Cheukting/mathqa huggingface dataset:
Question (general): for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 7 + 3 and * 7 + 7 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "7 ! = 720 * 7 = 5040 # in question = 5043 , 5044 , 5045 , 5046 , 5047 none of these are prime answer - a"
Answer: a
Question (physics): two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 12 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 288 , c ) 266 , d ) 120 , e ) 126
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 12 sec = 27 * 10 = 270 m . the length of the faster train = 120 m . answer : d"
Answer: d
Question (general): two trains of equal are running on parallel lines in the same direction at 44 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 40 m , b ) 72 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 44 - 36 = 8 km / hr . = 8 * 5 / 18 = 20 / 9 m / sec . 2 x / 36 = 20 / 9 = > x = 40 . answer : a"
Answer: a
Question (gain): a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 50 to incur a loss 20 % ?
Options: a ) 25 , b ) 36 , c ) 40 , d ) 50 , e ) 48
Rationale: production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 50 * ( 100 % + 20 % ) = $ 60 number of articles to be sold for $ 60 to incur a 20 % loss : $ 60 / $ 2.40 = 25 thus , solution a is correct .
Answer: a
Question (general): each of the 59 members in lourdes school class is required to sign up for a minimum of one and a maximum of 3 academic clubs . the 3 clubs to choose from are the poetry club , the history club , and the writing club . a total of 22 students sign up for the poetry club , 27 students for the history club , and 28 students for the writing club . if 6 students sign up for exactly two clubs , how many students sign up for all 3 clubs ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: each of the 59 members in lourdes school class is required to sign up for a minimum of one and a maximum of three academic clubs . total = g 1 + g 2 + g 3 - ( # in exactly 2 ) - 2 * ( # in 3 sets ) 59 = 22 + 27 + 28 - ( 6 ) - 2 x so , # in 3 sets = 6 = c
Answer: c
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 22 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 565 , b ) 444 , c ) 676 , d ) 456 , e ) 663
Rationale: "1 h - - - - - 6 ? - - - - - - 60 12 h rs = 16 + 22 = 38 t = 12 d = 38 * 12 = 456 answer : d"
Answer: d
Question (physics): bruce and bhishma are running on a circular track of length 600 m . speed of bruce is 30 m / s and that of bhishma is 20 m / s . they start fro the same point at the same time in the same direction . when will they meet again for the first time ?
Options: a ) 60 sec , b ) 70 sec , c ) 80 sec , d ) 90 sec , e ) 100 sec
Rationale: actually arjun has to make a lead of 600 m , because when arjun will be 600 m ahead of bhishma , they will be together again as a person when completes the total length it starts retracing he same path and thus arjun and bhishma can be together again . since , they make a difference of 10 m in 1 second . so , he will create 600 m difference in 60 second . d
Answer: d
Question (general): if a certain computer is capable of printing 4700 monthly credit card bills per hour , while a new model is capable of printing at a rate of 6800 per hour , the old model will take approximately how much longer than the new model to print 10000 bills ?
Options: a ) 19 mins , b ) 29 mins , c ) 39 mins , d ) 38 mins , e ) 37 mins
Rationale: old model ' s 1 hr work = 4700 new model ' s 1 hr work = 6800 old model ' time taken to print 10000 cards for 1 hr - - 4700 cards x - - 10000 x = 10000 / 4700 = 100 / 47 new model ' time taken to print 10000 cards for 1 hr - - 6800 cards y - - 10000 y = 10000 / 6800 = 100 / 68 x = 10000 / 4700 = 100 / 47 = 2 6 / 47 hr difference is 100 / 47 - 100 / 68 = 6800 - 4700 / ( 47 * 68 ) 2100 / 3196 = 0.66 hrs = > 39 minutes old model ll take 39 minutes longer to print 10000 cards than new model ans : 39 mins answer : c
Answer: c
Question (general): average between two sets of numbers is closer to the set withmore no ' s ?
Options: a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 × 90 + 2 × 805 = 4305 = 86.3 × 90 + 2 × 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b"
Answer: b
Question (other): in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number w and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: "official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number w of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d ."
Answer: d
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 .
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 % = ( 97 / 556 ) * 100 = 17.4 % answer : b"
Answer: b
Question (general): a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 70 points . to the nearest tenth of a point , what was the student ’ s average grade for the entire two - year period ?
Options: a ) 79 , b ) 89 , c ) 95 , d ) 86.36 , e ) 97.2
Rationale: "let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 70 * 5 = 350 student ' s average = ( 600 + 350 ) / 11 = 86.36 answer d"
Answer: d
Question (physics): if m : n is 3 : 9 and n : p is 9 : 12 then m : p is equal to
Options: a ) 1 : 5 , b ) 1 : 4 , c ) 1 : 6 , d ) 1 : 8 , e ) 1 : 7
Rationale: "the two ratios given are having the same number 9 for n in both the ratios . hence - m : n = 3 : 9 n : p = 9 : 12 = > m : p = 3 : 12 = > 1 : 4 answer b"
Answer: b
Question (gain): the ration of the number of boys and girls in a college is 7 : 8 . if the percentage is increase in the number of boys and girls be 20 % and 10 % respectively . what will be the new ration ?
Options: a ) 5 : 7 , b ) 15 : 21 , c ) 21 : 22 , d ) 13 : 17 , e ) 23 : 42
Rationale: let the number of boys and girls be 7 x and 8 x their increased number is 120 % of 7 x and 110 % of 8 x 7 x * 120 / 100 and 8 x * 110 / 100 42 x / 5 and 44 x / 5 required ratio = 42 x / 5 : 44 x / 5 = 21 : 22 answer is c
Answer: c
Question (physics): a and b can do a piece of work in 50 days and 50 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ?
Options: a ) 30 days , b ) 35 days , c ) 40 days , d ) 44 days , e ) 45 days
Rationale: "explanation : ( a + b ) ’ s 10 days work = 10 [ 1 / 50 + 1 / 50 ] = 10 [ 1 + 1 / 50 ] = 2 / 5 a complete remaining work in 2 / 5 * 50 = 20 total work = 10 + 20 = 30 days answer : option a"
Answer: a
Question (general): of all the homes on gotham street , 1 / 3 are termite - ridden , and 2 / 5 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?
Options: a ) a ) 2 / 15 , b ) b ) 3 / 15 , c ) c ) 4 / 5 , d ) d ) 2 / 5 , e ) e ) 1 / 5
Rationale: let total homes be 15 termite ridden = 1 / 3 ( 15 ) = 5 termite ridden and collapsing = 2 / 5 ( 5 ) = 2 thus homes that are termite ridden , but not collapsing = 5 - 2 = 3 thus required ratio = 3 / 15 = 1 / 5 answer e
Answer: e
Question (general): how many 3 - digit numerals begin with a digit that represents a odd prime and end with a digit that represents a prime number ?
Options: a ) 16 , b ) 80 , c ) 160 , d ) 120 , e ) 240
Rationale: "prime digits 2 , 3,5 and 7 . three digit numbers _ _ _ 1 st place can be filled in 3 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 4 ways total = 3 * 10 * 4 = 120 ans : d"
Answer: d
Question (general): a certain mixture of nuts consists of 5 parts almonds to 1 parts walnuts , by weight . what is the number of pounds of almonds in 140 pounds of the mixture ?
Options: a ) 116 , b ) 84 , c ) 40 , d ) 28 , e ) 20
Rationale: "almonds : walnuts = 5 : 1 total mixture has 6 parts in a 140 pound mixture , almonds are 5 / 6 ( total mixture ) = 5 / 6 * 140 = 116 pounds answer ( a )"
Answer: a
Question (physics): a certain number of workers can do a work in 45 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?
Options: a ) 25 , b ) 30 , c ) 28 , d ) 24 , e ) 35
Rationale: "number of workers = 10 * ( 45 - 10 ) / 10 = 35 answer is e"
Answer: e
Question (general): the smallest number which when diminished by 9 , is divisible 13 , 26 , 39 , 52 and 65 is :
Options: a ) 789 , b ) 769 , c ) 790 , d ) 787 , e ) 788
Rationale: "required number = ( l . c . m . of 13 , 26 , 39 , 52,65 ) + 9 = 780 + 7 = 789 answer : option a"
Answer: a
Question (gain): sheela deposits rs . 4500 in bank savings account . if this is 28 % of her monthly income . what is her monthly income in ?
Options: a ) 22000 , b ) 27000 , c ) 16071 , d ) 16789 , e ) none of these
Rationale: "explanation : 28 % of income = rs . 4500 100 % of income = 4500 x 100 / 28 = rs . 16071 answer : c"
Answer: c
Question (general): the difference between the ages of two persons is 10 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the elder person is ?
Options: a ) 35 yr , b ) 25 yr , c ) 20 yr , d ) 30 yr , e ) 40 yr
Rationale: "let their ages be x years and ( x + 10 ) years then , ( x + 10 ) - 15 = 2 ( x - 15 ) x - 5 = 2 x - 30 x = 25 present age of the elder person = 25 + 10 = 35 years answer is a"
Answer: a
Question (gain): two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 216 marks in the second test and failed by 75 marks in that test . find the pass mark in the first test ?
Options: a ) 768 , b ) 243 , c ) 246 , d ) 288 , e ) 224
Rationale: let the maximum mark in each test be m . the candidate failed by 75 marks in the second test . pass mark in the second test = 249 + 75 = 324 45 / 100 m = 324 pass mark in the first test = 40 / 100 m = 40 / 45 * 324 = 288 . answer : d
Answer: d
Question (general): simplify : 0.4 * 0.5 + 0.3 * 0.2
Options: a ) 0.52 , b ) 0.26 , c ) 0.48 , d ) 0.64 , e ) 0.46
Rationale: "given exp . = 0.4 * 0.5 + ( 0.3 * 0.2 ) = 0.2 + 0.06 = 0.26 answer is b ."
Answer: b
Question (general): elena purchased brand x pens for $ 4.00 apiece and brand y for $ 2.80 apiece . if elena purchased a total of 12 of these pens for $ 40.00 , how many brand x pens did she purchase ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 8 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : e ."
Answer: e
Question (general): if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 10000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ?
Options: a ) $ 40000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 10,000 * 2 ) * 2 = $ 40,000 ( after 9 years investment will become $ 10,000 * 2 = $ 20,000 and in another 9 years it ' ll become $ 20,000 * 2 = $ 40,000 ) . answer : a .
Answer: a
Question (other): in a ratio which is equal to 4 : 6 , if the antecedent is 30 , then the consequent is ?
Options: a ) 72 , b ) 85 , c ) 64 , d ) 51 , e ) 45
Rationale: "we have 4 / 6 = 30 / x 4 x = 30 * 6 x = 45 consequent = 45 answer is e"
Answer: e
Question (gain): a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 560 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 737 , d ) 861 , e ) 1,560
Rationale: "let weight of side of beef before processing = x ( 65 / 100 ) * x = 560 = > x = ( 560 * 100 ) / 65 = 861 answer d"
Answer: d
Question (general): 49 , 98 , 686 , 1372 . . . .
Options: a ) 9052 , b ) 8711 , c ) 9279 , d ) 9604 , e ) 9086
Rationale: "49 x 2 = 98 98 x 7 = 684 684 x 2 = 1372 1372 x 7 = 9604 answer = d"
Answer: d
Question (general): a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 240 per month . what is his monthly salary ?
Options: a ) 5000 , b ) 2999 , c ) 6000 , d ) 2990 , e ) 2771
Rationale: "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 â € “ 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 240 = > 6000 answer : c"
Answer: c
Question (general): a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent q of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?
Options: a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %
Rationale: cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is q = . 25 / 1 * 100 = 25 % d is the answer .
Answer: d
Question (other): in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 78 per kg ?
Options: a ) 5 : 8 , b ) 4 : 7 , c ) 3 : 7 , d ) 9 : 5 , e ) 9 : 8
Rationale: "( 96 - 78 ) / ( 78 - 68 ) = 18 / 10 = 9 / 5 answer : d"
Answer: d
Question (general): arjun started a business with rs . 20000 and is joined afterwards by anoop with rs . 4000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: suppose anoop joined after 3 months . then , 20000 * 12 = 40000 * ( 12 – x ) = > = > x = 6 . answer : d
Answer: d
Question (geometry): the length of a rectangle is increased by 20 % and its breadth is decreased by 20 % . what is the effect on its area ?
Options: a ) 1288 , b ) 9600 , c ) 1000 , d ) 10000 , e ) 2887
Rationale: "100 * 100 = 10000 120 * 80 = 9600 answer : b"
Answer: b
Question (geometry): a perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer . how many positive integers n are there such that n is less than 100,000 and at the same time n is a perfect square and a perfect cube ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "if n is a perfect square and a perfect cube , then n = a ^ 6 for some integer a . the numbers are 1 ^ 6 = 1 , 2 ^ 6 = 64 , 3 ^ 6 = 729 , 4 ^ 6 = 4096 , 5 ^ 6 = 15,625 , 6 ^ = 46,656 . the answer is d ."
Answer: d
Question (general): what is the sum of the integers from - 90 to 95 , inclusive ?
Options: a ) 450 , b ) 550 , c ) 650 , d ) 750 , e ) 465
Rationale: "in an arithmetic progression , the nth term is given by tn = a + ( n - 1 ) d here tn = 95 , a = - 90 , d = 1 hence , 95 = - 90 + ( n - 1 ) or n = 186 sum of n terms can be calculated by sn = n / 2 ( a + l ) a = first term , l = last term , n = no . of terms sn = 186 * ( - 90 + 95 ) / 2 sn = 186 * 5 / 2 = 465 answer : e"
Answer: e
Question (gain): a sum fetched a total simple interest of rs . 4016.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) rs 4462.50 , b ) rs . 8032.50 , c ) rs . 8900 , d ) rs . 8925 , e ) none
Rationale: "solution principal = rs . ( 100 * 4016.25 / 9 * 5 ) = rs . ( 401625 / 45 ) = rs . 8925 answer d"
Answer: d
Question (physics): a train 110 m long is running with a speed of 40 km / h . in how many seconds will the train pass a man who is running at 4 km / h in the direction opposite to that in which the train is going ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the speed of the train relative to the man = 40 + 4 = 44 km / h . 44000 m / h * 1 h / 3600 s = ( 440 / 36 ) m / s ( 110 m ) / ( 440 / 36 m / s ) = ( 110 * 36 ) / 440 = 36 / 4 = 9 seconds the answer is d ."
Answer: d
Question (gain): vijay sells a cupboard at 16 % below cost price . had he got rs . 1200 more , he would have made a profit of 16 % . what is the cost price of the cupboard ?
Options: a ) 3750 , b ) 3600 , c ) 7400 , d ) 7500 , e ) none of these
Rationale: "explanation : cost price = 1200 / ( 0.16 + 0.16 ) = 1200 / 0.32 = rs . 3750 answer a"
Answer: a
Question (other): the dimensions of a field are 16.5 m by 10 m . a pit 10 m long , 5.5 m wide and 4 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field . what will be the rise in the height of field as a result of this operation ?
Options: a ) 2 m , b ) 3 m , c ) 1 m , d ) 2.5 m , e ) 3.5 m
Rationale: "the volume of the earth removed is 10 * 5.5 * 4 = 220 m ^ 3 . the remaining area of the field is 16.5 * 10 - 10 * 5.5 = 110 m ^ 2 . 220 m ^ 3 of the earth evenly spread over the area of 110 m ^ 2 will rise the height by ( height ) = ( volume ) / ( area ) = 220 / 110 = 2 m . answer : a"
Answer: a
Question (general): a class of 35 students has an average height of 180 cm . 7 students whose average height is 120 cm , left the class and 7 others whose average height is 140 cm , joined . calculate the new average height of the students of the class ( in cm ) is ?
Options: a ) 204.6 cm , b ) 404.6 cm , c ) 224.6 cm , d ) 205.6 cm , e ) 256.6 cm
Rationale: total height = 180 * 35 = 6300 cm . total height of those who left = 120 * 7 = 840 total height of those who joined = 140 * 7 = 980 new average = [ 6300 - 120 + 980 ] / 35 = 7160 / 35 cm . = 204.6 cm answer : a
Answer: a
Question (physics): convert the 11 / 36 m / s into kilometers per hour ?
Options: a ) 2.9 kmph , b ) 1.1 kmph , c ) 1.3 kmph , d ) 1.2 kmph , e ) 5.7 kmph
Rationale: "11 / 36 m / s = 11 / 36 * 18 / 5 = 11 / 10 = 1.1 kmph . answer : b"
Answer: b
Question (general): a shop produces sarongs . the daily average production is given by 5 n + 20 , where n is the number of workers aside from the owner . in the first k days , 500 units are produced , and then 5 workers are added to the team . after another k days , the cumulative total is 800 . how many workers were part of the latter production run ?
Options: a ) a ) 6 , b ) b ) 10 , c ) c ) 11 , d ) d ) 21 , e ) e ) 23.5
Rationale: "the daily average production is given by 5 n + 20 - given in the first k days , 500 units are produced = ( 5 n + 20 ) k = 500 k = 500 / 5 n + 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 workers were added = 5 ( n + 5 ) + 20 = 5 n + 45 cumulative is 1250 . . thus for the current period = 800 - 500 = 300 ( 5 n + 45 ) k = 300 k = 300 / 5 n + 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 equate 1 and 2 500 / 5 n + 20 = 300 / 5 n + 45 500 ( 5 n + 45 ) = 300 ( 5 n + 20 ) 2500 n + 22500 = 1500 n + 6000 1000 n = - 16500 n = 16 thus n + 5 = 21 hence d"
Answer: d
Question (general): at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 56 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 50 ¢ ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if the average price is 56 , then mary has 8 oranges and 2 apples ( a ratio of 4 : 1 ) . for the average price to be 50 , the ratio should be 1 : 1 . mary must put back 6 oranges . the answer is e ."
Answer: e
Question (gain): if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 12 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 200 , b ) 210 , c ) 220 , d ) 225 , e ) 230
Rationale: ( 3500 * 2 * 3 ) / 100 = > 210 answer : b
Answer: b
Question (general): think of a number , divide it by 5 and add 10 to it . the result is 21 . what is the number thought of ?
Options: a ) 24 , b ) 55 , c ) 297 , d ) 267 , e ) 29
Rationale: explanation : 21 - 10 = 11 11 x 5 = 55 answer : b
Answer: b
Question (gain): what percent is 5 gm of 1 kg ?
Options: a ) 1.5 % , b ) 0.5 % , c ) 2.5 % , d ) 3.5 % , e ) 4 %
Rationale: "1 kg = 1000 gm 5 / 1000 × 100 = 500 / 1000 = 1 / 2 = 0.5 % b )"
Answer: b
Question (gain): a sum fetched a total simple interest of 4025.25 at the rate of 9 % . p . a . in 5 years . what is the sum ?
Options: a ) 5768 , b ) 8925 , c ) 2345 , d ) 8945 , e ) 8723
Rationale: "principal = ( 100 x 4025.25 ) / ( 9 x 5 ) = 402525 / 45 = 8945 . answer d"
Answer: d
Question (physics): steve traveled the first 2 hours of his journey at 40 mph and the last 4 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 53.33 mph , b ) 56.67 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "average speed = total distance / total time = ( 40 * 2 + 80 * 4 ) / ( 2 + 4 ) = 400 / 6 = 66.6 answer : e"
Answer: e
Question (gain): if each edge of cube increased by 10 % , the percentage increase in
Options: a ) 21 , b ) 22 , c ) 25 , d ) 19 , e ) 15
Rationale: "100 × ( 110 ) / 100 × ( 110 ) / 100 = 121 = > 21 % answer is a ."
Answer: a
Question (general): the average of 6 numbers is 3.9 . the average of two of them is 3.4 , while the average of the other two is 3.85 . what is the average of the remaining two numbers ?
Options: a ) 4.7 , b ) 4.45 , c ) 4.2 , d ) 4.1 , e ) 4.9
Rationale: explanation : sum of the remaining two numbers = ( 3.9 * 6 ) - [ ( 3.4 * 2 ) + ( 3.85 * 2 ) ] = 23.40 - ( 6.8 + 7.7 ) = 23.40 - 14.5 = 8.90 . required average = ( 8.9 / 2 ) = 4.45 . answer : b ) 4.45
Answer: b