Cheukting/mathqa huggingface dataset:
Question (physics): a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey ?
Options: a ) 288 , b ) 390 , c ) 287 , d ) 266 , e ) 161
Rationale: "the total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = sum of 10 terms in ap whose first term is 30 and last term is 48 = 10 / 2 [ 30 + 48 ] = 390 km . answer : b"
Answer: b
Question (other): in a sports club with 35 members , 15 play badminton and 18 play tennis and 5 do not play either . how many members play both badminton and tennis ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "15 + 18 = 33 but where as total number is 35 - 5 = 30 therefore answer is 33 - 30 = 3 hence answer is a"
Answer: a
Question (general): on day one , a store sold 96 pens . on each of the next d days , the company sold 44 pens . if the average daily sales of pens over this time period ( including day one ) is 48 pens , what is the value of d ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: 96 + 44 d = 48 ( d + 1 ) . 4 d = 48 . d = 12 . the answer is d .
Answer: d
Question (gain): walking 7 / 6 of his usual rate , a boy reaches his school 5 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 28 , c ) 99 , d ) 35 , e ) 66
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 5 - - - - - - - - - ? = 35 m answer : d"
Answer: d
Question (general): carrie likes to buy t - shirts at the local clothing store . they cost $ 9.15 each . one day , she bought 22 t - shirts . how much money did she spend ?
Options: a ) $ 150 , b ) $ 248.75 , c ) $ 200 , d ) $ 201.3 , e ) $ 190
Rationale: $ 9.15 * 22 = $ 201.3 . answer is d .
Answer: d
Question (gain): there were two candidates in an election . winner candidate received 56 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
Options: a ) 776 , b ) 1344 , c ) 299 , d ) 257 , e ) 125
Rationale: "w = 56 % l = 44 % 56 % - 44 % = 12 % 12 % - - - - - - - - 288 56 % - - - - - - - - ? = > 1344 answer : b"
Answer: b
Question (general): 243 has been divided into 3 parts such that half of the first part , one - third of the second part and one - fourth of the third part are equal . the largest part is ?
Options: a ) 12628 , b ) 23488 , c ) 26688 , d ) 26667 , e ) 12672
Rationale: explanation : ratio of their shares = ( 35000 * 8 ) : ( 42000 * 10 ) = 2 : 3 . reena ' s share rs . 31570 * ( 2 / 5 ) = rs . 12628 . answer : a ) 12628
Answer: a
Question (geometry): in the rectangular coordinate system , points ( 8 , 0 ) and ( – 8 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
Options: a ) 2
b ) 4
c ) 8
d ) 16
e ) none of the above
Rationale: the answer is c it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 8 c
Answer: c
Question (gain): a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party e . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: "s = 100 not ( e and b ) = 35 only e = 20 ( e and b ) / b = 1 / 2 let ( e and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans"
Answer: a
Question (general): if y ¤ w = y ^ ( 2 w ) for all positive integers , then ( 3 ¤ 4 ) ¤ 2 =
Options: a ) 3 ^ 8 , b ) 3 ^ 12 , c ) 3 ^ 16 , d ) 3 ^ 24 , e ) 3 ^ 32
Rationale: y ¤ w = y ^ ( 2 w ) 3 ¤ 4 = 3 ^ ( 8 ) ( 3 ¤ 4 ) ¤ 2 = ( 3 ^ 8 ) ¤ 2 = ( 3 ^ 8 ) ^ 4 = 3 ^ 32 correct option : e
Answer: e
Question (geometry): a circular rim a having a diameter of 45 inches is rotating at the rate of x inches / min . another circular rim b with a diameter of 30 inches is rotating at the rate of y inches / min . what is the value of y in terms of x , if both the rims reach their starting positions at the same time after every rotation .
Options: a ) 3 x / 2
b ) 4 x / 5
c ) 7 x / 5
d ) 5 x / 7
e ) 3 x / 4
Rationale: t = s 1 / v 1 = s 2 / v 2 or , 45 / x = 30 / y or , y = 45 x / 30 = 3 x / 2 ( answer a )
Answer: a
Question (gain): a typist uses a sheet measuring 20 cm by 30 cm lengthwise . if a margin of 2 cm is left on each side and a 3 cm margin on top and bottom , then percent of the page used for typing is
Options: a ) 40 , b ) 60 , c ) 64 , d ) 72 , e ) none
Rationale: solution area of the sheet = ( 20 x 30 ) cm ² = 600 cm ² area used for typing = [ ( 20 - 4 ) x ( 30 - 6 ) ] cm ² = 384 cm ² required percentage = ( 384 / 600 x 100 ) % = 64 % . answer c
Answer: c
Question (general): the h . c . f . of two numbers is 12 and their difference is 12 . the numbers are :
Options: a ) 66 , 78 , b ) 70 , 82 , c ) 94 , 106 , d ) 84 , 96 , e ) none of these
Rationale: explanation : out of the given numbers , the two with h . c . f . 12 and difference 12 are 84 and 96 . answer is d
Answer: d
Question (other): john , james and jim ' investment ratio in a business is 4 : 7 : 9 . if total total investment is 80000 . find jim ' s investment ?
Options: a ) 35000 , b ) 40000 , c ) 16000 , d ) 36000 , e ) 60000
Rationale: let the investment of john james and jim is 4 x 7 x and 9 x 4 x + 7 x + 9 x = 80000 20 x = 80000 x = 4000 jim ' investment = 9 * 4000 = 36000 answer : d
Answer: d
Question (physics): two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 3 days ?
Options: a ) 1 / 5 , b ) 1 / 1 , c ) 1 / 6 , d ) 1 / 3 , e ) 1 / 7
Rationale: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 3 days = 3 ( 1 / 18 ) = 1 / 6 . answer : c"
Answer: c
Question (gain): calculate how long it will take a swimmer to swim a distance of 8 km against the current of a river which flows at 1.4 km / hr , given that he can swim in still water at 3 km / h
Options: a ) 20 seconds , b ) 3 , c ) 4 , d ) 1 , e ) 5
Rationale: swim in still water at = 3 speed of river = 1.4 us = 3 - 1.4 = 1.6 distance = 8 t = 8 / 1.6 = 5 answer : e
Answer: e
Question (general): if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 39
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "p ã · 44 = 432 = > p = 432 * 44 = 19008 p / 39 = 19008 / 39 = 487 , remainder = 15 c"
Answer: c
Question (general): a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 8 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 8 , e ) 1 / 24
Rationale: "let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 8 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 8 ) = 3 x . the fraction of sensors which have been upgraded is x / ( x + 3 x ) = x / 4 x = 1 / 4 the answer is a ."
Answer: a
Question (general): if the operation ø is defined for all positive integers x and w by x ø w = ( 2 ^ x ) / ( 2 ^ w ) then ( 4 ø 2 ) ø 1 = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 4 ø 1 = 2 ^ 4 / 2 = 8 the answer is c ."
Answer: c
Question (general): if 3 ^ x * 4 ^ y = 531,441 and x – y = 12 , then x = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since 531,441 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 12 and y = 0 , then x = 12 . the answer is c ."
Answer: c
Question (gain): a man buys a cycle for rs . 2300 and sells it at a loss of 30 % . what is the selling price of the cycle ?
Options: a ) s . 1690 , b ) s . 1610 , c ) s . 1890 , d ) s . 1602 , e ) s . 1092
Rationale: "s . p . = 70 % of rs . 2300 = rs . 70 x 2300 / 100 = rs . 1610 answer : option b"
Answer: b
Question (physics): how many hours are there in 660 minutes ?
Options: a ) 60 hours , b ) 6 hours , c ) 30 hours , d ) 11 hours , e ) 10 hours
Rationale: "solution : number of minutes in 1 hour = 60 minutes so just divide 660 by 60 660 ã · 60 = 11 , so there are 11 hours in 660 minutes option d"
Answer: d
Question (physics): a is twice as good a workman as b and they took 9 days together to do the work b alone can do it in ?
Options: a ) 25 days , b ) 88 days , c ) 21 days , d ) 27 days , e ) 13 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 9 x = 1 / 27 = > 27 days answer : d"
Answer: d
Question (general): tom read a book containing 480 pages by reading the same number of pages each day . if he would have finished the book 5 days earlier by reading 16 pages a day more , how many days did tom spend reading the book ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: "say the number of days tom spent reading the book was dd . then : the number of pages he read per day would be 480 / d the number of pages he would read per day with an increased speed would be 480 / d − 5 e are told that the number of pages for the second case was 16 pages per day more , so 480 / d = 480 / d − 5 − 16 at this point it ' s much better to plug answer choices rather than solve for dd . answer choice cc fits : 480 / 15 = 32 = 480 / 15 − 5 − 16 answer : c"
Answer: c
Question (general): ajay and vijay have some marbles with them . ajay told vijay ` ` if you give me ' x ' marbles , both of us will have equal number of marbles ' ' . vijay then told ajay ` ` if you give me twice as many marbles , i will have 30 more marbles than you would ' ' . find ' x ' ?
Options: a ) 7 , b ) 5 , c ) 6 , d ) 4 , e ) 3
Rationale: if vijay gives ' x ' marbles to ajay then vijay and ajay would have v - x and a + x marbles . v - x = a + x - - - ( 1 ) if ajay gives 2 x marbles to vijay then ajay and vijay would have a - 2 x and v + 2 x marbles . v + 2 x - ( a - 2 x ) = 30 = > v - a + 4 x = 30 - - - ( 2 ) from ( 1 ) we have v - a = 2 x substituting v - a = 2 x in ( 2 ) 6 x = 30 = > x = 5 . answer : b
Answer: b
Question (general): the average of temperatures at noontime from monday to friday is 45 ; the lowest one is 42 , what is the possible maximum range of the temperatures ?
Options: a ) 15 , b ) 25 , c ) 40 , d ) 45 , e ) 75
Rationale: "there are 5 days so the sum of temperature can be 45 * 5 = 225 lowest is 42 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 42 = 168 . on the fifth day it is 225 - 168 = 57 range is therefore 57 - 42 = 15 answer a"
Answer: a
Question (general): david is 12 years older than his daughter rosy . in 4 years david will be twice as old as rosy . what is rosy current age .
Options: a ) 9 , b ) 10 , c ) 11 , d ) 8 , e ) 12
Rationale: "now : rosy = x , david = x + 12 in 4 years rosy = x + 4 , david = x + 12 + 4 or 2 ( x + 4 ) x + 16 = 2 x + 8 x = 8 rosy is 8 years old answer : d"
Answer: d
Question (gain): one - third of 1200 is what percent of 236 ?
Options: a ) 169.49 , b ) 30 , c ) 120.32 , d ) 125.32 , e ) 15.152
Rationale: "answer let one - third of 1200 is n % of 236 . ∵ 1200 / 3 = ( n x 236 ) / 100 ∴ n = ( 400 x 100 ) / 236 = 169.49 correct option : a"
Answer: a
Question (physics): if 2 is the remainder when m is divided by 5 , what is the remainder when 3 m is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: let ' s find a number which when divided by 5 leaves remainder 2 = 5 + 2 = 7 i . e . one possible value of m = 7 value of 3 m = 3 * 7 = 21 when em is divided by 5 then remainder = rem ( 21 / 5 ) = 1 answer : option b
Answer: b
Question (gain): the population of a town is 8100 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9000 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8100 × 100 / 90 × 100 / 90 = 10000 e )"
Answer: e
Question (general): average age of students of an adult school is 48 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
Options: a ) 1200 , b ) 160 , c ) 360 , d ) 240 , e ) none of these
Rationale: explanation : let the original no . of students be x . according to situation , 48 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 40 so , required no . of students after joining the new students = x + 120 = 160 . answer : b
Answer: b
Question (general): if 9 - 4 / x = 7 + 8 / x , then x =
Options: a ) 15 , b ) 6 , c ) 1 , d ) 5 , e ) 12
Rationale: we ' re given the equation 9 - 4 / x = 7 + 8 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we have to multiple 2 of the numbers to give them that denominator . . . 9 x - 4 x / x = 7 x + 8 x / x we can then eliminate that denominator , which gives us . . . . 9 x - 4 = 7 x + 8 12 = 2 x both 2 x and 12 have a common denominator of 2 , so we divide both sides by 2 for our final answer . . . 6 = x b
Answer: b
Question (physics): calculate the circumference of a circular field whose radius is 4 centimeters .
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "circumference c is given by c = 2 ï € r = 2 ï € * 4 = 8 ï € cm correct answer d"
Answer: d
Question (physics): it costs $ 4 for the first 1 / 4 hour to use the laundry machine at the laundromat . after the first ¼ hour it costs $ 12 per hour . if a certain customer uses the laundry machine for 3 hours and 25 minutes , how much will it cost him ?
Options: a ) $ 25 , b ) $ 32 , c ) $ 36 , d ) $ 40 . , e ) $ 42 .
Rationale: "3 hrs 25 min = 205 min first 15 min - - - - - - > $ 4 time left is 190 min . . . now , 60 min costs $ 12 1 min costs $ 12 / 60 190 min costs $ 12 / 60 * 190 = > $ 38 so , total cost will be $ 38 + $ 4 = > $ 42 hene answer will be ( e ) $ 42"
Answer: e
Question (other): the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 637 , krishan has ?
Options: a ) s . 2890 , b ) s . 2330 , c ) s . 3757 , d ) s . 1620 , e ) s . 2680
Rationale: "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 637 : n & there n = 289 x 637 / 49 = rs . 3757 answer : c"
Answer: c
Question (general): last week david spent 40 percent of his wages on recreation . this week , his wages are 5 percent less than last week ʼ s wages and he spent 50 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week
Options: a ) 118.75 % , b ) 128.75 % , c ) 116.75 % , d ) 117.75 % , e ) 114.75 %
Rationale: say david ' s wages last week were $ 100 , so he spent 0.40 * 100 = $ 40 on recreation ; this week ' s wages is 0.95 * 100 = $ 95 , so he spends 0.5 * 95 = $ 47.5 on recreation ; 47.5 / 40 = 1.1875 , hence the amount he spends on recreation this week is 118.75 % of the amount he spent on recreation last week : 40 * 1.1875 = 47.5 answer : a
Answer: a
Question (general): the data a and b are equal to the data subtracted c ; the data b is 3 times the data a ; if the data a is equal to 12 what is the sum of the data a , b and c ?
Options: a ) 86 , b ) 92 , c ) 84 , d ) 102 , e ) 96
Rationale: the equations raised . a + b = c b = 3 a a = 12 then b = 36 and c = 48 a + b + c = 96 answer : e
Answer: e
Question (gain): the population of a town is 30000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 4300 , b ) 19200 , c ) 5120 , d ) 5230 , e ) 5366
Rationale: "30000 × 80 / 100 × 80 / 100 = 19200 answer ; b"
Answer: b
Question (general): a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 150 more than a :
Options: a ) 2348 , b ) 7250 , c ) 4350 , d ) 1998 , e ) 2771
Rationale: "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 150 total earning = \ inline \ frac { 58 xy } { 100 } = 4350 answer : c ) rs . 4350"
Answer: c
Question (physics): a man can row downstream at 18 kmph and upstream at 6 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 9
Rationale: let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 6 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 24 = > x = 12 , y = 6 . answer : c
Answer: c
Question (other): the ratio of 3 numbers is 1 : 2 : 4 and the sum of their squares is 1701 . the sum of the numbers is ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9
Rationale: let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 1701 21 x ^ 2 = 1701 x ^ 2 = 81 x = 9 answer is e
Answer: e
Question (geometry): a lady builds 10 cm length , 18 cm width , and 4 cm height box using 12 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 107 , b ) 70 , c ) 78 , d ) 60 , e ) 111
Rationale: "number of cubes required = volume of box / volume of cube = 10 * 18 * 4 / 12 = 60 cubes answer : d"
Answer: d
Question (general): the sum of the first 80 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ?
Options: a ) 5,050 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600
Rationale: "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 80 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 80 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 80 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 8000 + 2500 = 10500 c is the answer ."
Answer: c
Question (physics): a 300 m long train crosses a platform in 45 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 287 , b ) 350 , c ) 828 , d ) 450 , e ) 122
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 45 = 50 / 3 3 x + 900 = 2250 = > x = 450 m . answer : d"
Answer: d
Question (other): in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 10 and the other one , that is cheaper , costs $ 3.5 . the factory holds a $ 45 worth stock of 11 modules . how many of the modules in the stock are of the cheaper kind ?
Options: a ) 30 , b ) 28 , c ) 25 , d ) 20 , e ) 10
Rationale: so the number of $ 3.50 modules must be 10 so that the leftover 1 modules are of $ 10 which will give a total value $ 45 . 10 * 3.50 + 1 * 10 = 35 + 10 = 45 answer : e
Answer: e
Question (general): the average salary of all the workers in a workshop is rs . 10000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 8000 . the total number of workers in the workshop is :
Options: a ) 14 , b ) 21 , c ) 88 , d ) 37 , e ) 29
Rationale: "explanation : lot the total number of workers be v then , 10000 v = ( 12000 * 7 ) + 8000 ( v - 7 ) < = > 2000 v = 28000 < = > v = 14 answer : a ) 14"
Answer: a
Question (general): a salt manufacturing company produced a total of 4000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?
Options: a ) 140 , b ) 149 , c ) 156 , d ) 195 , e ) 100
Rationale: "total production of salt by the company in that year = 4000 + 4100 + 4200 + . . . . + 5100 = 54600 . average monthly production of salt for that year = 54600 / 365 â ‰ ˆ 149 answer : b"
Answer: b
Question (physics): a little girl is numbering her collection of butterflies by placing single - digit stickers under each specimen . if the girl has 330 butterflies , how many stickers does she need ? ( the numbers are consecutive and the number of the first butterfly is 1 ) .
Options: a ) 882 , b ) 901 , c ) 1001 , d ) 1003 , e ) 1346
Rationale: for the first 9 butterflies we need 9 stickers . for the next 90 we need 2 stickers each or 180 stickers . for the next 900 butterflies we need 3 stickers each . the first 99 butterflies correspond to 189 stickers . subtract 99 from the total number of butterflies ( 330 ) . this leaves 231 butterflies that use 3 stickers each . so , multiply 231 by 3 to get 693 . add 693 to 189 stickers to get 882 stickers . answer : a
Answer: a
Question (general): a batsman in his 17 th innings makes a score of 80 , and thereby increases his average by 2 . what is his average after the 17 th innings ? he had never been ’ not out ’ .
Options: a ) 48 , b ) 37 , c ) 39 , d ) 43 , e ) 42
Rationale: "average score before 17 th innings = 80 - 2 × 17 = 46 average score after 17 th innings = > 46 + 2 = 48 answer : a"
Answer: a
Question (general): 19 times a number gives 342 . the number is
Options: a ) 18 , b ) 19 , c ) 16 , d ) none , e ) can not be determined
Rationale: "explanation : let the number be ' n ' 19 × n = 342 ⇒ n = 18 correct option : a"
Answer: a
Question (general): 1.45 , 2.56 , 4.78 , 8.11 , 12.55 , ( . . . . )
Options: a ) 17.3 , b ) 16.2 , c ) 15.3 , d ) 19.5 , e ) 18.1
Rationale: "explanation : 1.11 , 2.22 , 3.33 , 4.44 , 5.55 , hence 5.55 = 18.1 answer : e"
Answer: e
Question (general): how many positive integers less than 1000 are multiples of 5 but not of 4 or 7 ?
Options: a ) 114 , b ) 121 , c ) 122 , d ) 129 , e ) 136
Rationale: "there are 1000 / 5 = 200 multiples of 5 . now we have to find the number of multiples of 5 and 4 that is 20 between 0 to 1000 and 5 and 7 that is 35 between 0 to 1000 . multiples of 20 = 1000 / 20 = 50 multiples . and multiples of 35 = 1000 / 35 = 28.5 so 28 multiples of 35 . so multiples of 5 between o to 1000 not including multiples of 20 and 35 are equal to 200 - 78 = 122 multiples . so the answer is c ."
Answer: c
Question (gain): a trader bought a car at 20 % discount on its original price . he sold it at a 45 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) a ) 10 % , b ) b ) 12 % , c ) c ) 16 % , d ) d ) 20 % , e ) e ) 22 %
Rationale: "original price = 100 cp = 80 s = 80 * ( 145 / 100 ) = 116 100 - 116 = 16 % c )"
Answer: c
Question (geometry): the diagonal of the floor of a rectangular closet is 7 feet . the shorter side of the closet is 4 feet . what is the area of the closet in square feet ?
Options: a ) 20 sq . ft
b ) 27 sq . ft
c ) 37 sq . ft
d ) 47 sq . ft
e ) 57 sq . ft
Rationale: other side = 15 2 - 9 2 2 2 ft = 225 - 81 4 4 ft = 144 4 ft = 6 ft . area of closet = ( 6 x 4.5 ) sq . ft = 27 sq . ft . b )
Answer: b