Cheukting/mathqa huggingface dataset:
Question (general): exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 8 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 24 , b ) 35 , c ) 39 , d ) 60 , e ) 65
Rationale: "the total number of the people in the room must be a multiple of both 7 and 8 ( in order 3 / 7 and 5 / 8 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 8 , which is 56 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 56 people in the room . therefore there are 3 / 7 * 56 = 24 people in the room under the age of 21 . answer : a ."
Answer: a
Question (general): alice picked a number of pears , each of which she sold , canned , or poached . she canned 20 percent more than she poached , and she poached 50 percent less than she sold . if there were a total of 42 pears , then how many pears did she sell ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: let x be the amount of pears that she sold . then she poached 0.5 x . then she canned 1.2 * 0.5 x = 0.6 x . the total amount of pears is x + 0.5 x + 0.6 x = 2.1 x the fraction of pears that she sold is 1 / 2.1 = 10 / 21 . the number of pears she sold is ( 10 / 21 ) * 42 = 20 . the answer is a .
Answer: a
Question (general): the value of x + x ( x ^ x ) when x = 10 is
Options: a ) 100000000010 , b ) 10000000010 , c ) 10000000000 , d ) 1200000000 , e ) 12000000010
Rationale: solution : x + x ( x ^ x ) put the value of x = 10 in the above expression we get , 10 + 10 ( 10 ^ 10 ) = 10 + 10 ( 10 ã — 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 ) = 10 + 10 ( 10000000000 ) = 10 + 100000000000 = 100000000010 answer : ( a )
Answer: a
Question (general): if k is a non - negative integer and 30 ^ k is a divisor of 929260 then 3 ^ k - k ^ 3 =
Options: a ) 0 , b ) 1 , c ) 45 , d ) 130 , e ) 520
Rationale: 9 + 2 + 9 + 2 + 6 + 0 = 28 , so this number is not divisible by 3 and thus not divisible by 30 . therefore , k = 0 3 ^ k - k ^ 3 = 1 - 0 = 1 the answer is b .
Answer: b
Question (gain): a sum was put at simple interest at a certain rate for 4 years had it been put at 2 % higher rate , it would have fetched 56 more . find the sum .
Options: a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) none of these
Rationale: "difference in s . i . = p × t / 100 ( r 1 − r 2 ) ⇒ 56 = p × 4 × 2 / 100 ( ∵ r 1 - r 2 = 2 ) ⇒ p = 56 × 100 / 4 × 2 = 700 answer c"
Answer: c
Question (general): a vending machine randomly dispenses 4 different types of fruit candy . there are twice as many apple candies as orange candies , twice as many strawberry candies as grape candies , and twice as many apple candies as strawberry candies . if each candy cost $ 0.1 , and there are exactly 90 candies , what is the minimum amount of money required to guarantee that you would buy at least 3 of each type of candy ?
Options: a ) $ 8.30 , b ) $ 20.75 , c ) $ 22.50 , d ) $ 42.75 , e ) $ 45.00
Rationale: let number of apple , orange , strawberry and grape candies be a , o , s and g respectively . a = 2 o s = 2 g a = 2 s a = 4 g a + o + s + g = 90 = > a + a / 2 + a / 2 + a / 4 = 90 = > 9 a / 4 = 90 = > a = 40 o = 20 s = 20 g = 10 cost of each candy = . 1 $ mininum amount of money required to guarantee that you would buy at least three of each type of candy we can buy 40 apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies . total = 83 candies amount required = 83 * . 1 = 8.30 $ answer a
Answer: a
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 4 days . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 0.1 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) 0.5
Rationale: "b work 1 / 8 * 4 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 take reciprocal 4 * remaining work = 2 * 1 / 4 = 0.5 answer : e"
Answer: e
Question (general): the tax on a commodity is diminished by 20 % and its consumption increased by 25 % . the effect on revenue is ?
Options: a ) 2 % decrease , b ) 8 % decrease , c ) 9 % decrease , d ) 0 % no change , e ) 2 % decrease
Rationale: "100 * 100 = 10000 80 * 125 = 10000 - - - - - - - - - - - 10000 - - - - - - - - - - - 0 100 - - - - - - - - - - - ? = > 0 % no change answer : d"
Answer: d
Question (general): if n is a prime number greater than 4 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 2 , c ) 1 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question including the one under the spoiler . but the easiest way is as follows : since we can not have two correct answersjust pick a prime greater than 4 , square it and see what would be the remainder upon division of it by 12 . n = 7 - - > n ^ 2 = 49 - - > remainder upon division 49 by 12 is 1 . answer : c ."
Answer: c
Question (physics): a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 3680 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) s . 380 , b ) s . 600 , c ) s . 460 , d ) s . 400 , e ) s . 480
Rationale: "explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 3680 × ( 1 / 8 ) = 460 answer : option c"
Answer: c
Question (physics): in what time will a train 100 meters long cross an electric pole , if its speed is 36 km / hr
Options: a ) 8.5 seconds , b ) 10 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds
Rationale: "first convert speed into m / sec speed = 36 * ( 5 / 18 ) = 10 m / sec time = distance / speed = 100 / 10 = 10 seconds answer : b"
Answer: b
Question (general): if x / ( 12 p ) is an odd prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 72
Rationale: "x / ( 12 p ) = odd prime number x = odd prime number * 11 p least value of x = lowest odd prime number * 11 * lowest value of p = 3 * 12 * 2 = 72 answer e"
Answer: e
Question (general): given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 16 = f ( x – 6 ) ?
Options: a ) 1 , b ) 4 , c ) 6 , d ) 7 , e ) 13
Rationale: "2 ( 3 x - 5 ) - 16 = 3 ( x - 6 ) - 5 3 x = 3 x = 1 the answer is a ."
Answer: a
Question (general): a batsman in his 12 th innings makes a score of 80 and thereby increases his average by 3 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 47
Rationale: let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 3 ) + 80 ∴ x = 47 answer e
Answer: e
Question (physics): each of the three people individually can complete a certain job in 4 , 5 , and 8 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?
Options: a ) 9 / 20 , b ) 11 / 20 , c ) 11 / 32 , d ) 13 / 40 , e ) 17 / 40
Rationale: "the two slowest people work at rates of 1 / 5 and 1 / 8 of the job per hour . the sum of these rates is 1 / 5 + 1 / 8 = 13 / 40 of the job per hour . the answer is d ."
Answer: d
Question (physics): a train travels from new york to chicago , a distance of approximately 840 miles , at an average rate of 60 miles per hour and arrives in chicago at 7 : 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 ) 5 : 00 , d ) 6 : 00 , e ) 7 : 00
Rationale: "7 : 00 in evening in chicago = 8 : 00 in evening in new york . so , the train was in chicago 8 : 00 in the evening , new york time . the trip took t = d / r = 840 / 60 = 14 hours . therefore , the train depart from new york at 8 : 00 - 14 hours = 6 : 00 in the morning , new york time . answer : d ."
Answer: d
Question (other): if the ratio of a to b is 4 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
Options: a ) 4 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6
Rationale: a : b = 4 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 4 : 15 answer a
Answer: a
Question (other): the h . c . f . of two numbers is 63 and the other two factors of their l . c . m . are 11 and 17 . the larger of the two numbers is :
Options: a ) 3421 , b ) 2132 , c ) 1111 , d ) 4323 , e ) 1071
Rationale: ": explanation : clearly , the numbers are ( 63 x 11 ) and ( 63 x 17 ) . { \ color { blue } \ therefore } larger number = ( 63 x 17 ) = 1071 . answer : e ) 1071"
Answer: e
Question (geometry): a rectangular swimming pool is 10 feet by 12 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 360 square feet . what is the width of the deck ?
Options: a ) 7 , b ) 2 , c ) 3 , d ) 4 , e ) 6
Rationale: "let the width = w total area of the pool and deck = ( 2 w + 10 ) ( 2 w + 12 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 14 * 16 has unit digit 4 . . . . . . . . . . eliminate b ) 2.5 feet . . . . . . . . . 15 * 17 has unit digit 5 . . . . . . . . . . eliminate c ) 3 feet . . . . . . . . . . . . 16 * 18 has unit digit 8 . . . . . . . . . . . eliminate d ) 4 feet . . . . . . . . . . . . 18 * 20 has unit digit 0 . . . . . . . . . . . hold e ) 5 feet . . . . . . . . . . . . 20 * 22 has unit digit 0 . . . . . . . . . . . eliminate ( bigger size ) answer : d w = 4"
Answer: d
Question (probability): find the probability that a leap year selected at random will not have 53 sundays or mondays .
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7
Rationale: "there are 366 days in a leap year : 52 weeks and 2 more days . so , 52 sundays , 52 mondays and 2 days . these 2 days can be : { mon , tue } , { tue , wed } , { wed , thu } , { thu , fri } , { fri , sat } , { sat , sun } and { sun , mon } ( 7 cases ) . in order to have 53 sundays or 53 mondays we should have either { mon , tue } { sat , sun } or { sun , mon } case . the probability of that is 3 / 7 . so probability of not having 53 sundays or mondays , probability is 1 - 3 / 7 = 4 / 7 answer : c ."
Answer: c
Question (physics): a copy machine , working at a constant rate , makes 25 copies per minute . a second copy machine , working at a constant rate , makes 55 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?
Options: a ) 90 , b ) 2,400 , c ) 4,500 , d ) 5,400 , e ) 324,000
Rationale: "together the two machines make 25 + 55 = 80 copies per minute . so , in half an hour they will make 80 * 30 = 2,400 copies . answer : b ."
Answer: b
Question (general): a student multiplied a number by 3 / 5 instead of 5 / 3 . what is the percentage error .
Options: a ) 64 % , b ) 65 % , c ) 66 % , d ) 67 % , e ) none of these
Rationale: "explanation : let the number be x , then , 5 / 3 − 3 / 5 = 16 / 15 x error % = ( 16 / 15 x ∗ 3 / 5 ∗ 100 ) option a"
Answer: a
Question (general): solve the given equation 9 ^ y = 3 ^ 12 , what is y ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 3 ^ 2 y = 3 ^ 12 2 y = 12 , therefore y = 6 e
Answer: e
Question (geometry): the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) 2277 , b ) 2977 , c ) 2677 , d ) 4530 , e ) 1971
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 5 = rs . 4530 answer : d"
Answer: d
Question (gain): a , b and c started a partnership business by investing rs . 30000 , rs . 45000 , rs . 50000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ?
Options: a ) 70000 , b ) 60000 , c ) 80000 , d ) 90000 , e ) 50000
Rationale: "a : b : c = 30000 : 45000 : 50000 = 6 : 9 : 10 let total profit = p then p ã — 10 / 25 = 36000 p = ( 36000 ã — 25 ) / 10 = 90000 answer is d ."
Answer: d
Question (general): if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 4 is subtracted and divided by 10 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3
Rationale: "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 4 ) / 10 = ( 54 - 4 ) / 10 = 5 answer : option d"
Answer: d
Question (other): integer m has 4 different prime factors and n has 3 different prime factors . if m and n has the greatest common factor of 15 , how many different prime factors does mn have ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: as m and n has gcf of 15 , 3 * 5 should be common factor for both m and n . m = 3 * 5 * p 1 * p 2 n = 3 * 5 * p 3 mn = 3 ^ 2 * 5 ^ 2 * p 1 * p 2 * p 3 mn has prime numbers of 3,5 , p 1 , p 2 p 3 b
Answer: b
Question (general): if x ^ 2 + ( 1 / x ^ 2 ) = 5 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 23 , b ) 11 , c ) 12 , d ) 14 , e ) 15
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 5 ^ 2 - 2 = 23 . thus , the answer is a ."
Answer: a
Question (gain): on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 609 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 2 % , b ) 3 % , c ) 4 % , d ) 5 % , e ) 6 %
Rationale: "difference in c . i . and s . i for 2 years = $ 609 - $ 600 = $ 9 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 9 rate = ( 100 * 9 ) / ( 300 ) = 3 % the answer is b ."
Answer: b
Question (general): in arun ' s opinion , his weight is greater than 62 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 65 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 86.5 kg , b ) 63.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg
Rationale: "let arun ' s weight be x kg . according to arun , 62 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 65 . the values satisfying all the above conditions are 63 and 64 . required average = ( 63 + 64 ) / 2 = 63.5 kg answer : b"
Answer: b
Question (general): x and y are two towns . ganesh covers the distance from x to y at an average speed of 60 km / hr . however , he covers the distance from y to x at an average speed of 36 km / hr . his average speed during the whole journey in km / hr . is :
Options: a ) 45 , b ) 43 , c ) 40 , d ) 38 , e ) 29
Rationale: solution : average speed = 2 xy / x + y = 2 * 60 * 36 / 60 + 36 = 45 answer : a
Answer: a
Question (general): ( 12 ) ^ 3 x 6 ^ 4 ÷ 432 = ?
Options: a ) 5184 , b ) 5060 , c ) 5148 , d ) 5084 , e ) none of them
Rationale: = ( 12 ) ^ 3 x 6 ^ 4 / 432 = ( 12 ) ^ 3 x 6 ^ 4 / 12 x 6 ^ 2 = ( 12 ) ^ 2 x 6 ^ 2 = ( 72 ) ^ 2 = 70 answer is e
Answer: e
Question (geometry): two cylinders are of the same height . their radii are in the ratio 1 : 3 . if the volume of the first cylinder is 40 cc . find the volume of the second cylinder ?
Options: a ) 360 cc
b ) 60 cc
c ) 300 cc
d ) 36 cc
e ) 39 cc
Rationale: r 1 = x r 2 = 3 x π * x 2 * h = 40 π 9 x 2 h = 40 * 9 = 360 answer : a
Answer: a
Question (general): a grocer has a sale of rs . 2500 , rs . 4000 , rs . 3540 for 3 consecutive months . how much sale must he have in the fourth month so that he gets an average sale of rs . 2890 ?
Options: a ) rs . 3500 , b ) rs . 1520 , c ) rs . 4996 , d ) rs . 4000 , e ) rs . 900
Rationale: total sale for 5 months = rs . ( 2500 + 4000 + 3540 ) = rs . 10040 . required sale = rs . [ ( 2890 x 4 ) - 10040 ] = rs . ( 11560 - 10040 ) = rs . 1520 . b )
Answer: b
Question (general): if 3 ^ x * 4 ^ y = 4 , 782,969 and x – y = 14 , then x = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since 4 , 782,969 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 14 and y = 0 , then x = 14 . the answer is e ."
Answer: e
Question (general): if x , y , and z are positive real numbers such that x + y - z = 100 , y - z + x = 120 , and z - x + y = 50 , then find the x + y + z value ?
Options: a ) 100 , b ) 120 , c ) 150 , d ) 200 , e ) 160
Rationale: "x + y - z = 100 , - - - - - - 1 ) y - z + x = 120 , - - - - - - 2 ) z - x + y = 50 - - - - - - 3 ) from ( 1 ) & ( 2 ) 2 z = 20 z = 10 from ( 2 ) & ( 3 ) 2 y = 170 y = 85 then x = 100 - 75 = 25 x + y + z = 120 correct option is b"
Answer: b
Question (geometry): the volume of a cube is 3375 cc . find its surface .
Options: a ) 1350 , b ) 1150 , c ) 1456 , d ) 1254 , e ) 1489
Rationale: a 3 = 3375 = > a = 15 6 a 2 = 6 * 15 * 15 = 1350 answer : a
Answer: a
Question (gain): if the cost price of 10 articles is equal to the selling price of 20 articles , what is the % profit or loss made by the merchant ?
Options: a ) 25 % loss , b ) 25 % profit , c ) 20 % loss , d ) 20 % profit , e ) 50 % loss
Rationale: "let the cost price of 1 article be $ 1 . therefore , cost price of 10 articles = 10 * 1 = $ 10 the selling price of 20 articles = cost price of 10 articles = $ 10 . now , we know the selling price of 20 articles . let us find the cost price of 20 articles . cost price of 20 articles = 20 * 1 = $ 20 . therefore , profit made on sale of 20 articles = selling price of 20 articles - cost price of 20 articles = 10 - 20 = - $ 10 . as the profit is in the negative , the merchant has made a loss of $ 10 . therefore , % loss = loss / cp * 100 % loss = - 10 / 20 * 100 = 50 % loss . e"
Answer: e
Question (general): ( 0.76 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.76 ) ( power 2 ) + 0.076 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.66 , b ) 0.68 , c ) 0.96 , d ) 0.69 , e ) 0.76
Rationale: "given expression = ( 0.76 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.76 ) ( power 2 ) + ( 0.76 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.76 - 0.1 ) = 0.66 answer is a ."
Answer: a
Question (gain): one - third of 1206 is what percent of 134 ?
Options: a ) 3 , b ) 30 , c ) 300 , d ) none of these , e ) can not be determined
Rationale: "answer let one - third of 1206 is n % of 134 . ∵ 1206 / 3 = ( n x 134 ) / 100 ∴ n = ( 402 x 100 ) / 134 = 300 correct option : c"
Answer: c
Question (general): the digit sum of the year 2007 is 2 + 0 + 0 + 7 = 9 , which is a square number . how many years during the 20 - first century have a square digital sum ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: the twenty - first century runs from the year 2001 to 2100 inclusive , so with the exception of the year 2100 , for which the digital sum is three anyway , the first two digits of all the other years are fixed as 20 . hence for the sum of all the digits to be square the sum of the last two digits number be two less than a perfect square . as the maximum sum of the last two digits is 18 , the greatest sum will be 20 . therefore we can obtain digital sums of 4 , 9 , or 16 , with the last two digits adding to 2 , 7 , or 14 respectively . 4 : 2002 , 2011 , 2020 9 : 2007 , 2016 , 2025 , 2034 , 2043 , 2052 , 2061 , 2070 16 : 2059 , 2068 , 2077 , 2086 , 2095 that is , there are sixteen years during the twenty - first century for which the digital sum is square . answer : d
Answer: d
Question (physics): a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 2 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 40 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 30 , b ) 64 , c ) 60 , d ) 70 , e ) 90
Rationale: total vehicle = 2 / 3 of speedster + 1 / 3 of others . speedster convertibles = 2 / 3 total vehicle * 4 / 5 given : 1 / 3 constitutes 40 vehicles . hence 2 / 3 constitutes 80 speedster convertibls = 80 * 4 / 5 = 64 b
Answer: b
Question (physics): earl can stuff advertising circulars into envelopes at the rate of 36 envelopes per minutes and ellen requires a minutes and half to stuff the same number of envelops . working together , how long will it take earl and ellen to stuff 180 envelopes
Options: a ) 6 minutes , b ) 5 minutes , c ) 7 minutes , d ) 3 minutes , e ) 4 minutes
Rationale: earl takes 1 min . for 36 envelopes . ellen takes 3 / 2 mins for the same . so ellen can stuff ( ( 36 ) / ( 3 / 2 ) ) in 1 min . i . e . , 24 envelopes a min . so both of them when work together can stuff 36 + 24 = 60 envelopes in 1 min . for 180 envelopes they will take 180 / 60 mins . i . e . , 3 mins . answer : d
Answer: d
Question (gain): boy sells a book for rs . 810 he gets a loss of 10 % , to gain 10 % , what should be the sp ?
Options: a ) 430 , b ) 990 , c ) 550 , d ) 590 , e ) 600
Rationale: "cost price = 810 / 90 x 100 = 900 to gain 10 % = 900 x 10 / 100 = 90 sp = cp + gain = 900 + 90 = 990 answer : b"
Answer: b
Question (gain): a discount electronics store normally sells all merchandise at a discount of 2 percent to 50 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 100 before any discount ?
Options: a ) $ 100.00 , b ) $ 40.00 , c ) $ 50.00 , d ) $ 30.00 , e ) $ 10.00
Rationale: "original price : 100 $ max first discount = - 50 % thus : 100 â ˆ — ( 1 â ˆ ’ 50 / 100 ) = 50 second discount on the discounted price = - 20 % thus : 50 â ˆ — ( 1 â ˆ ’ 20 / 100 ) = 40 answer b ."
Answer: b
Question (physics): how many pieces of 85 cm length can be cut from a rod of 34 meters long ?
Options: a ) 50 , b ) 40 , c ) 30 , d ) 20 , e ) 10
Rationale: "number of pieces = 3400 / 85 = 40 the answer is b ."
Answer: b
Question (general): if 525 / 999 = 0.525 , what is the 81 st digit to the right of the decimal point in the decimal equivalent of the fraction ?
Options: a ) - 1 , b ) 0 , c ) 3 , d ) 4 , e ) 5
Rationale: "0 . [ u ] 125 [ / u = 0.525525525 . . . . . every 3 rd digit is 5 and every multiple of 3 will be the digit 5 . since 81 is multiple of 3 , the 81 st digit is 5 . answer e"
Answer: e
Question (gain): p and q invested in a business . the profit earned was divided in the ratio 4 : 5 . if p invested rs 52000 , the amount invested by q is
Options: a ) 30000 , b ) 50000 , c ) 40000 , d ) 20000 , e ) 65000
Rationale: "let the amount invested by q = q 52000 : q = 4 : 5 ⇒ 52000 × 5 = 4 q ⇒ q = ( 52000 × 5 ) / 4 = 65000 answer is e ."
Answer: e
Question (general): the number 152 is equal to the sum of the cubes of two integers . what is the product of those integers ?
Options: a ) 8 , b ) 15 , c ) 21 , d ) 27 , e ) 39
Rationale: "actually , decomposition into factors can easily give you the answer here . you should just do the decomposition of the right thing i . e . the options since they represent the product of those integers . since the sum of cubes is 152 , the numbers can not be larger than 5 since 6 ^ 3 itself is 216 . 21 , 27 , 39 - the factors are too large so ignore 8 - ( 2 , 4 ) does not satisfy 15 - ( 3 , 5 ) yes . 3 ^ 3 + 5 ^ 3 = 152 - answer answer : b"
Answer: b