Cheukting/mathqa huggingface dataset:
Question (general): a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 75 , the runs scored by c are ?
Options: a ) 11 , b ) 18 , c ) 45 , d ) 17 , e ) 12
Rationale: "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 15 / 25 * 75 = 45 answer : c"
Answer: c
Question (general): if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 9 , what is the least possible value of n ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 12 , e ) 7
Rationale: we need at least 2 factors of three , which means n must be at least 6 , so b is the correct answer .
Answer: b
Question (general): √ 289 - √ 625 ÷ √ 25 is equal to ?
Options: a ) 17 , b ) 15 , c ) 12 , d ) - 8 / 5 , e ) none
Rationale: answer √ 289 - √ 625 ÷ √ 25 = √ 17 x 17 - √ 25 x 25 ÷ √ 5 x 5 = 17 - 25 ÷ 5 = 17 - 5 = 12 correct option : 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 83 , 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 ) 28
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 = 83 thus m = 664 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 664 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 28 ans : e
Answer: e
Question (gain): what is the compound interest on rs . 9500 at 6 % p . a . compounded half - yearly for 1 1 / 2 years .
Options: a ) 810.91 , b ) 840.91 , c ) 880.91 , d ) 887.91 , e ) 980.91
Rationale: "compound interest : a = p ( 1 + r / n ) nt a = 10 , 380.91 c . i . > > 10 , 380.91 - 9500 > > rs . 880.91 answer : c"
Answer: c
Question (gain): a and b ’ s salaries together amount to rs . 4,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is b ’ s salary ?
Options: a ) 2777 , b ) 1000 , c ) 2789 , d ) 2776 , e ) 2881
Rationale: "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 1000 4 b = 1000 = > b = 1000 answer b"
Answer: b
Question (general): the population of a bacteria culture doubles every 6 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 54 , e ) 18
Rationale: "this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 6 minutes so answer is 9 * 6 = 54 minutes answer ( d )"
Answer: d
Question (general): can you solve it ? 2 + 3 = 8 , 3 + 7 = 27 , 4 + 5 = 32 , 5 + 8 = 60 , 6 + 7 = 72 , 7 + 8 = ? ?
Options: a ) 68 , b ) 78 , c ) 88 , d ) 98 , e ) 56
Rationale: 2 + 3 = 2 * [ 3 + ( 2 - 1 ) ] = 8 3 + 7 = 3 * [ 7 + ( 3 - 1 ) ] = 27 4 + 5 = 4 * [ 5 + ( 4 - 1 ) ] = 32 5 + 8 = 5 * [ 8 + ( 5 - 1 ) ] = 60 6 + 7 = 6 * [ 7 + ( 6 - 1 ) ] = 72 therefore 7 + 8 = 7 * [ 8 + ( 7 - 1 ) ] = 98 x + y = x [ y + ( x - 1 ) ] = x ^ 2 + xy - x correct answer is d ) 98
Answer: d
Question (general): if the remainder is 10 when positive integer n is divided by 14 , what is the remainder when n is divided by 7 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "assume x is quotient here , n = 14 x + 7 - - - - - - - - - - ( 1 ) and n = 7 x + ? we can also write equation ( 1 ) as : n = ( 14 x + 7 ) + 3 . ie 7 ( 2 x + 1 ) + 3 ie the first term is perfectly divisible by 7 . so , the remainder left is 3 . so , answer ( d ) is right choice ."
Answer: d
Question (general): if x ^ 2 + 1 / x ^ 2 = 2 , what is the value of x ^ 4 + 1 / x ^ 4 ?
Options: a ) 10 , b ) 2 , c ) 4 , d ) 16 , e ) 18
Rationale: important : i notice that if we square x ² , we get x ⁴ , and if we square 1 / x ² , we get 1 / x ⁴ , so let ' s see what happens if we take the equation x ² + 1 / x ² = 2 andsquareboth sides : ( x ² + 1 / x ² ) ² = 4 so , ( x ² + 1 / x ² ) ( x ² + 1 / x ² ) = 4 expand to get : x ⁴ + 1 + 1 + 1 / x ⁴ = 4 simplify : x ⁴ + 1 / x ⁴ = 2 answer : b
Answer: b
Question (general): a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 12 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 12 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?
Options: a ) 443 , b ) 450 , c ) 460 , d ) 468 , e ) 475
Rationale: "total number of installments = 52 payment per installment for the first 12 installments = 410 payment per installment for the remaining 32 installments = 410 + 65 = 475 average = ( 12 * 410 + 40 * 475 ) / 52 = 460 answer c"
Answer: c
Question (gain): at what rate percent of simple interest will a sum of money double itself in 22 years ?
Options: a ) 6.54 % , b ) 4.54 % , c ) 8 . 2 % , d ) 4.94 % , e ) 5.54 %
Rationale: "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 22 ) = 100 / 22 = 4.54 % answer : b"
Answer: b
Question (geometry): consider a square of diagonal length d . let another square be formed with d as its side . find the ratio of the area of the bigger square to that of the smaller square .
Options: a ) 2
b ) 3
c ) 4
d ) 16
e ) 41
Rationale: d ^ 2 / ( 1 / 2 ) * d ^ 2 = 2 answer : a
Answer: a
Question (general): find the missing value : ? - 1936248 = 1635773
Options: a ) 3572021 , b ) 3570221 , c ) 3572012 , d ) 3752012 , e ) none of them
Rationale: "let x - 1936248 = 1635773 . then , x = 1635773 + 1936248 = 3572021 answer is a ."
Answer: a
Question (general): the tax on a commodity is diminished by 14 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2.1 % , b ) 8.1 % , c ) 5.1 % , d ) 6.1 % , e ) 1.1 %
Rationale: "100 * 100 = 10000 86 * 115 = 9890 - - - - - - - - - - - 10000 - - - - - - - - - - - 110 100 - - - - - - - - - - - ? = > 1.1 % decrease answer : e"
Answer: e
Question (general): the sum of the ages of 4 children born at the intervals of 5 years each is 58 years . what is the age of the youngest child ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) none of these , e ) can not be determined
Rationale: "explanation : let x = the youngest child . each of the other four children will then be x + 5 , x + 10 , x + 15 we know that the sum of their ages is 58 . so , x + ( x + 5 ) + ( x + 10 ) + ( x + 15 ) = 58 x = 7 the youngest child is 4 years old . answer : a"
Answer: a
Question (general): in a party every person shakes hands with every other person . if there were a total of 136 handshakes in the party then what is the number of persons present in the party ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 136 n ( n - 1 ) / 2 = 136 â ˆ ´ n = 17 answer : c"
Answer: c
Question (general): set a consists of all the prime numbers between 12 and 32 . what is the range of set a ?
Options: a ) 12 , b ) 18 , c ) 16.6 , d ) 17 , e ) 23
Rationale: "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 31 lowest number = 13 range = highest - lowest = 31 - 13 = 18 option b"
Answer: b
Question (general): caleb spends $ 74.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?
Options: a ) 5 , b ) 10 , c ) 20 , d ) 40 , e ) 49
Rationale: "solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 74.50 . by solving the equations y = 49 . ans e ."
Answer: e
Question (general): the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 40 degrees . if the temperature on monday was 42 degrees . find the temperature on friday ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 12 , e ) 16
Rationale: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 40 = 160 m = 42 tu + w + th = 192 - 42 = 150 f = 160 – 150 = 10 answer : c"
Answer: c
Question (physics): if eight machines working at the same rate can do 3 / 4 of a job in 30 minutes , how many minutes would it take two machines working at the same rate to do 3 / 5 of the job ?
Options: a ) 45 , b ) 60 , c ) 75 , d ) 96 , e ) 100
Rationale: "using the std formula m 1 d 1 h 1 / w 1 = m 2 d 2 h 2 / w 2 substituting the values we have 8 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 16 / 3 = 10 / 3 * x x = 8 / 5 hour so 96 minutes answer : d"
Answer: d
Question (general): if the sum of the 4 th term and the 12 th term of an arithmetic progression is 8 , what is the sum of the first 15 terms of the progression ?
Options: a ) 60 , b ) 120 , c ) 160 , d ) 240 , e ) 840
Rationale: "let a = first term , d = common difference . 4 th term = a + 3 d 12 th term = a + 11 d a + 3 d + a + 11 d = 8 2 a + 14 d = 8 a + 7 d = 4 . sum of the first 15 terms = 15 / 2 ( 2 a + 14 d ) = 15 ( a + 7 d ) = 15 ( 4 ) = 60 . ans ( a )"
Answer: a
Question (general): niki covers a distance in 45 min , if she drives at a speed of 60 km / h on an average . find the speed at which she must drive at to reduce the time of the journey by 50 % .
Options: a ) 101.02 kmph , b ) 121.62 kmph , c ) 100.62 kmph , d ) 111.00 kmph , e ) 121.00 kmph
Rationale: given speed = 60 kmph . it means niki covered 60 km in 60 min ( 1 hour ) . so , in 45 min he will cover 45 km . 50 % time reduced = 45 - 50 % of 45 = 22.5 min . thus , niki needs to cover 45 km in 22.5 min ( 0.37 hour ) . speed * time = distance . speed * 0.37 = 45 speed = 121.62 kmph . answer : option b
Answer: b
Question (physics): a man complete a journey in 20 hours . he travels first half of the journey at the rate of 10 km / hr and second half at the rate of 15 km / hr . find the total journey in km .
Options: a ) 220 km , b ) 240 km , c ) 230 km , d ) 232 km , e ) 234 km
Rationale: "0.5 x / 10 + 0.5 x / 15 = 20 - - > x / 10 + x / 15 = 40 - - > 5 x = 30 x 40 - - > x = ( 30 x 40 ) / 5 = 240 km . answer : b ."
Answer: b
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 / 4 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , 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 / 4 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 4 ) = 6 x . the fraction of sensors which have been upgraded is x / ( x + 6 x ) = x / 7 x = 1 / 7 the answer is d ."
Answer: d
Question (physics): 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many b hours will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) b = 5 . , d ) b = 6 . , e ) b = 8 .
Rationale: "c . 5 hrs if there were 10 beavers it could have taken double b = 6 hrs . . so closest to that option is 5 . c"
Answer: c
Question (general): | x + 3 | – | 2 - x | = | 8 + x | how many solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "you have | x + 3 | - | 4 - x | = | 8 + x | first , look at the three values independently of their absolute value sign , in other words : | x + 3 | - | 4 - x | = | 8 + x | ( x + 3 ) - ( 4 - x ) = ( 8 + x ) now , you ' re looking at x < - 8 , so x is a number less than - 8 . let ' s pretend x = - 10 here to make things a bit easier to understand . when x = - 10 i . ) ( x + 3 ) ( - 10 + 3 ) ( - 7 ) ii . ) ( 4 - x ) ( 4 - [ - 10 ] ) ( double negative , so it becomes positive ) ( 4 + 10 ) ( 14 ) iii . ) ( 8 + x ) ( 8 + - 10 ) ( - 2 ) in other words , when x < - 8 , ( x + 3 ) and ( 8 + x ) are negative . to solve problems like this , we need to check for the sign change . here is how i do it step by step . i . ) | x + 3 | - | 4 - x | = | 8 + x | ii . ) ignore absolute value signs ( for now ) and find the values of x which make ( x + 3 ) , ( 4 - x ) and ( 8 + x ) = to zero as follows : ( x + 3 ) x = - 3 ( - 3 + 3 ) = 0 ( 4 - x ) x = 4 ( 4 - 4 ) = 0 ( 8 + x ) x = - 8 ( 8 + - 8 ) = 2 c"
Answer: c
Question (gain): from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 10 percent . the enrollment on january 1 , 1993 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "1.10 x = 45 - - > 11 / 10 * x = 45 - - > x = 45 * 10 / 11 = 450 / 11 = ~ 41 . answer : d ."
Answer: d
Question (geometry): if a 2 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ?
Options: a ) 50 % , b ) 100 % , c ) 150 % , d ) 200 % , e ) 250 %
Rationale: "the area a of the large cube is 2 * 2 * 6 = 24 square cm . the area of the 8 small cubes is 8 * 6 = 48 = 2 a , an increase of 100 % . the answer is b ."
Answer: b
Question (general): a group of 4 investment bankers and 5 clients recently frequented the bonbon ribs restaurant . the total bill for the meal , including 20 % gratuity , came to $ 756 . on average , how much did the meal of each individual cost before gratuity ?
Options: a ) $ 160 , b ) $ 70 , c ) $ 90 , d ) $ 80 , e ) $ 55
Rationale: 4 ibs and 5 clients - so total 9 people the bill $ 756 includes 20 % gratuity . . . so the actual cost of dinner was $ 630 now , the cost per person will be $ 630 / 9 which is $ 70 option b
Answer: b
Question (general): a salesman ' s income consists of a commission and a base salary of $ 370 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?
Options: a ) $ 150 , b ) $ 345 , c ) $ 365 , d ) $ 715 , e ) $ 730
Rationale: "total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2070 = $ 1430 from this , we subtract base salary for 2 weeks i . e $ 370 * 2 = $ 740 therefore , commission = $ 1430 - $ 740 = $ 690 for 2 weeks avg weekly commission = $ 345 answer b"
Answer: b
Question (physics): a car is running at a speed of 60 kmph . what distance will it cover in 8 sec ?
Options: a ) 100 m , b ) 136 m , c ) 180 m , d ) 200 m , e ) 250 m
Rationale: "speed = 60 kmph = 60 * 5 / 18 = 17 m / s distance covered in 8 sec = 17 * 8 = 136 m answer is b"
Answer: b
Question (physics): without stoppages , a train travels certain distance with an average speed of 300 km / h , and with stoppages , it covers the same distance with an average speed of 200 km / h . how many minutes per hour the train stops ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "due to stoppages , it covers 100 km less . time taken to cover 100 km = 100 â  „ 300 h = 1 â  „ 3 h = 1 â  „ 3 ã — 60 min = 20 min answer a"
Answer: a
Question (general): a fruit drink is made of grapefruit , lemon , and orange juice , where 25 percent of the drink is grapefruit juice and 35 percent is lemon juice . if the drink is made with 20 ounces of orange juice , how many ounces is the drink total ?
Options: a ) 60 , b ) 80 , c ) 50 , d ) 100 , e ) 40
Rationale: let the total number of ounces in the drink be x % of orange = 25 % % of watermelon = 35 % % of grape = 100 % - 60 % = 40 % but this number is given as 20 ounces so 40 % of x = 20 and x = ( 20 ) ( 100 / 40 ) = ( 20 ) ( 5 / 2 ) x = 50 therefore there a total of 50 ounces in the drink . correct answer - c
Answer: c
Question (general): ` ` how old are you , alchemerion ? ' ' asked one of the wizards appearances the wizards answer with a riddle , ` ` i am still very young as wizards go . i am only 3 times my son ' s age . my father is 40 year more than twice of my age . together the 3 of us are a 1240 year old ' ' . how old is alchemerion
Options: a ) 300 , b ) 320 , c ) 340 , d ) 360 , e ) 380
Rationale: let alchemerion be a let son be s let father be f a = 3 * s f = 40 + ( 2 * a ) therefore 1240 = ( s + f + a ) 1240 = ( a / 3 ) + ( 40 + ( 2 * a ) ) + a a = 360 answer : d
Answer: d
Question (gain): in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 16 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 128 %
Rationale: "0,128 r = x / 100 * 0.1 r answer e"
Answer: e
Question (general): if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance travelled by him is
Options: a ) 50 km , b ) 56 km , c ) 70 km , d ) 80 km , e ) 90 km
Rationale: let the actual distance travelled be x km . then x / 10 = ( x + 20 ) / 14 - - > 14 x = 10 x + 200 - - > 4 x = 200 - - > x = 50 km . answer : a .
Answer: a
Question (general): at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 300 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 200 ?
Options: a ) 1,108 , b ) 2,500 , c ) 2,108 , d ) 2,124 , e ) 2,256
Rationale: "we have $ 200 and we have to maximize the number of hot dogs that we can buy with this amount . let ' s try to find out what is the maximum number of hot dogs that we can buy for a lesser amount of money , which in this case is 300 for $ 22.95 . for the sake of calculation , let ' s take $ 23 . 23 x 8 gives 184 , i . e . a total of 300 x 8 = 2400 hot dogs . we are left with ~ $ 16 . similarly , let ' s use $ 3 for calculation . we can buy 5 20 - pack hot dogs ( 3 x 5 ) , a total of 20 x 5 = 100 hot dogs . so we have 2500 hot dogs . 2108 looks far - fetched ( since we are not likely to be left with > $ 1.55 ) . hence , ( b ) 2500 ( answer b )"
Answer: b
Question (gain): find the 25 % of rs . 300 .
Options: a ) s . 50 , b ) s . 70 , c ) s . 100 , d ) s . 80 , e ) s . 75
Rationale: "explanation : 25 % of 300 = > 25 / 100 * 300 = rs . 75 answer : e"
Answer: e
Question (gain): a reduction of 50 % in the price of apples would enable a man to obtain 50 more for rs . 50 , what is reduced price per dozen ?
Options: a ) 1 , b ) 3 , c ) 6 , d ) 7 , e ) 10
Rationale: "c 50 * ( 50 / 100 ) = 25 - - - 50 ? - - - 12 = > rs . 6"
Answer: c
Question (physics): a 1000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ?
Options: a ) 6 , b ) 12 , c ) 18 , d ) 24 , e ) 48
Rationale: "in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 500 by that net inflow to get the minutes ) - 6 min . answer a ."
Answer: a
Question (general): working simultaneously and independently at an identical constant rate , 4 machines of a certain type can produce a total of x units of product p in 6 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 2 x units of product p in 3 days ?
Options: a ) 24 , b ) 18 , c ) 16 , d ) 12 , e ) 8
Rationale: "4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 2 x units in 3 days therefore , we need to get to 2 x / 3 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 2 x done in 3 days . 2 x / 3 work needs to be done by machines that work at x / 24 rate . let ' s assign a constant y for the number of machines : ( x / 24 ) * y = 2 x / 3 y = 2 x / 3 * 24 / x cancel 3 with 24 , and x with x and get - > 16 . answer choice c"
Answer: c
Question (general): a bag of potatoes weighs 36 lbs divided by half of its weight . how much does the bag of potatoes weight ?
Options: a ) 20 lb , b ) 30 lb , c ) 10 lb , d ) 15 lb , e ) 36 lb
Rationale: sol . 36 ÷ 3 = 12 . answer : e
Answer: e
Question (physics): p , q and r together earn rs . 1800 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 . 50 , b ) s . 70 , c ) s . 90 , d ) s . 100 , e ) s . 120
Rationale: explanation : amount earned by p , q and r in 1 day = 1800 / 9 = 200 - - - ( 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 - 200 = 50 = > amount earned by r in 1 day = 50 answer : option a
Answer: a
Question (gain): jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume , respectively . if these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid , approximately how many liters of the 2 percent solution will be required ?
Options: a ) 18 , b ) 20 , c ) 24 , d ) 36 , e ) 42
Rationale: "use weighted average : 2 % and 12 % solutions mix to give 5 % solution . w 1 / w 2 = ( a 2 - avg ) / ( avg - a 1 ) = ( 12 - 5 ) / ( 5 - 2 ) = 7 / 3 you need 7 parts of 2 % solution and 3 parts of 12 % solution to get 10 parts of 5 % solution . if total 5 % solution is actually 60 litres , you need 7 * 6 = 42 litres of 2 % solution and 3 * 6 = 18 litres of 12 % solution . answer ( e )"
Answer: e
Question (physics): in a kilo meter race , if a gives b a 40 m start , a wins by 19 s . but if a gives b a 30 s start , b wins by 40 m . find the time taken by b to run 5,000 m ?
Options: a ) 150 s , b ) 450 s , c ) 750 s , d ) 825 s , e ) 925 s
Rationale: when b is given a 40 m start then b runs 960 m in t secs and a runs 1000 m in t - 19 secs . when b is given a 30 second start then b runs 1000 m in t secs and a runs 960 m in t - 30 secs . assume that the speed of a ( va ) and b ( vb ) is constant in both situations . then vb = 960 ÷ t = 1000 ÷ t , and va = 1000 ÷ ( t - 19 ) = 960 ÷ ( t - 30 ) so 960 t = 1000 t , and 1000 t - 30000 = 960 t - 18240 . then 40 t = - 40 t + 11760 , t = - t + 294 . substituting for t in 960 t = 1000 t gives : - 960 t + 282240 = 1000 t 1960 t = 282240 t = 144 b ' s speed is 960 / t = 960 / 144 = 6.67 metres per second . assuming the same constant speed to run 5000 metres then the time taken is 5000 / 6.67 = 750 seconds answer : c
Answer: c
Question (general): 0.9999 + 0.1111 = ?
Options: a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.111 , e ) 1.1111
Rationale: "0.9999 + 0.1111 = 0.9999 + 0.111 + 0.0001 = ( 0.9999 + 0.0001 ) + 0.111 = 1 + 0.111 = 1.111 d"
Answer: d