oa is a , then we have not inclusive case ."
Answer: a
Question (general): at the end of the month , a certain ocean desalination plant ’ s reservoir contained 14 million gallons of water . this amount is twice the normal level . if this amount represents 70 % of the reservoir ’ s total capacity , how many million gallons short of total capacity is the normal level ?
Options: a ) 2 , b ) 5 , c ) 10 , d ) 12 , e ) 15
Rationale: the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 14 mg = 70 % of total . . total = 14 / . 7 = 20 mg . . normal level = 1 / 2 of 20 = 10 mg . . shortage of normal level = 20 - 10 = 10 mg . . c
Answer: c
Question (general): of the 14,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
Options: a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %
Rationale: "the number of employees is not reqd . . . 1 / 2 of 2 / 7 are shunted out so 1 / 7 left . . . there are another 5 equal parts ( 5 / 7 ) . . so total remaining parts = 6 , in which 1 part is journeyman . . . . therefore % = 1 / 6 * 100 = 16.67 % answer : b"
Answer: b
Question (general): what is the value of x ^ 2 yz − xyz ^ 2 , if x = 1 , y = 1 , and z = 3 ?
Options: a ) 20 , b ) - 6 , c ) 30 , d ) 32 , e ) 48
Rationale: "1 * 1 * 3 - ( 1 * 1 * 9 ) = 3 - 9 = - 6 ans : b"
Answer: b
Question (gain): a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 24 % home electronics ; 10 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 54 ° , e ) 52 °
Rationale: "14 % microphotonics ; 24 % home electronics ; 10 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; 100 - ( 14 + 24 + 10 + 29 + 8 ) = 15 % basic astrophysics . 15 % of 360 ° is 54 ° . answer : d ."
Answer: d
Question (general): the difference between a 7 digit number and the number formed by reversing its digit is not a multiple of
Options: a ) 121 , b ) 11 , c ) 9 , d ) 10 , e ) 3
Rationale: "another approach is to test a number . let ' s say the original number is 1231231 so , the reversed number is 1321321 the difference = 1321321 - 1231231 = 90090 no check the answer choices 90090 is a multiple of 3,9 , 10,11 121 is not a multiple of 90090 answer : a"
Answer: a
Question (geometry): f and e are midpoints of ab and ad respectively . if the side of square abcd is 8 , what is the area of triangle cef ?
Options: a ) 8 √ 2
b ) 9 √ 3
c ) 18
d ) 16 √ 2
e ) 24
Rationale: area of shaded figure = area of square - ( area of triangle aef + area of triangle fbc + area of triangle edc ) = 8 * 8 - ( 1 / 2 * 4 * 4 + 1 / 2 * 4 * 8 + 1 / 2 * 4 * 8 ) = 24 . answer e .
Answer: e
Question (physics): two trains of length 120 meter and 150 meter crosses a stationary man in 10 and 15 seconds respectively . in what time they will cross each other when they are moving in same direction .
Options: a ) 120 sec , b ) 125 sec , c ) 135 sec , d ) 140 sec , e ) none of these
Rationale: explanation : 120 = a * 10 , a = 12 m / sec ( speed of first train ) 150 = b * 15 , b = 10 m / sec ( speed of second train ) 270 = ( 2 ) * t , t = 135 seconds answer – c
Answer: c
Question (physics): a , b two inlet pipes takes 15,18 minutes to fill the tank and c an oulet pipe takes 45 minutes to empty the tank respectively . in what time the tank be filled if all of them are operated together ?
Options: a ) 11 minutes , b ) 10 minutes , c ) 12 minutes , d ) 13 minutes , e ) 14 minutes
Rationale: lcm = 90 no of days = [ 90 / ( 90 / 15 + 90 / 18 - 90 / 45 ) = [ 90 / ( 6 + 5 - 2 ) ] = [ 90 / 9 ] = 10 minutes answer : b
Answer: b
Question (physics): a car traveled from san diego to san francisco at an average speed of 63 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 24 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 63 x total distance traveled = 2 * 63 x = 126 x total time taken = x + 2 x = 3 x average speed = 126 x / 3 x = 42 answer : d"
Answer: d
Question (general): at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 6 . if the price per share of stock k was $ 8 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?
Options: a ) 1.4 % , b ) 5.9 % , c ) 11.1 % , d ) 12.5 % , e ) 33.33 %
Rationale: "opening = 6 closing = 8 rise in price = 2 so , percent increase = 2 / 6 * 100 = 33.33 % answer : e"
Answer: e
Question (general): a man engaged a servant on the condition that he would pay him rs . 900 and a uniform after one year service . he served only for 9 months and received uniform and rs . 650 , find the price of the uniform ?
Options: a ) 377 , b ) 197 , c ) 187 , d ) 100 , e ) 822
Rationale: "explanation : 9 / 12 = 3 / 4 * 900 = 675 650 - - - - - - - - - - - - - 25 1 / 4 - - - - - - - - 25 1 - - - - - - - - - ? = > rs . 100 answer : d"
Answer: d