Cheukting/mathqa huggingface dataset:
Question (geometry): one side of a rectangular field is 13 m and one of its diagonal is 17 m . find the area of the field .
Options: a ) 100 , b ) 141.7 , c ) 150 , d ) 180 , e ) none
Rationale: "solution other side = √ ( 17 ) 2 - ( 13 ) 2 = √ 289 - 169 = √ 120 = 10.9 m . ∴ area = ( 13 x 10.9 ) m 2 = 141.7 m 2 . answer b"
Answer: b
Question (general): a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 16000 left with him . find salary . .
Options: a ) $ 10800 , b ) $ 18000 , c ) $ 160000 , d ) $ 1800 , e ) none
Rationale: "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 16000 , = [ 1 - 9 / 10 ] * total salary = $ 16000 , total salary = $ 16000 * 10 = $ 160000 , correct answer ( c )"
Answer: c
Question (gain): a has 10000 chocolates . 20 % of the chocolates are eaten . what percentage of the uneaten chocolates must be eaten so that 3 / 2 of all chocolates are eaten ?
Options: a ) 39.25 , b ) 37.25 , c ) 37.26 , d ) 38.21 , e ) 38.32
Rationale: number of chocolates = 10,000 currently eaten = 10,000 * 20 / 100 = 2000 uneaten chocolates = 10000 - 2000 = 8000 2 / 3 of all chocolates = 5000 the number of chocolates to be eaten to make 2 / 3 of all chocolates eaten = 5000 - 2000 = 3000 so now the question remains - 3000 is how much percentage of uneaten chocolates ( 8000 ) = 3000 * 100 / 8000 = 37.5 answer ( b )
Answer: b
Question (general): a school has 4 section of chemistry in class x having 60 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
Options: a ) 50 , b ) 52 , c ) 51 , d ) 53 , e ) none of the above
Rationale: "required average marks = 60 ã — 50 + 35 ã — 60 + 45 ã — 55 + 42 ã — 45 / 60 + 35 + 45 + 42 = 3000 + 2100 + 2475 + 1890 / 182 = 9465 â  „ 182 = 52 answer b"
Answer: b
Question (general): the number of employees in obelix menhir co . is a prime number and is less than 300 . the ratio of the number of employees who are graduates and above , to that of employees who are not , can possibly be : -
Options: a ) 101 : 88 , b ) 87 : 100 , c ) 110 : 111 , d ) 85 : 98 , e ) 97 : 84
Rationale: explanation : going through the given options , option 1 : - 101 : 88 = > 189 . [ divisible by 3 ] option 2 : - 87 : 100 = > 187 . [ divisible by 11 ] option 3 : - 85 : 98 = > 183 . [ divisible by 3 ] option 4 : - 97 : 84 = > 181 . [ prime number ] hence , only 181 is the prime number i . e the total number of employee in the company and the required ratio is 97 : 84 . answer : e
Answer: e
Question (gain): 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 ?
Options: a ) rs . 1020.80 , b ) rs . 1025 , c ) rs . 1055 , d ) data inadequate , e ) none of these
Rationale: "solution s . i . = rs . ( 956 - 825 ) = rs . 131 rate = ( 100 x 131 / 825 x 3 ) = 524 / 99 % new rate = ( 524 / 99 + 4 ) % = 920 / 99 % new s . i . = rs . ( 825 x 920 / 99 x 3 / 100 ) rs . 230 . ∴ new amount = rs . ( 825 + 230 ) = rs . 1055 . answer c"
Answer: c
Question (gain): mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 496.80 ?
Options: a ) 22 , b ) 27 , c ) 20 , d ) 21 , e ) 12
Rationale: "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 496.80 , discount = 621 - 496.80 = 124.20 discount % = 124.2 / 621 * 100 = 20 % . answer : c"
Answer: c
Question (geometry): a 45 ° - 45 ° - 90 ° right triangle has hypotenuse of length h . what is the area of the triangle t in terms of h ?
Options: a ) h / √ 2
b ) h / 2
c ) h / 4
d ) ( h ) ^ 2
e ) ( h ) ^ 2 / 4
Rationale: if . . . each of the two shorter sides = 3 , then the hypotenuse = h = 3 ( root 2 ) . the area t = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 3 ) ( 3 ) = 9 / 2 . so we ' re looking for an answer that = 9 / 2 when h = 3 ( root 2 ) . there ' s only one answer that matches . . . e
Answer: e
Question (geometry): the perimeter of a triangle is 40 cm and the in radius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 76 , b ) 88 , c ) 66 , d ) 55 , e ) 50
Rationale: "area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 40 / 2 = 50 cm 2 answer : e"
Answer: e
Question (physics): a man swims downstream 54 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "54 - - - 3 ds = 18 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 18 + 6 ) / 2 = 12 answer : e"
Answer: e
Question (general): the average of 11 results is 52 , if the average of first 6 results is 49 and that of the last 6 is 52 . find the sixth result ?
Options: a ) a ) 46 , b ) b ) 34 , c ) c ) 66 , d ) d ) 76 , e ) e ) 74
Rationale: 1 to 11 = 11 * 52 = 572 1 to 6 = 6 * 49 = 294 6 to 11 = 6 * 52 = 312 6 th = 294 + 312 – 572 = 34 answer : b
Answer: b
Question (general): sum of the squares of 3 no . is 138 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 21 , c ) 25 , d ) 26 , e ) 27
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 138 + 2 * 131 a + b + c = √ 400 = 20 a"
Answer: a
Question (general): the total of 324 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is :
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 324 - x ) . 0.20 × ( x ) + 0.25 ( 324 - x ) = 71 = > x = 200 . answer : d"
Answer: d
Question (other): 120 liters of a mixture contains milk and water in the ratio 4 : 2 . if 10 liters of this mixture be replaced by 10 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 8 : 6 , b ) 9 : 3 , c ) 9 : 4 , d ) 9 : 6 , e ) 8 : 2
Rationale: quantity of milk in 120 liters if mix = 120 * 4 / 6 = 80 liters quantity of milk in 130 liters of new mix = 80 + 10 = 90 liters quantity of water in it = 130 - 90 = 40 liters ratio of milk and water in new mix = 90 : 40 = 9 : 4 answer is c
Answer: c
Question (other): 170 kg of an alloy a is mixed with 250 kg of alloy b . if alloy a has lead and tin in the ratio 1 : 3 and alloy b has tin and copper in the ratio 3 : 5 , then the amount of tin in the new alloy is ?
Options: a ) 210.6 kg , b ) 221.3 kg , c ) 229.5 kg , d ) 110.8 kg , e ) 114 kg
Rationale: "quantity of tin in 170 kg of a = 170 * 3 / 4 = 127.5 kg quantity of tin in 250 kg of b = 250 * 3 / 8 = 93.75 kg quantity of tin in the new alloy = 127.5 + 93.75 = 221.25 kg answer is b"
Answer: b
Question (physics): a train 360 m long can cross an electric pole in 30 sec and then find the speed of the train ?
Options: a ) 88 kmph , b ) 43 kmph , c ) 72 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: "length = speed * time speed = l / t s = 360 / 30 s = 12 m / sec speed = 12 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 43 kmph answer : b"
Answer: b
Question (physics): a can do a piece of work in 4 hours ; b and c together can do it in 2 hours , which a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 2 hours , b ) 3 hours , c ) 4 hours , d ) 5 hours , e ) 6 hours
Rationale: "a ' s 1 hour work = 1 / 4 ; ( b + c ) ' s 1 hour work = 1 / 2 ; ( a + c ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 4 + 1 / 2 ) = 3 / 4 b ' s 1 hour work = ( 3 / 4 - 1 / 2 ) = 1 / 4 b alone will take 4 hours to do the work . answer : c"
Answer: c
Question (general): the maximum number of student amoung them 1204 pens and 840 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 91 , b ) 28 , c ) 56 , d ) 89 , e ) none of these
Rationale: "solution required number of student = h . c . f of 1204 and 840 = 28 . answer b"
Answer: b
Question (other): in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 7 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 105
Rationale: "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 7 * 180 / 12 = 105 ounces of water e"
Answer: e
Question (general): the product of three consecutive numbers is 120 . then the sum of the smallest two numbers is ?
Options: a ) 9 , b ) 15 , c ) 20 , d ) 38 , e ) 56
Rationale: "product of three numbers = 120 120 = 2 * 2 * 5 * 6 = 4 * 5 * 6 so , the three numbers are 4,5 and 6 . and sum of smallest of these two = 4 + 5 = 9 . answer : option a"
Answer: a
Question (gain): a company pays 12.5 % dividend to its investors . if an investor buys rs . 40 shares and gets 25 % on investment , at what price did the investor buy the shares ?
Options: a ) 20 , b ) 66 , c ) 18 , d ) 19 , e ) 01
Rationale: "explanation : dividend on 1 share = ( 12.5 * 40 ) / 100 = rs . 5 rs . 25 is income on an investment of rs . 100 rs . 5 is income on an investment of rs . ( 5 * 100 ) / 25 = rs . 20 answer : a"
Answer: a
Question (general): how many even number in the range between 10 to 140 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 31 , d ) 33 , e ) 44
Rationale: we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 140 using ap formula , we can say 140 = 10 + ( n - 1 ) * 2 or n = 66 . for 6 , 12,18 , . . . 138 using ap formula , we can say 138 = 12 + ( n - 1 ) * 6 or n = 22 . hence , only divisible by 2 but not 3 = 66 - 22 = 44 . hence , answer e
Answer: e
Question (general): the average of 15 result is 55 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th result ?
Options: a ) 760 , b ) 720 , c ) 700 , d ) 786 , e ) 797
Rationale: "sum of all the 13 results = 15 * 55 = 825 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 825 + 399 - 427 = 797 . e"
Answer: e
Question (physics): a train of length 250 m crosses a bridge of length 150 m in 32 seconds . what is the speed of train ?
Options: a ) 33 , b ) 27 , c ) 25 , d ) 22 , e ) 45
Rationale: "sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 150 ) = 32 x speed speed = 400 / 32 = 12.5 m / s = 45 km / h answer = e"
Answer: e
Question (general): a cricketer scored 142 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 57.75 % , b ) 54.54 % , c ) 63 % , d ) 70 % , e ) none of these
Rationale: "explanation : number of runs made by running = 142 - ( 12 x 4 + 2 x 6 ) = 142 - ( 60 ) = 82 now , we need to calculate 82 is what percent of 142 . = > 82 / 142 * 100 = 57.75 % answer : a"
Answer: a
Question (physics): a train running at the speed of 54 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 288 , b ) 279 , c ) 135 , d ) 272 , e ) 150
Rationale: "speed = 54 * 5 / 18 = 15 m / sec length of the train = speed * time = 15 * 9 = 135 m answer : c"
Answer: c
Question (general): one half of a two digit number exceeds its one third by 6 . what is the sum of the digits of the number ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 12 , e ) 15
Rationale: "explanation : x / 2 – x / 3 = 6 = > x = 6 3 + 6 = 9 b )"
Answer: b
Question (general): a box contains 5 pairs of shoes ( 10 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 92
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 20 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 9 ( as after taking one at random there are 9 shoes left and only one is the pair of the first one ) = 1 / 9 answer : c ."
Answer: c
Question (general): in a company of 16 employees , 8 employees earn $ 38,000 , 4 employees earn $ 42,000 , and the 4 highest - paid employees earn the same amount . if the average annual salary for the 16 employees is $ 44,000 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 54,000 , b ) $ 55,000 , c ) $ 56,000 , d ) $ 57,000 , e ) $ 58,000
Rationale: "8 * 38,000 + 4 * 42,000 + 4 x = 16 * 44,000 4 x = 704,000 - 304,000 - 168,000 4 x = 232,000 x = 58,000 the answer is e ."
Answer: e
Question (general): if the price of petrol increases by 32 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 25 % , b ) 20 % , c ) 24.2 % , d ) 33.33 % , e ) none of these
Rationale: explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 32 ) i . e 132 . now , his consumption should be reduced to : - = ( 132 − 100 ) / 132 ∗ 100 . hence , the consumption should be reduced to 24.2 % . answer : c
Answer: c
Question (geometry): 108 . triangle a ’ s base is 7 % greater than the base of triangle b , and a ’ s height is 7 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?
Options: a ) 9 % less , b ) 1 % less , c ) equal to each other , d ) 1 % more , e ) 2.1 % more
Rationale: "wish the question specified that we are talking about corresponding height . base of a = 8 / 7 * base of b height of a = 6 / 7 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 8 / 7 * 6 / 7 * area of b = 48 / 49 * area of b area of a is 2.1 % more than the area of b . answer ( e )"
Answer: e
Question (general): if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 64 ) which of these integers could be the value of z ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 8
Rationale: "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 64 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 65 incorrect c . 2 / 2 = 2 / 3 + 2 / 66 incorrect d . 2 / 3 = 2 / 4 + 2 / 69 incorrect e . 2 / 4 = 2 / 5 + 2 / 72 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case"
Answer: e
Question (other): praveen starts business with rs . 3360 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?
Options: a ) s . 7500 , b ) s . 8640 , c ) s . 8500 , d ) s . 9000 , e ) s . 6000
Rationale: let hari ’ s capital be rs . x . then , 3360 * 12 / 7 x = 2 / 3 = > 14 x = 120960 = > x = 8640 . answer : b
Answer: b
Question (general): the average ( arithmetic mean ) of 10 , 20 , and 60 is 5 more than the average of 10 , 40 , and what number ?
Options: a ) 25 , b ) 60 , c ) 50 , d ) 30 , e ) 40
Rationale: "a 1 = 90 / 3 = 30 a 2 = a 1 - 5 = 25 sum of second list = 25 * 3 = 75 therefore the number = 75 - 50 = 25 a"
Answer: a
Question (gain): jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: solution : first of all , notice the magic word “ approximately ” — the test - writer is letting us know estimation is perfectly fine . furthermore , the answer choices are nicely spread out , which will facilitate estimating . ok , get ready for some fast & furious estimation . the interest rate 3.96 % is an ugly number , so i ’ m going to approximate that as 4 % . it compounds semiannually , so that means that there ’ s 2 % every six months , and that happens four times in two years . well , 2 % of $ 10000 is $ 200 . if you get $ 200 , or a little more , on four occasions , that ’ s a little more than $ 800 in interest . we expect an answer slightly higher than $ 10800 , so of course ( b ) is just right . notice , i estimated so that everything up until the last sum was single - digit math . single - digit calculations are a good standard for which to strive when you are practicing estimation . by the way , if you find the bank that will do answer ( e ) , double your money in only two years , that ’ s terrific , but it probably is something wildly illegal , a ponzi scheme or worse ! in the real world , that just doesn ’ t happen . on word problems , especially in financial situations , you should always have your antenna up for what ’ s realistic or unrealistic . answer ( b )
Answer: b
Question (physics): 250 men work for 16 days and finish a work . how many men would do a job 3 times the previous one in 20 days ?
Options: a ) 700 , b ) 666 , c ) 600 , d ) 400 , e ) 800
Rationale: number of men needed to finish the required work ( variation , proportion method ) = 3 * 16 * 250 / 20 = 600 answer : c
Answer: c
Question (general): solution for 1.35 + . 123 + . 321
Options: a ) 2.91 , b ) 1.794 , c ) 1.338 , d ) 1.986 , e ) 1.999
Rationale: "1.35 + . 123 + . 321 = 0 0 = 0 - 1.35 - 0.123 - 0.321 0 = - 1.794 answer : b"
Answer: b
Question (gain): the population of a town increases 25 % and 15 % respectively in two consecutive years . after the growth the present population of the town is 1150 . then what is the population of the town 2 years ago ?
Options: a ) a ) 400 , b ) b ) 500 , c ) c ) 600 , d ) d ) 700 , e ) e ) 800
Rationale: explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1150 * 100 / 125 * 100 / 115 = 800 answer : option e
Answer: e
Question (general): if 16 machine can finish a job in 45 days , then how many more machines would be needed to finish the job in one - third less time ?
Options: a ) a . 3 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16
Rationale: "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 16 machines ( identical ones , i assume ) work simultaneously for 45 days , they will do a total of 16 * 45 machine - days of work . so the job requires 16 * 45 days of machine work in total . we instead want the job done in 1 / 3 less time , so in 30 days . so we ' ll need 16 * 36 / 30 = 19.2 ~ = 19 machines , or 3 additional machines . a"
Answer: a
Question (physics): two trains start simultaneously from opposite ends of a 160 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 160 - km trip in 5 hours . train y , travelling at a constant rate , completes the 160 - km trip in 3 hours . how many kilometers had train x traveled when it met train y ?
Options: a ) 56 , b ) 58 , c ) 60 , d ) 62 , e ) 64
Rationale: if the two trains cover a total distance d , then train x travels ( 3 / 8 ) * d while train y travels ( 5 / 8 ) * d . if the trains travel 160 km to the meeting point , then train x travels ( 3 / 8 ) * 160 = 60 km . the answer is c .
Answer: c
Question (gain): a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the total share of a & b in profit of rs . 12100 after a year ?
Options: a ) rs . 6030 , b ) rs . 4050 , c ) rs . 6050 , d ) rs . 7050 , e ) rs . 6080
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 a ' share = 3 / 10 * 12100 = 3630 b ' s share = 2 / 10 * 12100 = 2420 required total share = 3630 + 2420 = 6050 answer : c"
Answer: c
Question (physics): an athlete runs 200 metres race in 40 seconds . what is his speed ?
Options: a ) 23 , b ) 38 , c ) 18 , d ) 30 , e ) 28
Rationale: "speed = distance / time = 200 / 40 = 5 m / s = 5 * 18 / 5 = 3618 km / hr answer : c"
Answer: c
Question (gain): company p had 15 percent more employees in december than it had in january . if company p had 490 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 426 , c ) 410 , d ) 423 , e ) 445
Rationale: "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 490 j = 490 / 1.15 j = 49,000 / 115 = 426 thus b is the correct answer ."
Answer: b
Question (gain): the present worth of rs . 1404 due in two equal half - yearly instalments at 8 % per annum simple interest is :
Options: a ) rs . 1325 , b ) rs . 1300 , c ) rs . 1350 , d ) rs . 1500 , e ) none
Rationale: solution required sum = p . w . of rs . 702 due 6 month hence + p . w . of rs . 702 due 1 year hence = rs . [ ( 100 x 702 / 100 + 8 x 1 / 2 ) + ( 100 x 702 / 100 + ( 8 x 1 ) ) ] = rs . ( 675 + 650 ) = rs . 1325 . answer a
Answer: a
Question (general): the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 3 type b widgets , and the weight of 5 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6
Rationale: "5 b = 7 c and so b = 7 c / 5 7 a = 3 b and so a = 3 b / 7 = 3 c / 5 a + b = 3 c / 5 + 7 c / 5 = 10 c / 5 b + c = 7 c / 5 + c = 12 c / 5 the ratio of a + b : b + c = 10 : 12 = 5 : 6 the answer is e ."
Answer: e
Question (gain): a shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 4 a rupee . find his net profit or loss percent ?
Options: a ) 34 % , b ) 39 % , c ) 50 % , d ) 35 % , e ) 33 %
Rationale: "the total number of mangoes bought by the shopkeeper be 24 . if he buys 6 a rupee , his cp = 4 he selling at 4 a rupee , his sp = 6 profit = sp - cp = 6 - 4 = 2 profit percent = 2 / 4 * 100 = 50 % answer : c"
Answer: c
Question (general): in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 60 percent of the male and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25
Rationale: "percent of students who are 25 years old or older is 0.6 * 48 + 0.2 * 52 = ~ 39 , so percent of people who are less than 25 years old is 100 - 39 = 61 . answer : b ."
Answer: b
Question (physics): the cross - section of a cannel is a trapezium in shape . if the cannel is 15 m wide at the top and 4 m wide at the bottom and the area of cross - section is 1900 sq m , the depth of cannel is ?
Options: a ) 150 , b ) 200 , c ) 140 , d ) 240 , e ) 145
Rationale: "1 / 2 * d ( 15 + 4 ) = 1900 d = 200 answer : b"
Answer: b
Question (gain): 20 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
Options: a ) 14.4 , b ) 180 , c ) 50.4 , d ) 60 , e ) 90
Rationale: "20 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 20 ) * 100 = 180 square feet answer : option b"
Answer: b