Cheukting/mathqa huggingface dataset:
Question (general): an object thrown directly upward is at a height of h feet after t seconds , where h = - 12 ( t - 3 ) ^ 2 + 120 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?
Options: a ) 48 , b ) 54 , c ) 60 , d ) 66 , e ) 72
Rationale: "we see that h will be a maximum h = 120 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 12 * ( 5 - 3 ) ^ 2 + 120 = - 12 ( 4 ) + 120 = 72 the answer is e ."
Answer: e
Question (general): if | x - 5 | = 23 what is the sum of all the values of x .
Options: a ) 46 , b ) 10 , c ) 56 , d ) - 46 , e ) 28
Rationale: "there will be two cases x - 5 = 23 and x - 5 = - 23 solve for x = > x = 23 + 5 = > x = 28 or x = - 23 + 5 = > x = - 18 the sum of both values will be 28 + - 18 = 10 answer is b"
Answer: b
Question (other): the number of stamps that kaye and alberto had were in the ration of 6 : 4 respectively . after kaye gave alberto 5 of her stamps , the ration of the number of kaye had to the number of alberto had was 8 : 6 . as a result of the gift , kaye had how many more stamps than alberto ?
Options: a ) 22 , b ) 25 , c ) 15 , d ) 35 , e ) 30
Rationale: "k 1 = 6 x a 1 = 4 x k 2 = 6 x - 5 a 2 = 4 x + 5 k 2 / a 2 = 8 / 6 ( 6 x - 5 ) / ( 4 x + 5 ) = 8 / 6 6 * ( 6 x - 5 ) = 8 * ( 4 x + 5 ) 36 x - 30 = 32 x + 40 4 x = 70 x = 17.5 k 2 = 6 * 17.5 - 5 = 100 a 2 = 4 * 17.5 + 5 = 75 k 2 - a 2 = 100 - 75 = 25 answer : b"
Answer: b
Question (general): find √ ? / 11 = 4 ?
Options: a ) 76 , b ) 1936 , c ) 1304 , d ) 1296 , e ) none
Rationale: answer let √ n / 11 = 4 then √ n = 11 x 4 = 44 ∴ n = 44 x 44 = 1936 . correct option : b
Answer: b
Question (general): on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price w per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."
Answer: d
Question (physics): two pipes p and q can fill a cistern in 12 and 13 minutes respectively . both are opened together , but at the end of 3 minutes the first is turned off . how much longer will the cistern take to fill ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 2 / 4 , d ) 1 / 4 , e ) 3 / 4
Rationale: "3 / 12 + x / 13 = 1 x = 7 3 / 4 answer : e"
Answer: e
Question (physics): i flew my tiny seaplane to visit my mother . on the flight up , i flew at 130 mph . on the way home , i flew 88 mph . what was my average speed for the trip ?
Options: a ) 198 mph , b ) 110 mph , c ) 88 mph , d ) 100 mph , e ) 109 mph
Rationale: "( 130 mph + 88 mph ) / 2 = 109 mph correct answer is : e"
Answer: e
Question (gain): a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 10 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 37.5 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.9 * 150 x = 135 x hence total profit = 35 % option c"
Answer: c
Question (geometry): if the radius of a circle is decreased 20 % , what happens to the area ?
Options: a ) 10 % decrease , b ) 20 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 50 % decrease
Rationale: "area of square = pi * radius ^ 2 new radius = 4 / 5 * old radius so new area = ( 4 / 5 ) ^ 2 old area = > 16 / 25 of old area = > 64 % old area answer : c"
Answer: c
Question (general): a man has some hens and cows . if the number of heads be 44 and the number of feet equals 128 , then the number of hens will be
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28
Rationale: "explanation : let number of hens = h and number of cows = c number of heads = 44 = > h + c = 44 - - - ( equation 1 ) number of feet = 128 = > 2 h + 4 c = 128 = > h + 2 c = 64 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 64 - 44 = > c = 20 substituting the value of c in equation 1 , we get h + 22 = 44 = > h = 44 - 20 = 24 i . e . , number of hens = 24 answer : b"
Answer: b
Question (physics): in a 200 meters race a beats b by 35 m or 7 seconds . a ’ s time over the course is :
Options: a ) 40 sec , b ) 47 sec , c ) 33 sec , d ) 35 sec , e ) none of these
Rationale: "solution b runs 35 m in 7 sec . ∴ b covers 200 m in ( 7 / 35 x 200 ) = 40 sec b ’ s time over the course = 40 sec . ∴ a ’ s time over the course = ( 40 - 7 ) sec = 33 sec answer c"
Answer: c
Question (physics): a and b can do a piece of work in 8 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ?
Options: a ) 13 1 / 3 , b ) 878 , c ) 30 , d ) 88 , e ) 11
Rationale: "c = 1 / 5 â € “ 1 / 8 = 3 / 40 = > 40 / 3 = 13 1 / 3 days answer : a"
Answer: a
Question (general): - 84 * 29 + 365 = ?
Options: a ) 2436 , b ) 2801 , c ) - 2801 , d ) - 2071 , e ) none of these
Rationale: "= > - 84 * ( 30 - 1 ) + 365 ; = > - ( 84 * 30 ) + 84 + 365 ; = > - 2520 + 449 = - 2071 . correct option : d"
Answer: d
Question (geometry): approximately how many cubic feet of water are needed to fill a circular swimming pool that is 80 feet across and 10 feet deep ?
Options: a ) 10000 , b ) 50000 , c ) 80000 , d ) 85000 , e ) 90000
Rationale: "answer should be b . v = \ pir ^ 2 h = \ pi * 40 ^ 2 * 10 = approximately 50000"
Answer: b
Question (other): if shares of two persons in profits are rs . 300 and rs . 500 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 5
Rationale: "total profit = 1000 ratio = 300 / 500 = 3 : 5 answer : b"
Answer: b
Question (other): there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability r that the both positions will be taken by members of just one party ?
Options: a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2
Rationale: "r probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total candidates . since this result can happen for both parties , ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) answer : d"
Answer: d
Question (physics): a train 270 m long , running with a speed of 108 km / hr will pass a tree in
Options: a ) 12 sec , b ) 9 sec , c ) 16 sec , d ) 20 sec , e ) none
Rationale: "sol . speed = ( 108 x 5 / 18 ) m / sec . = 30 m / sec . time taken = ( 270 x 1 / 30 ) sec = 9 sec answer b"
Answer: b
Question (other): a container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 12 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 2 : 5 , b ) 3 : 7 , c ) 3 : 5 , d ) 4 : 7 , e ) 7 : 17
Rationale: "container 1 has 12 ounces in the ratio 1 : 2 or , x + 2 x = 12 gives x ( alcohol ) = 4 and remaining water = 8 container 2 has 12 ounces in the ratio 1 : 3 or , x + 3 x = 12 gives x ( alcohol ) = 3 and remaining water = 9 mixing both we have alcohol = 4 + 3 and water = 8 + 9 ratio thus alcohol / water = 7 / 17 answer e"
Answer: e
Question (gain): a and b invests rs . 3000 and rs . 4500 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 6 : 8 , b ) 9 : 8 , c ) 7 : 9 , d ) 9 : 5 , e ) 1 : 1
Rationale: "( 3 * 6 + 6 * 6 ) : ( 4.5 * 12 ) 54 : 54 = > 1 : 1 answer : e"
Answer: e
Question (physics): a train of length l is traveling at a constant velocity and passes a pole in t seconds . if the same train travelling at the same velocity passes a platform in 2 t seconds , then what is the length of the platform ?
Options: a ) 0.5 l , b ) l , c ) 1.5 l , d ) 2 l , e ) 3
Rationale: "the train passes a pole in t seconds , so velocity v = l / t ( l + p ) / v = 2 t ( l + p ) / ( l / t ) = 2 t p = l the answer is b ."
Answer: b
Question (general): on a test average ( arithmetic mean ) test score for 4 students is 85 . what must be 5 th student ' s score that average score for 5 students to be 86 ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 110
Rationale: ( 4 * 85 + x ) / 5 = 86 x = ( 5 * 86 ) - ( 4 * 85 ) x = 430 - 340 total score required 430 - 340 = 90 correct answer is c
Answer: c
Question (physics): a 200 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
Options: a ) 210 m , b ) 300 m , c ) 230 m , d ) 240 m , e ) 250 m
Rationale: "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 200 / 9 = 500 / 9 x = 300 ans is 300 m answer : b"
Answer: b
Question (physics): sharmila works 10 hours per day on monday , wednesday and friday , and 8 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 460 per week . how much does she earn in dollars per hour ?
Options: a ) 8 , b ) 9 , c ) 9.5 , d ) 10 , e ) 11
Rationale: so , she works 30 hours in 3 days so , she works 16 hours in 2 days so in a week she works 46 hours ( 30 + 16 ) and earns $ 460 so , hourly wage is 460 / 46 = > 10 hence answer will be ( d ) 10
Answer: d
Question (general): ( 0.86 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.86 ) ( power 2 ) + 0.086 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.86 , b ) 0.68 , c ) 0.96 , d ) 0.69 , e ) 0.76
Rationale: given expression = ( 0.86 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.86 ) ( power 2 ) + ( 0.86 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.86 - 0.1 ) = 0.76 answer is e
Answer: e
Question (general): find the ratio in which wheat of inferior quality ( rs . 14 / kg ) be mixed with wheat of superior quality ( rs . 28 / kg ) so that the shopkeeper gains rs . 2 by selling the resulting mixture at rs . 20 / kg .
Options: a ) 5 : 2 , b ) 5 : 9 , c ) 5 : 3 , d ) 5 : 1 , e ) 5 : 8
Rationale: explanation : let the resulting mixture be 1 kg , and x kg be the amount of wheat of inferior quality . therefore , ( 1 - x ) kg is the amount of wheat of superior quality . as the shopkeeper gains rs . 2 , the cost of the mixture is rs . 18 14 * x + 28 * ( 1 - x ) = 18 14 x - 28 x + 28 = 18 14 x = 10 x = 5 / 7 ( 1 – x ) = 2 / 7 x : ( 1 - x ) = 5 / 7 : 2 / 7 = 5 : 2 answer : a
Answer: a
Question (general): george baked a total of 75 pizzas for 7 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ?
Options: a ) 5 , b ) 4 , c ) 2 , d ) 6 , e ) 7
Rationale: "3 / 5 of the 75 pizzas cooked on saturday = 45 pizzas 3 / 5 of the remaining pizzas on sunday = 18 pizzas we ' re left with ( 75 - 45 - 18 ) = 12 pizzas for the remaining 5 days . the prompt tells us that each day has fewer pizzas than the day before it , so we ca n ' t have duplicate numbers . m t w th f 5 4 2 1 0 = 12 w = 2 c"
Answer: c
Question (general): - - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 150 students answered yes only for subject m , how many of the students did not answer yes for either subject ?
Options: a ) 100 , b ) 250 , c ) 300 , d ) 400 , e ) 500
Rationale: "since 150 students answered yes only for subject m , then the remaining 350 students who answered yes for subject m , also answered yes for subject r . so , 350 students answered yes for both subjects . if 350 students answered yes for both subjects , then 400 - 350 = 50 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 50 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 50 + 300 ) = 250 students did not answer yes for either subject . answer : b ."
Answer: b
Question (probability): a bag contains 6 red , 2 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
Options: a ) 12 / 55 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Rationale: "total number of balls = 6 + 2 + 4 = 12 n ( s ) = 12 c 3 = 12 * 11 * 10 / 3 * 2 = 220 n ( e ) = 6 c 1 * 2 c 1 * 4 c 1 = 48 probability = 48 / 220 = 12 / 55 answer is a"
Answer: a
Question (gain): in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 50 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 30 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: "total men in company 50 % means total women in company 50 % ( assume total people in company 100 % ) no of men employees attended picnic = 50 x ( 20 / 100 ) = 10 no of women employees attend picnic = 50 x ( 40 / 100 ) = 20 total percentage of employees attend the picnic = 10 + 20 = 30 % answer : a"
Answer: a
Question (physics): a trader sells 80 meters of cloth for rs . 10000 at the profit of rs . 7 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 118 , b ) 88 , c ) 90 , d ) 42 , e ) 22
Rationale: "sp of 1 m of cloth = 8925 / 85 = rs . 125 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 125 - rs . 7 = rs . 118 answer : a"
Answer: a
Question (other): the present ratio of students to teachers at a certain school is 35 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "we are given that the ratio of students to teacher is 35 to 1 . we can rewrite this using variable multipliers . students : teachers = 35 x : x we are next given that student enrollment increases by 50 and the number of teachers increases by 5 . with this change the new ratio becomes 25 to 1 . we can put all this into an equation : students / teachers  25 / 1 = ( 35 x + 50 ) / ( x + 5 ) if we cross multiply we have : 25 ( x + 5 ) = 35 x + 50 25 x + 125 = 35 x + 50 7.5 = x x ~ 8 since x is the present number of teachers , currently there are 8 teachers . answer b ."
Answer: b
Question (general): if x and y are the two digits of the number 653 xy . such that this number is divisible by 80 , then x + y is equal to
Options: a ) 3 , b ) 2 , c ) 4 , d ) 1 , e ) 0
Rationale: since 653 xy is divisible by 5 as well as 2 . so y = 0 now 653 x 0 must be divisible by 8 so 3 x 0 must be 8 this happens when x = 2 hence , x + y = 2 + 0 = 2 answer b 2
Answer: b
Question (general): 22 + 23 + 24 + . . . 61 + 62 + 63 = ?
Options: a ) 1361 , b ) 1362 , c ) 1363 , d ) 1364 , e ) 1785
Rationale: "sum = 22 + 23 + 24 + . . . 61 + 62 + 63 sum of n consecutive positive integers starting from 1 is given as n ( n + 1 ) / 2 sum of first 63 positive integers = 63 * 64 / 2 sum of first 21 positive integers = 21 * 22 / 2 sum = 22 + 23 + 24 + . . . 61 + 62 + 63 = 63 * 64 / 2 - 21 * 22 / 2 = 1376 answer : e"
Answer: e
Question (physics): matt and peter can do together a piece of work in 24 days . after they have worked together for 12 days matt stops and peter completes the remaining work in 10 days . in how many days peter complete the work separately .
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "together they complete the job in 24 days means they complete 12 / 24 of the job after 12 days . peter completes the remaining ( 12 / 24 ) of the job in 10 days which means that the whole job ( 1 ) can be completed in x days . x = 12 / ( 12 / 24 ) = 24 a"
Answer: a
Question (physics): a train which has 600 m long , is running 60 kmph . in what time will it cross a person moving at 6 kmph in same direction ?
Options: a ) 42 sec , b ) 44 sec , c ) 46 sec , d ) 40 sec , e ) 50 sec
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 600 / ( ( 60 - 6 ) ( 5 / 18 ) = 600 / 54 * ( 5 / 18 ) = 600 / 15 = 40 sec answer : d"
Answer: d
Question (probability): when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 3 times , what is the probability that it will land on the same side each time ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 3 , d ) 3 / 8 , e ) 1 / 2
Rationale: "winning scenario is if we ' ll have either three tails ( ttt ) or three heads ( hhh ) : 1 / 2 * 1 / 2 * 1 / 2 + 1 / 2 * 1 / 2 * 1 / 2 = 1 / 4 . answer : b ."
Answer: b
Question (physics): machine p can print one lakh books in 8 hours . machine q can print the same number of books in 10 hours while machine r can print the same in 12 hours . all the machines started printing at 9 a . m . machine p is stopped at 11 a . m . and the remaining two machines complete work . approximately at what time will the printing of one lakh books be completed ?
Options: a ) 3 pm , b ) 2 pm , c ) 1 : 00 pm , d ) 11 am , e ) 12 am
Rationale: explanation : work done by p in 1 hour = 1 / 8 work done by q in 1 hour = 1 / 10 work done by r in 1 hour = 1 / 12 work done by p , q and r in 1 hour = 1 / 8 + 1 / 10 + 1 / 12 = 37 / 120 work done by q and r in 1 hour = 1 / 10 + 1 / 12 = 22 / 120 = 11 / 60 from 9 am to 11 am , all the machines were operating . ie , they all operated for 2 hours and work completed = 2 × ( 37 / 120 ) = 37 / 60 pending work = 1 - 37 / 60 = 23 / 60 hours taken by q an r to complete the pending work = ( 23 / 60 ) / ( 11 / 60 ) = 23 / 11 which is approximately equal to 2 hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm answer : option c
Answer: c
Question (general): three numbers are in the ratio 4 : 5 : 6 and their average is 30 . the largest number is :
Options: a ) 33 , b ) 77 , c ) 36 , d ) 18 , e ) 16
Rationale: "explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 30 15 x = 90 x = 6 largest number = 6 x = 36 . answer : c"
Answer: c
Question (gain): by selling a book for 270 , 20 % profit was earned . what is the cost price of the book ?
Options: a ) 215 , b ) 225 , c ) 230 , d ) 235 , e ) 240
Rationale: "sp = 120 % of cp ; : . cp = 270 × 100 / 120 = 225 option ' b '"
Answer: b
Question (general): the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 10 points after 5 games , what is the least number of the remaining matches it has to win to reach the 45 - point mark by the end of the tournament ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "to get 45 points as end of season we need another 35 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 option c = 8 * 3 + 7 * 1 = 31 option d = 9 * 3 + 6 * 1 = 33 option e = 10 * 3 + 5 * 1 = 35 hence option e - 10"
Answer: e
Question (general): the price of lunch for 15 people was $ 208.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) $ 11.73 , b ) $ 12.60 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
Rationale: "take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 208 is for 115 then we have to calculate for 100 for 115 208 for 100 x so by cross multiplication we get 115 x = 100 * 208 = > x = 100 * 208 / 110 by simplifying we get x as 189 which is the price of lunch before gratuity so the gratuity is 19 so as the question ask the average price person excluding gratuity is 189 / 15 = 12.6 so our answer is b )"
Answer: b
Question (geometry): if the area of a circle decreases by 36 % , then the radius of a circle decreases by
Options: a ) 20 % , b ) 18 % , c ) 36 % , d ) 64 % , e ) none of these
Rationale: "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 36 ) % = ( 100 − 10 √ 64 ) % = 100 - 80 = 20 % answer a"
Answer: a
Question (general): if n is a positive integer and n ^ 2 is divisible by 450 , then what is the largest positive integer that must divide n ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "450 = 2 * 3 ^ 2 * 5 ^ 2 if 450 divides n ^ 2 , then n must be divisible by 2 * 3 * 5 = 30 the answer is c ."
Answer: c
Question (gain): if the given two numbers are respectively 7 % and 14 % of a third number , then what percentage is the first of the second ?
Options: a ) 20 % , b ) 25 % , c ) 18 % , d ) 50 % , e ) none of these
Rationale: "here , l = 7 and m = 14 therefore , first number = l / m x 100 % of second number = 7 / 14 x 100 % of second number = 50 % of second number answer : d"
Answer: d
Question (general): the average of first 9 prime numbers is ?
Options: a ) 10.11 , b ) 11.11 , c ) 12.11 , d ) 13.11 , e ) 14.11
Rationale: "sum of 10 prime no . = 100 average = 100 / 9 = 11.11 answer : b"
Answer: b
Question (general): a trailer carries 3 , 4 and 6 crates on a trip . each crate weighs no less than 120 kg . what is the maximum weight of the crates on a single trip ?
Options: a ) 1250 , b ) 625 , c ) 600 , d ) 7500 , e ) 720
Rationale: "max no . of crates = 6 . max weight = 120 kg max . weight carried = 6 * 120 = 720 kg = e"
Answer: e
Question (general): the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 21 years . the ratio of their ages after 8 years will be
Options: a ) 2 : 3 , b ) 20 : 17 , c ) 5 : 4 , d ) 3 : 5 , e ) 6 : 11
Rationale: "let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 21 x = 3 mini ’ s age = 12 years and minakshi ’ s age = 9 years ratio of their ages after 8 years = ( 12 + 8 ) : ( 9 + 8 ) = 20 : 17 answer : b"
Answer: b
Question (physics): a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 1.7 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
Options: a ) 0.9 , b ) 1.2 , c ) 1.5 , d ) 1.8 , e ) 2.1
Rationale: "72 km / hr = 1.2 km / min the total distance is 1.8 km . 1.8 / 1.2 = 1.5 minutes the answer is c ."
Answer: c