Cheukting/mathqa huggingface dataset:
Question (other): in a group of 90 students , 30 are taking history , and 32 are taking statistics . if 59 students are taking history or statistics or both , then how many students are taking history but not statistics ?
Options: a ) 9 , b ) 19 , c ) 33 , d ) 27 , e ) 31
Rationale: "number of students taking history = h = 30 number of students taking statistics = s = 32 total number of students = t = 90 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 90 - 59 = 31 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 90 = 30 + 32 + 31 - x or x = 3 now , number of students taking only history will be h - x or 36 - 3 = 33 answer : - c"
Answer: c
Question (gain): calculate how long it will take a swimmer to swim a distance of 12 km against the current of a river which flows at 1.2 km / hr , given that he can swim in still water at 5 km / h
Options: a ) 3.26 , b ) 3.16 , c ) 2.34 , d ) 3.98 , e ) 3.17
Rationale: "swim in still water at = 5 speed of river = 1.2 us = 5 - 1.2 = 3.8 distance = 12 t = 12 / 3.8 = 3.16 answer : b"
Answer: b
Question (geometry): the ratio of the volumes of two cubes is 1331 : 2197 . what is the ratio of their total surface areas ?
Options: a ) 121 : 169 , b ) 169 : 122 , c ) 81 : 124 , d ) 81 : 126 , e ) 81 : 129
Rationale: "ratio of the sides = 3 √ 1331 : 3 √ 2197 = 11 : 13 ratio of surface areas = 11 ^ 2 : 13 ^ 2 = 121 : 169 answer : option a"
Answer: a
Question (general): find the value of ( 100 + 20 / 90 ) × 90
Options: a ) 4520 , b ) 9100 , c ) 9150 , d ) 8120 , e ) 9020
Rationale: "( 9000 + 20 ) / 90 * 90 = 9020 answer : e"
Answer: e
Question (general): a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 112 . what was the number he chose ?
Options: a ) 123 , b ) 267 , c ) 125 , d ) 267 , e ) 120
Rationale: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 112 x = 125 answer : c"
Answer: c
Question (physics): a train which has 500 m long , is running 100 kmph . in what time will it cross a person moving at 10 kmph in same direction ?
Options: a ) 20 sec , b ) 25 sec , c ) 30 sec , d ) 35 sec , e ) 40 sec
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 500 / ( ( 100 - 10 ) ( 5 / 18 ) = 500 / 90 * ( 5 / 18 ) = 500 / 25 = 20 sec answer : a"
Answer: a
Question (general): how many multiples of 3 are there between 15 and 246 ?
Options: a ) 128 , b ) 94 , c ) 89 , d ) 76 , e ) 60
Rationale: "it should be mentioned whether 15 and 246 are inclusive . if 15 and 246 are inclusive , then the answer is ( 246 - 15 ) / 3 + 1 = 78 . if 15 and 246 are not inclusive , then the answer is ( 243 - 18 ) / 3 + 1 = 76 . since oa is d , then we have not inclusive case ."
Answer: d
Question (geometry): the area of a square land is a square feet and the perimeter is p feet . if 5 a = 10 p + 45 , what is the perimeter of the land , in feet ?
Options: a ) 18
b ) 56
c ) 40
d ) 36
e ) 64
Rationale: you can also solve this via using the given numbers in the answer choices ! of course you need to be aware of the basic properties as outlined by the other posts above ( a = x ^ 2 and p = 4 x ) starting with b you will notice that x = 14 is way too big for your area ( 14 ^ 2 ) and will not satisfy : 5 a = 10 p + 45 or a = 2 p + 9 - - > eliminate b and e now pick d ( its either too big , then its a , or too small then you know its c or it is b itsself ) and picking d indeed solves the problem ! ( 36 / 4 - - > 9 ; a = 9 ^ 2 = 81 and 81 = 2 x 36 + 9 )
Answer: d
Question (geometry): a cube of edge 16 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?
Options: a ) 6 cm , b ) 8.25 cm , c ) 13.65 cm , d ) 15.12 cm , e ) 20.62 cm
Rationale: "increase in volume = volume of the cube = 16 * 16 * 16 cm ^ 3 rise in water level = volume / area = 16 * 16 * 16 / 20 * 15 = 13.65 cm answer is c"
Answer: c
Question (general): find the value of ( 45 + 23 / 89 ) × 89
Options: a ) 4028 , b ) 4026 , c ) 4248 , d ) 4538 , e ) 9028
Rationale: "= ( 45 + 23 / 89 ) × 89 = ( 4005 + 23 ) / 89 × 89 = 4028 / 89 × 89 = 4028 answer is a ."
Answer: a
Question (general): the average age of father and his two sons is 24 years . 5 years ago , the average age of the two sons was 15 years . if the difference between the ages of the two sons is 4 years , what is the present age of the father ?
Options: a ) 45 , b ) 32 , c ) 47 , d ) 48 , e ) 49
Rationale: the total present age of father and two sons is 3 x 24 = 72 yrs the total present age of sons is ( 15 + 5 ) x 2 = 40 years so , present age of father is 72 â € “ 40 = 32 yrs answer b
Answer: b
Question (general): a caterer ordered 225 ice - cream bars and 125 sundaes . if the total price was $ 200.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?
Options: a ) $ 0.52 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60
Rationale: let price of a sundae = s price of ice cream bar = . 6 $ 225 * . 6 + 125 * s = 200 = > 125 * s = 65 = > s = 0.52 answer a
Answer: a
Question (general): what is the remainder when 3 ^ 26 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of powers of 3 follow a repeating cycle of four : { 3 , 9 , 7 , 1 } 26 has the form 4 k + 2 , so the units digit of 3 ^ 26 is 9 . the remainder when dividing by 5 is 4 . the answer is e ."
Answer: e
Question (general): 15.06 * 0.00001 = ?
Options: a ) 15060000 , b ) 0.0001506 , c ) 0.01506 , d ) 0.1506 , e ) none of these
Rationale: "explanation : clearly after decimal 7 digits should be there . option b"
Answer: b
Question (general): a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 50 as remainder . find the no . is ?
Options: a ) 145646 , b ) 236578 , c ) 645353 , d ) 456546 , e ) 220050
Rationale: "( 555 + 445 ) * 2 * 110 + 50 = 220000 + 50 = 220050 e"
Answer: e
Question (general): if p and q are prime numbers , how many divisors does the product p ^ 4 * q ^ 5 have ?
Options: a ) 30 , b ) 40 , c ) 45 , d ) 50 , e ) 56
Rationale: when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is a . 5 * 6 = 30
Answer: a
Question (gain): if 20 % of a number = 300 , then 120 % of that number will be ?
Options: a ) 20 , b ) 120 , c ) 360 , d ) 1800 , e ) 1820
Rationale: "let the number x . then , 20 % of x = 300 x = ( 300 * 100 ) / 20 = 1500 120 % of x = ( 120 / 100 * 1500 ) = 1800 . answer : d"
Answer: d
Question (physics): a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 5 days . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 3 , e ) 5 / 2
Rationale: "b work 1 / 8 * 5 = 5 / 8 remaining work = 1 - 5 / 8 = 3 / 8 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 take remaining work is done in = 8 / 3 * 1 / 4 = 2 / 3 days answer : b"
Answer: b
Question (physics): a contractor undertook to do a certain piece of work in 6 days . he employed certain number of men , but 5 of them being absent from the very first day , the rest could finish the work in 10 days . the number of men originally employed were :
Options: a ) 12 , b ) 10 , c ) 13 , d ) 11 , e ) none of these
Rationale: explanation : let there be x men at the beginning . less men , more days ( indirect proportion ) 12 : 6 : : x : ( x - 5 ) 12 ( x - 5 ) = 6 x < = > 6 x = 60 x = 10 answer : b
Answer: b
Question (general): a card game called “ high - low ” divides a deck of 52 playing cards into 2 types , “ high ” cards and “ low ” cards . there are an equal number of “ high ” cards and “ low ” cards in the deck and “ high ” cards are worth 2 points , while “ low ” cards are worth 1 point . if you draw cards one at a time , how many ways can you draw “ high ” and “ low ” cards to earn 7 points if you must draw exactly 5 “ low ” cards ?
Options: a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "great question ravih . this is a permutations problem ( order matters ) with repeating elements . given thatlowcards are worth 1 pt andhigh cards 2 pts , and you must draw 3 low cards , we know that you must also draw 1 high card . the formula for permutations problems with repeating elements isn ! / a ! b ! . . . where n represents the number of elements in the group and a , b , etc . represent the number of times that repeating elements are repeated . here there are 4 elements and thelowcard is repeated 3 times . as a result , the formula is : 6 ! / 5 ! which represents ( 6 * 5 * 4 * 3 * 2 * 1 ) / ( 5 * 4 * 3 * 2 * 1 ) which simplifies to just 6 , giving you answer a ."
Answer: a
Question (physics): one gear of pulley rotates at a speed of 3 rev / sec another gear roates at 5 rev / sec . if both start together after how many seconds will they be together again
Options: a ) 3 sec , b ) 5 sec , c ) 15 sec , d ) 20 sec , e ) 25 sec
Rationale: 3 rotates 3 , 6,9 , 12,15 5 rotates 5 , 10,15 ans is 15 answer : c
Answer: c
Question (general): a group of n students can be divided into equal groups of 3 with 1 student left over or equal groups of 6 with 1 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 33 , b ) 46 , c ) 49 , d ) 53 , e ) 86
Rationale: "3 x + 1 = 6 y + 1 . . . . . . . . . . . ie : 3 x - 6 y = 0 x , y must be > 1 and y is even ie ( 2 , 4,6 , . . etc ) if y = 2 thus x = 4 and thus n = 13 if y = 4 thus x is = 8 and thus n = 25 13 + 25 = 38 e"
Answer: e
Question (gain): one type of liquid contains 10 % of water and the second type of liquid contains 15 % of water . a glass is filled with 5 parts of 1 st liquid and 2 parts of 2 nd liquid . the percentage of water in the new mixture in the glass is ?
Options: a ) 5.6 % , b ) 11.4 % , c ) 15.6 % , d ) 21.3 % , e ) 18.9 %
Rationale: "required percentage = ( 10 % of 5 + 15 % of 2 ) / 5 + 2 * 100 = 0.8 / 7 * 100 = 11.4 % answer is b"
Answer: b
Question (geometry): a cylindrical can has a radius of 3 centimeters and a height of 24 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ?
Options: a ) 16 pi
b ) 64 pi
c ) 96 pi
d ) 144 pi
e ) 576 pi
Rationale: they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 3 * 24 = 144 pi answer is d .
Answer: d
Question (other): mala and usha shared their water from a bottle . if mala and usha both drank for the same amount of time , but usha only drank 2 / 10 of the total bottle , what was the ratio of mala and usha speed ?
Options: a ) 1 : 4 , b ) 2 : 5 , c ) 4 : 1 , d ) 3 : 5 , e ) 2 : 3
Rationale: the answer is suppose to be c . 4 : 1 . it ' s from the gmatprep answer : option c
Answer: c
Question (geometry): the floor of a rectangular room is 18 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :
Options: a ) 124 m 2 , b ) 126 m 2 , c ) 136 m 2 , d ) 158 m 2 , e ) none of these
Rationale: "area of the outer rectangle = 22 ã — 16 = 352 m 2 area of the inner rectangle = 18 ã — 12 = 216 m 2 required area = ( 352 â € “ 216 ) = 136 m 2 answer c"
Answer: c
Question (general): the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 84 , and the average of the female students ’ grades was 92 , how many female students took the test ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 21 , e ) 24
Rationale: "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 84 thus m = 672 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 672 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 24 ans : e"
Answer: e
Question (probability): a box contains 21 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is
Options: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 19 , d ) 21 / 95 , e ) 31 / 88
Rationale: "solution p ( none is defective ) = 17 c 2 / 21 c 2 = 57 / 88 . p ( at least one is defective ) = ( 1 - 57 / 88 ) = 31 / 88 . answer e"
Answer: e
Question (physics): p , q and r together earn rs . 1710 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ?
Options: a ) s . 40 , b ) s . 60 , c ) s . 90 , d ) s . 100 , e ) s . 120
Rationale: "explanation : amount earned by p , q and r in 1 day = 1710 / 9 = 190 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + 130 - 190 = 60 = > amount earned by r in 1 day = 60 answer : option b"
Answer: b
Question (gain): simple interest on a certain sum at a certain annual rate of interest is 1 / 9 of the sum . if the numbers representing rate percent and time in years be equal , then the rate of interest is :
Options: a ) 5 , b ) 8 , c ) 3 1 / 3 , d ) 2 2 / 3 , e ) none of these
Rationale: explanation : let sum = x . then , s . i . = x / 9 let rate = r % and time = r years . [ x * r * r / 100 ] = x / 9 ? r ^ 2 = 100 / 9 r = 10 / 3 = 3 1 / 3 . hence , time = 3 1 / 3 % . answer : c
Answer: c
Question (gain): a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 32 . find the profit percentage ?
Options: a ) 80 % , b ) 50 % , c ) 59 % , d ) 40 % , e ) 60 %
Rationale: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 160 ( 32 * 5 ) profit percentage = ( 160 - 100 ) / 100 * 100 = 60 % answer : e"
Answer: e
Question (gain): a fraudulent dairy guy declares to market his dairy at price range but he combined it with water and therefore benefits 25 % . the percentage of water in the combination is :
Options: a ) 20 % , b ) 30 % , c ) 50 % , d ) 35 % , e ) 60 %
Rationale: explanation : - > if capability price of 1 l of milk = rs . 1 and s . price of 1 l of combination = rs . 1 benefits = 20 % capability price of 1 l of combination = [ ( 100 / 100 + 25 ) * 1 ] = rs . 100 / 125 = rs . 4 / 5 - > from the rule of allegation i . capability price of 1 l of water = 0 ii . capability price of 1 l of milk = 1 iii . ( p ) = 4 / 5 iv . d – m = 1 – 4 / 5 = 1 / 5 v . m – c = 4 / 5 – 0 = 4 / 5 ratio of milk to water = 4 / 5 : 1 / 5 = 4 : 1 % of water in the combination = ( 1 / 5 x 100 ) % = 20 % answer : a
Answer: a
Question (general): 49 ã — 49 = 7 ^ ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 16 , e ) none of these
Rationale: 49 ã — 49 = 7 ? or , 7 ( 2 ) ã — 7 ( 2 ) = 7 ? or 7 ( 4 ) = 7 ? or , ? = 4 answer a
Answer: a
Question (general): a batsman in his 12 th inning makes a score of 60 and their by increasing his average by 4 . what is his average after the 12 th inning ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: "11 x + 60 = 12 ( x + 4 ) x = 12 + 4 = 16 answer : b"
Answer: b
Question (general): find the ones digit of 73 ^ 351
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "the units digit of 73 ^ 351 will be the same as the units digit of 3 ^ 351 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 351 = 348 + 3 = ( multiple of 4 ) + 3 , then the units digit of 3 ^ 351 will be the third number in the pattern thus 7 . answer : d ."
Answer: d
Question (general): 5 is added to a certain number , the sum is multiplied by 7 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 66 . what is the number ?
Options: a ) 21 , b ) 20 , c ) 22 , d ) 30 , e ) 45
Rationale: let number is x . when 5 added to it , = ( x + 5 ) 7 multiplied to sum , = 7 * ( x + 5 ) now , = [ { 7 * ( x + 5 ) } / 5 ] and , = [ { 7 * ( x + 5 ) } / 5 ] - 5 according to question , [ { 7 * ( x + 10 ) } / 5 ] - 5 = half of 66 [ ( 7 x + 35 ) / 5 ) = 33 + 5 7 x + 35 = 38 * 5 x = 155 / 7 x = 22.14 = 22 so , required number is : 22 . answer : c
Answer: c
Question (gain): john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 17 , what was the price before the first discount ?
Options: a ) $ 45.10 , b ) $ 30.22 , c ) $ 28.44 , d ) $ 67.54 , e ) $ 65.23
Rationale: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 17 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 17 solve for x x = $ 30.22 correct answer b"
Answer: b
Question (gain): if a trader sold two cars each at rs . 325475 and gains 15 % on the first and loses 15 % on the second , then his profit or loss percent on the whole is ?
Options: a ) 1.44 % , b ) 1.74 % , c ) 1.84 % , d ) 1.97 % , e ) 2.25 %
Rationale: "sp of each car is rs . 325475 , he gains 15 % on first car and losses 15 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 15 ) ( 15 ) / 100 % = 1.44 % answer : e"
Answer: e
Question (physics): a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 5 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 487 , c ) 481 , d ) 729 , e ) 600
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 5 = 480 answer : e"
Answer: e
Question (general): an investor can sell her microtron stock for 36 $ per share and her dynaco stock for 60 $ per share , if she sells 300 shares altogether , some of each stock , at an average price per share of 40 $ , how many shares of dynaco stock has she sold ?
Options: a ) 50 , b ) 75 , c ) 92 , d ) 136 , e ) 184
Rationale: "w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) = ( 60 - 40 ) / ( 40 - 36 ) = 20 / 4 = 5 / 1 = number of microtron stocks / number of dynaco stocks so for every 5 microtron stock , she sold 1 dynaco stock . so out of 300 total stocks , ( 1 / 5 ) th i . e . 300 / 6 = 50 must be dynaco stock . answer ( a )"
Answer: a
Question (other): in township k , 1 / 5 of the housing units are equipped with cable television . if 1 / 10 of the housing units , including 1 / 3 of those that are equipped with cable television , are equipped with videocassette recorders , what fraction of the housing units have neither cable television nor videocassette recorders ?
Options: a ) 23 / 30 , b ) 11 / 15 , c ) 7 / 10 , d ) 1 / 6 , e ) 2 / 15
Rationale: let total housing units = 5 x . as per question , equipped with cable tv = x equipped with vcr = x / 2 , which includes x / 3 ctv . so , only vcr = x / 2 - x / 3 = x / 6 . so , cable tv + vcr = x + x / 6 = 7 x / 6 no cable tv and vcr = 5 x - 7 x / 6 = 23 x / 6 . fraction = 23 x / ( 6 * 5 x ) = 23 / 30 . hence , a
Answer: a
Question (general): every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word . what is the number value of the word ` ` hen ' ' ?
Options: a ) 69 , b ) 72 , c ) 75 , d ) 78 , e ) 81
Rationale: "` ` hen ' ' = ( 8 + 5 + 14 ) * 3 = 81 . the answer is e ."
Answer: e
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 16 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
Options: a ) 10 min . , b ) 41 min . , c ) 27 min . , d ) 23 min . , e ) 25 min .
Rationale: "the ratio is 2 : 3 = gym : ride , so ( 16 ) ( 3 / 2 ) = 24 minutes at the gym , and 24 + 16 = 40 minutes exercise , so ( 2 / 3 ) ( 40 ) = 27 minutes yoga . answer : c"
Answer: c
Question (physics): a cistern which could be filled in 8 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 99 hrs , c ) 55 hrs , d ) 90 hrs , e ) 40 hrs
Rationale: "1 / 8 - 1 / x = 1 / 10 = > 40 hrs answer : e"
Answer: e
Question (physics): a train travels from new york to chicago , a distance of approximately 270 miles , at an average rate of 30 miles per hour and arrives in chicago at 6 : 00 in evening , chicago time . at what hour in the morning , new york time , did the train depart for chicago ? ( note : chicago time is one hour earlier than new york time )
Options: a ) 3 : 00 , b ) 4 : 00 , c ) 10 : 00 , d ) 6 : 00 , e ) 7 : 00
Rationale: "6 : 00 in evening in chicago = 7 : 00 in evening in new york . so , the train was in chicago 7 : 00 in the evening , new york time . the trip took t = d / r = 270 / 30 = 9 hours . therefore , the train depart from new york at 7 : 00 - 9 hours = 10 : 00 in the morning , new york time . answer : c ."
Answer: c
Question (gain): in a certain pond , 35 fish were caught , tagged , and returned to the pond . a few days later , 35 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 ) 875 , d ) 2500 , e ) 10 000
Rationale: "if x is total number of fish in the pond : 4 = 35 / x * 100 = > x = 875 so answer is c"
Answer: c
Question (gain): a sum fetched a total simple interest of rs . 4016.25 at the rate of 1 % p . a . in 9 years . what is the sum ?
Options: a ) 42315 , b ) 42877 , c ) 44625 , d ) 38925 , e ) 22887
Rationale: "principal = ( 100 * 4016.25 ) / ( 1 * 9 ) = rs . 44625 . answer : c"
Answer: c
Question (general): average expenditure of a person for the first 3 days of a week is rs . 320 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
Options: a ) 350 , b ) 370 , c ) 390 , d ) 360 , e ) none
Rationale: explanation : assumed mean = rs . 320 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 320 + rs . 40 = rs . 360 correct option : d
Answer: d
Question (gain): a bookstore has a shelf that contains biographies which normally sell for $ 20 each and mysteries that normally sell for $ 12 each . during a sale , the biographies and mysteries are discounted at different rates so that a customer saves a total of $ 19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries . if the sum of the discount rates for the two types of books is 30 percent , what is the discount rate on mysteries ?
Options: a ) 17.18 % , b ) 12 % , c ) 13 % , d ) 14 % , e ) 15 %
Rationale: "let b be the discount on biographies and m be the discount on mysteries so . , b + m = 0.30 - - - - - ( 1 ) and ( 20 * 5 + 12 * 3 ) - ( 20 * 5 * ( 1 - b ) + 12 * 3 * ( 1 - m ) ) = 19 - - > 100 ( 1 - ( 1 - b ) ) + 36 ( 1 - ( 1 - m ) = 19 100 b + 36 m = 19 - - - - - - ( 2 ) solving 12 . , we get m = 0.1718 = 17.18 a"
Answer: a