Cheukting/mathqa huggingface dataset:
Question (general): the wages earned by robin is 40 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?
Options: a ) 14 % , b ) 23 % , c ) 30 % , d ) 50 % , e ) 100 %
Rationale: "let wage of erica = 10 wage of robin = 1.4 * 10 = 14 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 14 ) / 14 * 100 % = 2 / 14 * 100 % = 14 % answer a"
Answer: a
Question (gain): 25 is subtracted from 75.00001 % of a number , the result is 50 . find the number ?
Options: a ) 150 , b ) 75 , c ) 125 , d ) 95 , e ) 100
Rationale: "( 75 / 100 ) * x â € “ 25 = 50 7.5 x = 750 x = 100 answer : e"
Answer: e
Question (gain): an association of mathematics teachers has 1,500 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 21 %
Rationale: "total umber of members = 1500 number of members that cast votes = 525 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 525 = 315 percent of total membership that voted for winning candidate = ( 315 / 1500 ) * 100 = 21 % answer e"
Answer: e
Question (general): half a number plus 7 is 11 . what is the number ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 7 = 11 ( 1 / 2 ) x = 11 - 7 ( 1 / 2 ) x = 4 x = 8 correct answer is a"
Answer: a
Question (gain): if 5 % more is gained by selling an article for rs . 1000 than by selling it for rs . 20 , the cost of the article is ?
Options: a ) 127 , b ) 1600 , c ) 1200 , d ) 1680 , e ) 1800
Rationale: "let c . p . be rs . x . then , 5 % of x = 1000 - 20 = 80 x / 20 = 80 = > x = 1600 answer : b"
Answer: b
Question (general): of the total amount that jill spent on a shopping trip , excluding taxes , she spent 25 percent on clothing , 25 percent on food , and 50 percent on other items . if jill paid a 10 percent tax on the clothing , no tax on the food , and an 2 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 3 , b ) 4.5 , c ) 4 , d ) 3.5 , e ) 5
Rationale: "assume she has $ 200 to spend . tax clothing = 25 % = $ 50 = $ 5 food = 25 % = $ 50 = $ 0.00 items = 50 % = $ 100 = $ 2.00 total tax = $ 20.00 % of total amount = 7 / 200 * 100 = 3.5 % answer d"
Answer: d
Question (gain): in a certain pond , 55 fish were caught , tagged , and returned to the pond . a few days later , 55 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1250 , d ) 1528 , e ) 10 000
Rationale: "the percent of tagged fish in the second catch is 2 / 55 * 100 = 3.64 % . we are told that 3.64 % approximates the percent of tagged fish in the pond . since there are 55 tagged fish , then we have 0.036 x = 55 - - > x = 1,528 . answer : d ."
Answer: d
Question (general): how many 1 / 6 s are there in 37 1 / 2 ?
Options: a ) 225 , b ) 425 , c ) 520 , d ) 600 , e ) 700
Rationale: required number = ( 75 / 2 ) / ( 1 / 6 ) = ( 75 / 2 x 6 / 1 ) = 225 . answer : a
Answer: a
Question (geometry): what is the smallest positive perfect square that is divisible by 4 , 9 , and 18 ?
Options: a ) 36 , b ) 81 , c ) 144 , d ) 625 , e ) 900
Rationale: "the number needs to be divisible by 2 ^ 2 , 3 ^ 2 , and 2 * 3 ^ 2 . the smallest such perfect square is 2 ^ 2 * 3 ^ 2 = 36 the answer is a ."
Answer: a
Question (other): the ratio between the present ages of a and b is 7 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
Options: a ) 3 : 4 , b ) 3 : 0 , c ) 9 : 1 , d ) 9 : 2 , e ) 3 : 9
Rationale: "let the present ages of a and b be 7 x and 3 x years respectively . then , ( 7 x - 4 ) / ( 3 x + 4 ) = 1 / 1 4 x = 8 = > x = 2 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 18 : 2 = 9 : 1 . answer : c"
Answer: c
Question (other): two vessels contains equal number of mixtures milk and water in the ratio 3 : 2 and 4 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 1 : 3 , b ) 9 : 13 , c ) 5 : 11 , d ) 7 : 3 , e ) 15 : 4
Rationale: "the ratio of milk and water in the new vessel is = ( 3 / 5 + 4 / 5 ) : ( 2 / 5 + 1 / 5 ) = 7 / 5 : 3 / 5 = 7 : 3 answer is d"
Answer: d
Question (probability): from a pack of 52 cards , 1 card is drawn at random . what is the probability that a red king is drawn ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 13 , d ) 1 / 26 , e ) 1 / 52
Rationale: "the total number of cards is 52 . the number of red kings is 2 . p ( red king ) = 2 / 52 = 1 / 26 the answer is d ."
Answer: d
Question (general): if sharon ' s weekly salary increased by 15 percent , she would earn $ 460 per week . if instead , her weekly salary were to increase by 10 percent , how much would she earn per week ?
Options: a ) rs . 400 , b ) rs . 440 , c ) rs . 150 , d ) rs . 460 , e ) rs . 520
Rationale: soln : - 460 / 115 ) 110 = 385 in this case long division does not take much time . ( 4 / 1 ) 110 = rs . 440 answer : b
Answer: b
Question (gain): a fruit seller had some oranges . he sells 10 % oranges and still has 360 oranges . how many oranges he had originally ?
Options: a ) 420 , b ) 700 , c ) 220 , d ) 400 , e ) none of these
Rationale: "explanation : he sells 10 % of oranges and still there are 360 oranges remaining = > 90 % of oranges = 360 ⇒ ( 90 × total oranges ) / 100 = 360 ⇒ total oranges / 100 = 4 ⇒ total oranges = 4 × 100 = 400 answer : option d"
Answer: d
Question (gain): because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 20 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?
Options: a ) 22.5 % , b ) 24 % , c ) 30 % , d ) 33 % , e ) 20 %
Rationale: "say morks income is - 100 so tax paid will be 40 say mindys income is 4 * 100 = 400 so tax paid is 20 % * 400 = 80 total tax paid = 40 + 80 = 120 . combined tax % will be 120 / 100 + 400 = 24 %"
Answer: b
Question (physics): it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 10 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
Options: a ) 10 min . , b ) 41 min . , c ) 17 min . , d ) 23 min . , e ) 25 min .
Rationale: "the ratio is 2 : 3 = gym : ride , so ( 10 ) ( 3 / 2 ) = 15 minutes at the gym , and 15 + 10 = 25 minutes exercise , so ( 2 / 3 ) ( 25 ) = 17 minutes yoga . answer : c"
Answer: c
Question (physics): the length of the bridge , which a train 180 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 876 m , b ) 157 m , c ) 195 m , d ) 156 m , e ) 167 m
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 180 + x ) / 30 = 25 / 2 = > 2 ( 180 + x ) = 750 = > x = 195 m . answer : c"
Answer: c
Question (general): the difference of 2 digit number & the number obtained by interchanging the digits is 36 . what is the difference the sum and the number if the ratio between the digits of the number is 1 : 2 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: let the number be xy . given xy – yx = 36 . this means the number is greater is than the number got on reversing the digits . this shows that the ten ’ s digit x > unit digit y . also given ratio between digits is 1 : 2 = > x = 2 y ( 10 x + y ) – ( 10 y + x ) = 36 = > x – y = 4 = > 2 y – y = 4 . hence , ( x + y ) – ( x – y ) = 3 y – y = 2 y = 8 b
Answer: b
Question (other): at the faculty of aerospace engineering , 312 students study random - processing methods , 232 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?
Options: a ) 424 . , b ) 428 . , c ) 430 . , d ) 432 . , e ) 436
Rationale: "students studying random - processing methods = 312 students studying scramjet rocket engines = 232 students studying them both = 112 therefore ; students studying only random processing methods = 312 - 112 = 200 students studying only scramjet rocket engines = 232 - 112 = 120 students studying both = 112 students studying none = 0 ( as mentioned in question that every student in the faculty has to study one of the two subjects ) total students in faculty of aerospace engineering = students of only random processing methods + students of only scramjet rocket engines + both + none total number of students = 200 + 120 + 112 + 0 = 432 . . . . answer d"
Answer: d
Question (general): if the average ( arithmetic mean ) of a and b is 100 , and the average of b and c is 160 , what is the value of a − c ?
Options: a ) − 120 , b ) − 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given
Rationale: "question : a - c = ? ( a + b ) / 2 = 100 = = = > a + b = 200 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 200 - 320 = = = > a + b - b - c = - 120 = = = > a - c = - 120 answer : a"
Answer: a
Question (general): in a company of 11 employees , 5 employees earn $ 32,000 , 4 employees earn $ 45,000 , and the 2 highest - paid employees earn the same amount . if the average annual salary for the 11 employees is $ 48,000 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 90,000 , b ) $ 94,000 , c ) $ 98,000 , d ) $ 102,000 , e ) $ 106,000
Rationale: "5 * 32,000 + 4 * 45,000 + 2 x = 11 * 48,000 2 x = 528,000 - 160,000 - 180,000 2 x = 188,000 x = 94,000 the answer is b ."
Answer: b
Question (general): if n = 2 ^ 0.20 and n ^ b = 16 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 20 , d ) 5 / 3 , e ) 80 / 3
Rationale: "20 / 100 = 1 / 5 n = 2 ^ 1 / 5 n ^ b = 2 ^ 4 ( 2 ^ 1 / 5 ) ^ b = 2 ^ 4 b = 20 answer : c"
Answer: c
Question (gain): a man buys an item at rs . 800 and sells it at the loss of 20 percent . then what is the selling price of that item
Options: a ) rs . 640 , b ) rs . 760 , c ) rs . 860 , d ) rs . 960 , e ) none of these
Rationale: "explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 80 % of 800 = 80 / 100 * 800 = 640 option a"
Answer: a
Question (physics): find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 14 per cubic meter ?
Options: a ) 1386 , b ) 2799 , c ) 2890 , d ) 1485 , e ) 2780
Rationale: "22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 14 = 1386 answer : a"
Answer: a
Question (gain): rani bought more apples than oranges . she sells apples at ₹ 23 apiece and makes 15 % profit . she sells oranges at ₹ 10 apiece and makes 25 % profit . if she gets ₹ 653 after selling all the apples and oranges , find her profit percentage z .
Options: a ) 16.8 % , b ) 17.4 % , c ) 17.9 % , d ) 18.5 % , e ) 19.1 %
Rationale: "given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % z = ( 97 / 556 ) * 100 = 17.4 % answer : b"
Answer: b
Question (general): the sum of digits of a two digit number is 13 , the difference between the digits is 5 . find the number
Options: a ) 85 , b ) 94 , c ) 83 , d ) 72 , e ) none
Rationale: "description : = > x + y = 13 , x - y = 5 adding these 2 x = 18 = > x = 9 , y = 4 . thus the number is 94 answer b"
Answer: b
Question (physics): if 8 men or 12 women can do a piece of work in 25 days , in how many days can the same work be done by 6 men and 11 women ?
Options: a ) 10 days , b ) 11 days , c ) 13 days , d ) 15 days , e ) 17 days
Rationale: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 25 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 25 = 1 / 300 so , 20 women work = 20 / 300 = 1 / 15 ans : 15 days answer : d"
Answer: d
Question (physics): a train 140 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 60 kmph , e ) 79 kmph
Rationale: "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 140 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2520 < = > x = 79 speed of the train is 79 kmph . answer : option e"
Answer: e
Question (physics): a train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 10 km / hr , b ) 50 km / hr , c ) 14 km / hr , d ) 17 km / hr , e ) 77 km / hr
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 45 = = > x = 50 km / hr . answer : b"
Answer: b
Question (general): 0.002 x 0.6 = ?
Options: a ) 0.0012 , b ) 0.001 , c ) 0.01 , d ) 0.1 , e ) none of these
Rationale: "explanation : 2 x 6 = 12 . sum of decimal places = 4 0.002 x 0.6 = 0.0012 answer - a"
Answer: a
Question (general): find the average of all the number between 6 and 34 which are divisible by 5 .
Options: a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 32
Rationale: "solution average = ( 10 + 15 + 20 + 25 + 30 / 5 ) = 100 / 2 = 20 answer b"
Answer: b
Question (physics): if the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is ?
Options: a ) a ) 15 , b ) b ) 10 , c ) c ) 14 , d ) d ) 12 , e ) e ) 11
Rationale: "2 * 22 / 7 * 14 * x = 880 = > x = 10 answer : b"
Answer: b
Question (physics): a and b can do a piece of work in 7 days , b and c in 8 days , c and a in 9 days . how long will c take to do it ?
Options: a ) 14.1 days , b ) 18.8 days , c ) 21.4 days , d ) 24.3 days , e ) 26.5 days
Rationale: "2 c = 1 / 8 + 1 / 9 – 1 / 7 = 47 / 504 c = 47 / 1008 = > 1008 / 47 = 21.4 days the answer is c ."
Answer: c
Question (general): oil cans x and y are right circular cylinders and the height and radius of y are each 5 times those of x . if the oil in can x filled to capacity sells for $ 1 , how much does the oil in y sell for if y is only 1 / 5 th filled ?
Options: a ) $ 25 , b ) $ 26 , c ) $ 27 , d ) $ 28 , e ) $ 30
Rationale: "formula for vol of a cyl is pi * r ^ 2 * h so vy = 125 * vy y when half filled will cost 25 times x so ans is a"
Answer: a
Question (geometry): what is the smallest positive integer x , such that 1,152 x is a perfect cube ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 18
Rationale: "we need to make 1152 x a perfect cube , hence we need to have the powers a multiple of 3 1152 = 2 ^ 7 * 3 ^ 2 the minimum value of x for which 1152 x is a perfect cube = 2 ^ 2 * 3 = 12 correct option : d"
Answer: d
Question (physics): car x began traveling at an average speed of 35 miles per hour . after 36 minutes , car y began traveling at an average speed of 38 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 105 , b ) 140 , c ) 175 , d ) 210 , e ) 245
Rationale: "in 36 minutes , car x travels 21 miles . car y gains 3 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is e ."
Answer: e
Question (general): cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 51 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 0.00 , b ) $ 1.00 , c ) $ 3.75 , d ) $ 5.00 , e ) $ 6.80
Rationale: "0.85 * { original price } = $ 51 - - > { original price } = $ 60 . { final price } = $ 51 * 1.25 = $ 63.75 . the difference = $ 63.75 - 60 $ = $ 3.75 . answer : c ."
Answer: c
Question (physics): 2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations . what is the ratio of their speeds ?
Options: a ) 11 : 9 , b ) 11 : 2 , c ) 91 : 9 , d ) 11 : 1 , e ) 11 : 5
Rationale: in same time , they cover 110 km & 90 km respectively so ratio of their speed = 110 : 90 = 11 : 9 answer : a
Answer: a
Question (general): a grocer has a sale of rs . 4435 , rs . 4927 , rs . 4855 , rs . 5230 and rs . 4562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 4500 ?
Options: a ) 1991 , b ) 2991 , c ) 3991 , d ) 4521 , e ) 5991
Rationale: "total sale for 5 months = rs . ( 4435 + 4927 + 4855 + 5230 + 4562 ) = rs . 24009 . required sale = rs . [ ( 4500 x 6 ) - 24009 ] = rs . ( 27000 - 24009 ) = rs . 2991 answer : option b"
Answer: b
Question (probability): the set s consists of 5 numbers : { 1 , 2,3 , 4,5 } . if all possible subsets including the null set are created and one subset is chosen at random , what is the probability that the subset has 4 or 5 as its largest number ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 5 / 8 , e ) 11 / 16
Rationale: "the set s has 2 ^ 5 = 32 subsets . the number 5 is in half of these subsets . thus 5 is the largest number in 16 subsets of s . of the remaining 16 subsets , 4 is an element in 8 of them . thus 4 is the largest number in 8 subsets of s . the probability that 4 or 5 is the largest number is 24 / 32 = 3 / 4 . the answer is c ."
Answer: c
Question (general): at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 211 ?
Options: a ) 1,108 , b ) 2,100 , c ) 2,108 , d ) 2,124 , e ) 2,180
Rationale: "i think it should be e . i can buy 8 250 - pack for rs 22.95 * 8 = $ 183.60 now , i can buy 9 20 - pack for 3.05 * 9 = $ 15.25 now , i am left with only $ 1.15 . i can not but anything with this . hence total hotdogs = 250 * 8 + 20 * 9 = 2180"
Answer: e
Question (general): what is the sum of all 3 digit integers formed using the digits 34 and 5 ( repetition is allowed )
Options: a ) 11982 , b ) 11984 , c ) 11985 , d ) 11988 , e ) 11986
Rationale: n = 3 * 3 * 3 = 27 = ( 555 + 333 ) / 2 = 444 sum = number of integers x average value n * = 27 * 444 = 11988 answer = d
Answer: d
Question (physics): two men are going along a track rail in the opposite direction . one goods train crossed the first person in 20 sec . after 10 min the train crossed the other person who is coming in opposite direction in 18 sec . after the train has passed , when the two persons will meet ?
Options: a ) 95 minutes , b ) 90 minutes , c ) 88 minutes , d ) 95 minutes , e ) none of these
Rationale: explanation : let us consider that speed of train , first man and second man are respectively t , f and s . according to first given condition goods train crossed the first person moving in same direction in 20 sec . so length of the will be 20 ( t - f ) similarly train crossed the second man in 18 sec . so length of the train will be 18 ( t + s ) on comparing these two equations , we get 20 ( t - f ) = 18 ( t + s ) = > 2 t = 20 f + 18 s = > t = 10 f + 9 s now it is given that after 10 min the train crossed the other person who is coming in opposite direction . so , if we consider this way of train as l then the next equation will be l = 600 t ( here 600 is used for 10 minutes ) finally as asked in the question the time required to meet the two man after the train has passed will be given by time = ( l - 600 f ) / ( f + s ) { here 600 f is used for the distance traveled by first man in 10 minutes } = > = ( 600 t - 600 f ) / ( f + s ) = > = [ 600 ( 10 f + 9 s ) - 600 f ] / ( f + s ) = > = 600 ( 10 f + 9 s - f ) / ( f + s ) = 600 * 9 ( f + s ) / ( f + s ) = > = 600 * 9 seconds = > = 600 * 9 / 60 min = > = 90 minutes hence ( b ) is the correct answer . answer : b
Answer: b
Question (physics): one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill tank in 35 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 229 , b ) 787 , c ) 144 , d ) 128 , e ) 140
Rationale: "let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 35 4 / x = 1 / 35 = > x = 140 min . answer : e"
Answer: e
Question (general): if x ^ 2 + y ^ 2 = 20 and xy = 3 , then ( x − y ) ^ 2 =
Options: a ) 8 , b ) 11 , c ) 14 , d ) 17 , e ) 20
Rationale: "but you can not take xy + 3 to mean xy = - 3 . . only if xy + 3 = 0 , it will mean xy = - 3 . . rest your solution is perfect and you will get your correct answer as 20 - 2 * 3 = 14 . . answer c"
Answer: c
Question (geometry): what is the smallest positive integer x such that 108 x is the cube of a positive integer ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 10 , e ) 7
Rationale: "given 108 x is a perfect cube so we will take 216 = 6 * 6 * 6 108 x = 216 x = 216 / 108 = 2 correct option is a"
Answer: a
Question (general): there are 6 people in the elevator . their average weight is 150 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
Options: a ) 157 , b ) 168 , c ) 189 , d ) 190 , e ) 200
Rationale: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 150 ) = 1057 - 900 = 157 . answer a"
Answer: a
Question (general): average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 20 % the new mean is $ 860 . what was original rent of friend whose rent is increased ?
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1200
Rationale: "0.2 x = 4 ( 860 - 800 ) 0.2 x = 240 x = 1200 answer e"
Answer: e
Question (physics): if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 10 m of the same rod ?
Options: a ) 38 kg , b ) 25.6 kg , c ) 28 kg , d ) 26.5 kg , e ) none of these
Rationale: "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 10 : : 42.75 : x = > 11.25 x x = 10 x 42.75 = > x = ( 10 x 42.75 ) / 11.25 = > x = 38 answer : a"
Answer: a
Question (physics): 8 men can dig a pit in 20 days . if a man works half as much again a s a boy , then 4 men and 9 boys can dig a similar pit in :
Options: a ) 10 days , b ) 12 days , c ) 15 days , d ) 16 days , e ) 20 days
Rationale: explanation : 1 work done = 8 × 20 1 man = 3 / 2 boys 1 boy = 2 / 3 men then , 9 boys = 9 × 2 / 3 men = 6 men then , 4 men + 9 boys = 10 men then , 8 × 20 = 10 × ? days ? days = 8 × 20 / 10 = 16 days . answer : option d
Answer: d
Question (gain): john makes $ 40 a week from his job . he earns a raise and now makes $ 70 a week . what is the % increase ?
Options: a ) 16 % , b ) 16.66 % , c ) 17.9 % , d ) 18.12 % , e ) 75 %
Rationale: "increase = ( 30 / 40 ) * 100 = ( 3 / 4 ) * 100 = 75 % . e"
Answer: e