Cheukting/mathqa huggingface dataset:
Question (physics): pipe a usually fills a tank in 2 hours . on account of a leak at the bottom of the tank , it takes pipe a 30 more minutes to fill the tank . how long will the leak take to empty a full tank if pipe a is shut ?
Options: a ) 7 hours , b ) 8 hours , c ) 9 hours , d ) 10 hours , e ) 11 hours
Rationale: pipe a fills the tank normally in 2 hours . therefore , it will fill ½ of the tank in an hour . let the leak take x hours to empty a full tank when pipe a is shut . therefore , the leak will empty of the tank in an hour . the net amount of water that gets filled in the tank in an hour when pipe a is open and when there is a leak = of the tank . — ( 1 ) when there is a leak , the problem states that pipe a takes two and a half hours to fill the tank . i . e . hours . therefore , in an hour , of the tank gets filled . – ( 2 ) equating ( 1 ) and ( 2 ) , we get = > = > x = 10 hours . the problem can also be mentally done as follows . pipe a takes 2 hours to fill the tank . therefore , it fills half the tank in an hour or 50 % of the tank in an hour . when there is a leak it takes 2 hours 30 minutes for the tank to fill . i . e hours to fill the tank or or 40 % of the tank gets filled . on account of the leak , ( 50 - 40 ) % = 10 % of the water gets wasted every hour . therefore , the leak will take 10 hours to drain a full tank . answer : d
Answer: d
Question (physics): walking at 5 / 6 th of its usual speed a cab is 5 mnts late . find its usual time to cover the journey ?
Options: a ) 25 m , b ) 45 m , c ) 32 m , d ) 50 m , e ) 62 m
Rationale: "new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 5 m ut / 5 = 5 m ut = 25 m answer is a"
Answer: a
Question (general): what is the 8 th digit to the right of the decimal point in the decimal expansion of 1 / 37 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 7 , e ) 9
Rationale: "1 / 37 = 0.027027 . . . so , we have a repeating cycle of 027 . every third digit ( 2 nd , 4 th , 6 th , . . . ) to the right of the decimal point is alternating by 2 , 0,7 , thus 8 th digit to the right of the decimal point is 2 . answer : b ."
Answer: b
Question (general): find the value of x : 3 x ^ 2 - 6 x + 3 = 0
Options: a ) - 1 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: a = 3 , b = - 6 , c = 3 x 1,2 = ( 6 ± √ ( ( - 6 ) 2 - 4 × 3 × 3 ) ) / ( 2 × 3 ) = ( 6 ± √ ( 36 - 36 ) ) / 6 = ( 6 ± 0 ) / 6 x 1 = x 2 = 1 b
Answer: b
Question (physics): in a kilometer race , a beats b by 50 meters or 5 seconds . what time does a take to complete the race ?
Options: a ) 199 sec , b ) 190 sec , c ) 726 sec , d ) 90 sec , e ) 128 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 5 ) / 50 = 100 sec . time taken by a = 100 - 10 = 90 sec . answer : d"
Answer: d
Question (general): what is the smallest number which when increased by 3 is divisible by 27 , 35 , 25 , & 21 ?
Options: a ) 4722 , b ) 4725 , c ) 4728 , d ) 4731 , e ) 4733
Rationale: "here smallest number means lcm hence lcm of 27,35 , 25,21 = 3 ^ 3 x 5 ^ 2 x 7 = 4725 therefore required number is 4725 - 3 = 4722 ans - a"
Answer: a
Question (physics): a train 150 m long crosses a platform 130 m long in 20 sec ; find the speed of the train ?
Options: a ) 50 , b ) 60 , c ) 55 , d ) 45 , e ) 53
Rationale: "d = 150 + 130 = 280 t = 20 s = 280 / 20 * 18 / 5 = 50 kmph . answer : a"
Answer: a
Question (general): the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 245 , what is the difference between the ages of patrick and monica ?
Options: a ) 27 , b ) 48 , c ) 80 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 49 x = 245 x = 5 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 5 = 80 answer c"
Answer: c
Question (general): when 6 + 2 = 85 , 8 + 3 = 115 , 7 + 5 = 125 , then 5 + 8 = ?
Options: a ) 145 , b ) 185 , c ) 245 , d ) 135 , e ) 140
Rationale: "6 + 2 = > 6 + 2 = 8 = > 8 ã — 10 + 5 = 85 8 + 3 = > 8 + 3 = 11 = > 11 ã — 10 + 5 = 115 7 + 5 = > 7 + 5 = 12 = > 12 ã — 10 + 5 = 125 then 5 + 8 = > 5 + 8 = 13 = > 13 ã — 10 + 5 = 135 answer : d"
Answer: d
Question (physics): pipe a can fill a tank in 4 hours . due to a leak at the bottom , it takes 8 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 13 , b ) 17 , c ) 18 , d ) 8 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 4 - 1 / x = 1 / 8 = > 1 / x = 1 / 4 - 1 / 8 = ( 2 - 1 ) / 8 = 1 / 8 = > x = 8 . answer : d"
Answer: d
Question (probability): in how many ways 7 boys and 7 girls can be seated in a row so that boys and girls are alternate ?
Options: a ) 50803200 , b ) 50328000 , c ) 50003280 , d ) 50703200 , e ) 50603200
Rationale: "number of ways = 2 * 7 ! * 7 ! = 50803200 answer is a"
Answer: a
Question (general): how many two - element subsets of < 1 , 23 , 45 , 67 > are there that do not contain the pair of elements 2 and 4 ?
Options: a ) 11 , b ) 12 , c ) 14 , d ) 15 , e ) 20
Rationale: 7 c 2 - 1 = 20 answer is e
Answer: e
Question (probability): a certain junior class has 3000 students and a certain senior class has 800 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ?
Options: a ) 1 / 40000 , b ) 1 / 3600 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "let ' s see pick 60 / 3000 first then we can only pick 1 other pair from the 800 so total will be 60 / 800 * 3000 simplify and you get 1 / 40000 answer is a"
Answer: a
Question (physics): there is a sufficient food for 200 men for 20 days after 15 days 100 men leave the place . for how many days will the rest of the food last for the rest of the men ?
Options: a ) 10 days , b ) 5 days , c ) 15 days , d ) 12 days , e ) 10 days
Rationale: explanation : after 13 days , 100 men left , therefore 5 days * 200 men = x days * 100 men x = 10 days answer : option a
Answer: a
Question (physics): a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 30 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?
Options: a ) 90 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "a - b = 120 miles b - c = 60 miles avg speed = 30 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 30 = 180 / 4 t t = 90 b - c = 90 mph answer a"
Answer: a
Question (gain): how much 60 % of 50 is greater than 30 % of 30 ?
Options: a ) 21 , b ) 91 , c ) 11 , d ) 17 , e ) 12
Rationale: "( 60 / 100 ) * 50 – ( 30 / 100 ) * 30 30 - 9 = 21 answer : a"
Answer: a
Question (general): the average of 50 numbers id 50 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22 , b ) 33 , c ) 22 , d ) 41 , e ) 50
Rationale: "explanation : total of 50 numbers = ( 50 × 50 ) = 2500 total of 48 numbers = ( 2500 - ( 45 + 55 ) ] = 2400 required average = 2400 / 48 = 50 answer : e"
Answer: e
Question (physics): a can do a work in 9 days . b can do the same work in 18 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 6
Rationale: "a rate = 1 / 9 b rate = 1 / 18 ( a + b ) rate = ( 1 / 9 ) + ( 1 / 18 ) = 1 / 6 a & b finish the work in 6 days correct option is e"
Answer: e
Question (general): how many numbers between 100 and 672 are divisible by 2 , 3 , and 7 together ?
Options: a ) 112 , b ) 77 , c ) 267 , d ) 14 , e ) 99
Rationale: "explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 672 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 672 : 672 / 42 = 14 hence , 42 * 16 = 672 is the last number divisible by 42 within 672 hence , total numbers divisible by 2 , 3 , 7 together are ( 16 â € “ 2 ) = 14 answer : d"
Answer: d
Question (general): angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 3,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 15,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo ’ s and isabella ’ s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal base salary plus commission . so angelo ’ s earnings are 550 + ( 0.08 ) ( x – 3,000 ) , and isabella ’ s are 0.10 x . set up the equation and solve : 550 + ( 0.08 ) ( x – 3,000 ) = 0.10 x distribute the 0.08 : 550 + 0.08 x – 240 = 0.10 x combine terms and subtract 0.08 x from both sides : 310 = 0.02 x divide both sides by 0.02 : 15,500 = x your answer is b ."
Answer: b
Question (other): a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 586.75 . how many boxes of plain cookies did she sell ?
Options: a ) 0 , b ) 233 , c ) 500 , d ) 695 , e ) 789
Rationale: "let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1586.75 = > x = 789"
Answer: e
Question (general): a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 157 . find the unknown rate of two blankets ?
Options: a ) 420 , b ) 550 , c ) 490 , d ) 450 , e ) 520
Rationale: "10 * 157 = 1570 3 * 100 + 5 * 150 = 1050 1570 – 1050 = 520 answer : e"
Answer: e
Question (general): 0.0004 ? = 0.02
Options: a ) 0.02 , b ) 0.2 , c ) 2 , d ) 20 , e ) none of these
Rationale: "explanation : required answer = 0.0004 / 0.02 = 0.04 / 2 = 0.02 . answer : option a"
Answer: a
Question (probability): a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability t that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability t = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 2 / 19 answer : option b"
Answer: b
Question (geometry): the length of a rectangle is reduced by 25 % . by what % would the width have to be increased to maintainthe original area ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 33 % , e ) 40 %
Rationale: "sol . required change = ( 25 * 100 ) / ( 100 - 25 ) = 25 % d"
Answer: d
Question (gain): a survey was sent to 95 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 7 % , d ) 28 % , e ) 63 %
Rationale: "case 1 : ( 7 / 95 ) = x / 100 x = 7 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 7 ) % = 7 % answer is c"
Answer: c
Question (general): tough and tricky questions : word problems . ak car company wants to manufacture a new car known as model x , and it is trying to determine how many cars it needs to sell in order to make an annual profit of $ 30 , 500000 . the annual fixed costs for model x total $ 50 , 200000 . in addition , each model x car has an average cost of $ 5000 per vehicle to manufacture . if the company forecasts it will sell 20000 model x cars this year , at what price must the company sell the car to achieve the desired annual profit ?
Options: a ) $ 4035 , b ) $ 4036 , c ) $ 9035 , d ) $ 16140 , e ) $ 36140
Rationale: the ak company plans to make a profit of $ 30 , 500000 and it needs to earn the fixed costs of $ 50 , 200000 , so it needs to earn $ 80 , 700000 on top of the costs for the production of the 20000 cars . therefore , price of each car needs to be the unit costs plus $ 80 , 700000 / 20000 . after removing the 0 ' s , we end with the unit costs plus $ 8070 / 2 , which is $ 5000 plus $ 4035 . therefore , answer c is correct .
Answer: c
Question (general): according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 15 ounces of water to make a smoothie . how many 3 - ounce packets of smoothie mix are required to prepare 150 12 - ounce smoothies ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600
Rationale: "this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? c"
Answer: c
Question (general): how many 3 - digit numbers are divisible by 6 in all ?
Options: a ) 149 , b ) 150 , c ) 151 , d ) 166 , e ) none
Rationale: solution required numbers are 102 , 018114 , . . . . 996 . this is an a . p with a = 102 , d = 6 . let the number of its terms be n . then a + ( n - 1 ) d ‹ = › 102 + ( n - 1 ) × 6 = 996 ‹ = › n = 150 . answer b
Answer: b
Question (physics): two pipes can fill a tank in 10 minutes and 25 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 30 minutes , b ) 17 minutes , c ) 7 minutes , d ) 10 minutes , e ) 12 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 10 + 1 / 25 - 1 / 45 = ( 45 + 18 - 10 ) / 450 = 53 / 450 so , the tank becomes full in 7 minutes . answer : c"
Answer: c
Question (general): if 7 ^ k = 2 , then 7 ^ ( 4 k + 2 ) =
Options: a ) 729 , b ) 754 , c ) 784 , d ) 783 , e ) 108
Rationale: "7 ^ k = 2 7 ^ 4 k = 2 ^ 4 7 ^ 4 k = 16 7 ^ ( 4 k + 2 ) = 7 ^ 4 k * 7 ^ 2 = 16 * 49 = 784 answer : c"
Answer: c
Question (general): one day a car rental agency rented 3 / 4 of its cars , including 3 / 5 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 29 / 30 , b ) 24 / 25 , c ) 19 / 20 , d ) 14 / 15 , e ) 9 / 10
Rationale: "the cars with cd players which were not rented is ( 2 / 5 ) ( 3 / 5 ) = 6 / 25 of all the cars . the cars which were not rented is 1 / 4 of all the cars . the percent of non - rented cars which had cd players is ( 6 / 25 ) / ( 1 / 4 ) = 24 / 25 the answer is b ."
Answer: b
Question (general): little john had $ 5.10 . he spent $ 1.05 on sweets and gave to his two friends $ 1.00 each . how much money was left ?
Options: a ) $ 2.15 , b ) $ 2.05 , c ) $ 2.45 , d ) $ 2.25 , e ) $ 2.85
Rationale: "john spent and gave to his two friends a total of 1.05 + 1.00 + 1.00 = $ 3.05 money left 5.10 - 3.05 = $ 2.05 answer : b"
Answer: b
Question (probability): a fair coin is tossed 3 times . what is the probability of getting at least 2 heads ?
Options: a ) 3 / 4 , b ) 3 / 2 , c ) 1 / 4 , d ) 1 / 2 , e ) 1 / 5
Rationale: "let ' s find the probability of 2 heads , 3 heads p ( hhh ) = ( ( 1 / 2 ) ^ 3 = 1 / 8 . p ( hht ) = ( 3 ! / 2 ! ) * ( 1 / 2 ) ^ 3 = 3 / 8 total probablity = 1 / 8 + 3 / 8 = 1 / 2 answer ( d )"
Answer: d
Question (gain): a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18900 . a ' s share is ?
Options: a ) 6300 , b ) 2765 , c ) 6000 , d ) 1298 , e ) 1261
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18900 = 6300 answer : a"
Answer: a
Question (general): bottle r contains 250 capsules and costs $ 8.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?
Options: a ) $ 0.25 , b ) $ 0.01 , c ) $ 0.05 , d ) $ 0.03 , e ) $ 0.002
Rationale: "cost per capsule in r is 8.25 / 250 = 0.825 / 25 = 0.033 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.01 the answer is b"
Answer: b
Question (gain): if albert ’ s monthly earnings rise by 30 % , he would earn $ 598 . if , instead , his earnings rise by only 35 % , how much ( in $ ) would he earn this month ?
Options: a ) 621 , b ) 652 , c ) 660 , d ) 690 , e ) 693
Rationale: "= 598 / 1.3 ∗ 1.35 = 621 = 621 answer is a"
Answer: a
Question (general): the unit digit in the product 3421 * 6721 * 4584 * 6784 is ?
Options: a ) 0 , b ) 1 , c ) 6 , d ) 3 , e ) 4
Rationale: "unit digit in the given product = unit digit in 1 * 1 * 4 * 4 = 6 answer is c"
Answer: c
Question (general): the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 4 years hence ?
Options: a ) 22 , b ) 77 , c ) 70 , d ) 68 , e ) 71
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 4 years , their ages will be 44 and 24 . sum of their ages = 44 + 24 = 68 . answer : d"
Answer: d
Question (physics): robert is travelling on his cycle andhas calculated to reach point a at 2 pm . if he travels at 10 kmph , he will reach there at 12 pm if he travels at 15 kmph . at what speed must he travel to reach a at 1 pm ?
Options: a ) 8 kmph , b ) 9 kmph , c ) 12 kmph , d ) 14 kmph , e ) 16 kmph
Rationale: let the distance travelled by x km . then , x - x = 2 10 15 3 x - 2 x = 60 x = 60 km . time taken to travel 60 km at 10 km / hr = 60 hrs = 6 hrs . 10 so , robert started 6 hours before 2 p . m . i . e . , at 8 a . m . required speed = 60 kmph . = 12 kmph . 5 c
Answer: c
Question (general): let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 36 , what is the maximum value of y for which f ( x , y ) = 0 ?
Options: a ) 9 , b ) 12 , c ) 18 , d ) 20 , e ) 30
Rationale: "the question is finding y such that ( 36 - y ) ! is a multiple of 36 . that means we need to have 2 ^ 2 * 3 ^ 2 in ( 36 - y ) ! 6 ! is the smallest factorial number with 2 ^ 2 * 3 ^ 2 as a factor . 36 - y = 6 y = 30 the answer is e ."
Answer: e
Question (physics): a computer factory produces 4032 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 . , b ) 3.00 . , c ) 4.5 . , d ) 5.225 . , e ) 6.25 .
Rationale: number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 4032 / ( 28 * 24 * 2 ) = 3 answer b
Answer: b
Question (geometry): the ratio of the radius of two circles is 1 : 4 , and then the ratio of their areas is ?
Options: a ) 1 : 16 , b ) 1 : 6 , c ) 1 : 9 , d ) 1 : 3 , e ) 1 : 2
Rationale: "r 1 : r 2 = 1 : 4 π r 12 : π r 22 r 12 : r 22 = 1 : 16 answer : a"
Answer: a
Question (general): the average age of a class of 39 students is 15 years . if the age of the teacher be included , then the average increased by 3 months . find the age of the teacher ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 39
Rationale: "total age of 39 persons = 39 * 15 = 585 years average age of 40 persons = 15 yrs 3 months = 61 / 4 years total age of 40 persons = 61 / 4 * 40 = 610 years age of the teacher = 610 - 585 = 25 years answer is a"
Answer: a
Question (general): country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 488 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?
Options: a ) $ 1124 million , b ) $ 1120 million , c ) $ 1144 million , d ) $ 1240 million , e ) $ 1488 million
Rationale: convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 488 mill / 2 month i . e . $ 244 mill / month difference / month = 244 - 120 = 124 difference / year = $ 124 mill * 12 = $ 1488 mill answer : e
Answer: e
Question (other): the ratio of 2 numbers is 2 : 7 and their h . c . f . is 18 . their l . c . m . is ?
Options: a ) 252 , b ) 243 , c ) 521 , d ) 361 , e ) 600
Rationale: "let the numbers be 2 x and 7 x their h . c . f . = 18 so the numbers are 2 * 18 , 7 * 18 = 36,126 l . c . m . = 252 answer is a"
Answer: a
Question (other): 110 people are attending a newspaper conference . 45 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?
Options: a ) 34 , b ) 32 , c ) 30 , d ) 26 , e ) 28
Rationale: "{ total } = { writers } + { editors } - { both } + { neither } . { total } = 110 ; { writers } = 45 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 110 = 45 + { editors } - x + 2 x - - > x = 65 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 65 - 39 = 26 . answer : d ."
Answer: d
Question (general): in may mrs lee ' s earnings were 70 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 64 % , b ) 68 % , c ) 72 % , d ) 74 % , e ) 83 %
Rationale: "let in may lee family ' s total income = 100 in may mrs lee ' s income = 70 in may rest of the family ' s income = 30 in june mrs lees income = 70 * 120 / 100 = 84 in june total income = 84 + 30 = 114 % of mrs lee ' s income = 84 / 114 = 73.68 ( d )"
Answer: d
Question (other): one year ago , the ratio of roonie ’ s and ronaldo ’ s age was 6 : 7 respectively . 4 years hence , this ratio would become 7 : 8 . how old is ronaldo ?
Options: a ) 32 , b ) 33 , c ) 34 , d ) 35 , e ) 36
Rationale: 7 ( x - 1 ) = 6 ( y - 1 ) = > 7 x - 6 y - 1 = 0 - - - - eq 1 8 ( x + 4 ) = 7 ( y + 4 ) = > 8 x - 7 y + 4 = 0 - - - - eq 2 on solving eq 1 n eq 2 y = 36 answer : e
Answer: e