regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: - 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: ( 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
Problem: 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
Problem: 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
Problem: - - - - - - - - - - - - - - - - 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: the difference between a number and its two - fifth is 510 . what is 5 % of that number ?
Options: a ) 425 , b ) 300 , c ) 255 , d ) 300 , e ) 400
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 5 % of 850 = 425 . answer : a"
Answer: a
Problem: the contents of two vessels containing copper and tin in the ratio 1 : 2 and 2 : 5 are mixed in the ratio 1 : 4 . the resulting mixture will have copper and tin in the ratio ?
Options: a ) 15 : 32 , b ) 21 : 28 , c ) 31 : 74 , d ) 33 : 37 , e ) 41 : 92
Rationale: "the ratio of copper and tin the new vessel = ( 1 / 3 * 1 / 5 + 2 / 7 * 4 / 5 ) : ( 2 / 3 * 1 / 5 + 5 / 7 * 4 / 5 ) = 31 / 105 : 74 / 105 = 31 : 74 answer is c"
Answer: c
Problem: a can do a piece of work in 4 days . b can do it in 8 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 22 days , b ) 8 days , c ) 67 days , d ) 1 days , e ) 18 days
Rationale: "c = 1 / 2 - 1 / 4 - 1 / 8 = 1 / 8 = > 8 days answer : b"
Answer: b
Problem: a cargo ships engines failed 100 miles away from the port . due to the changing wind direction , it is moving 12 miles towards the port and 6 miles away from the port . if the wind pattern remains same , how many miles it will travel before reaching the port ?
Options: a ) a - 179 , b ) b - 240 , c ) c - 280 , d ) d - 100 , e ) e - 155
Rationale: ships overall distance covered per cycle is + 6 miles take 100 - 6 take 94 / 6 to lowest divisible number - 90 / 6 this means that it will take 15 ` ` overall ' ' actions to reach the 90 th mile . - 15 * 18 miles added later set cycle start at 90 . travel 10 miles and reach the anchor point - add 10 to total 15 * 18 + 10 = 280 miles in total answer : c
Answer: c
Problem: if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 8 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?
Options: a ) 6 , b ) 14 , c ) 22 , d ) 30 , e ) 174
Rationale: "the number of integers that belong to set x only is 8 - 6 = 2 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 2 + 12 = 14 . answer : b ."
Answer: b
Problem: a circular logo is enlarged to fit the lid of a jar . the new diameter is 50 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50 , b ) 80 , c ) 100 , d ) 125 , e ) 250
Rationale: "let old diameter be 4 , so radius is 2 old area = 4 π new diameter is 6 , so radius is 3 new area = 9 π increase in area is 5 π % increase in area = 5 / 4 * 100 so , % increase is 125 % answer will be ( d )"
Answer: d
Problem: a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 3.5 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 ) 3 , b ) 4.2 , c ) 3.4 , d ) 5.5 , e ) 5.7
Rationale: "72 km / hr = 1.2 km / min the total distance is 3.6 km . 3.6 / 1.2 = 3 minutes the answer is a ."
Answer: a
Problem: if 0.5 % of a = 80 paise , then the value of a is ?
Options: a ) rs . 170 , b ) rs . 160 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
Rationale: "answer ∵ 0.5 / 100 of a = 80 / 100 ∴ a = rs . ( 80 / 0.5 ) = rs . 160 correct option : b"
Answer: b
Problem: it takes 2 team of farm workers 12 days to completely prepare a piece of land for planting . if both team of workers were to work separately , one of them can complete the work 10 days earlier than the other , how many days will it take each of them to separately complete the work ?
Options: a ) 12 and 22 , b ) 11 and 21 , c ) 15 and 25 , d ) 9 and 19 , e ) 20 and 30
Rationale: work = ( a ) ( b ) / ( a + b ) where a and b are the individual times of each entity . here , we ' re told that ( working together ) the two team of workers would complete a job in 12 days . this means that ( individually ) each of team would take more than 12 days to do the job . answers d , a and b are illogical , since the individual times must both be greater than 12 days . so we can test the values for answers c and e . using the values for answers b and d . . . answer b : ( 15 ) ( 25 ) / ( 15 + 25 ) = 375 / 40 = 9.4 this is a match answer e : ( 20 ) ( 30 ) / ( 20 + 30 ) = 12 final answer : e
Answer: e
Problem: find compound interest on $ 8000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) 3109 , b ) 3209 , c ) 3108 , d ) 3107 , e ) 3100
Rationale: time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 8000 x ( 1 + ­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 8000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 11109 . . : . c . i . = rs . ( 11109 - 8000 ) = $ 3109 . answer a .
Answer: a
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 85 kg , d ) 80 kg , e ) 60 kg
Rationale: "explanation : total increase in weight = 8 ã — 2.5 = 20 if x is the weight of the new person , total increase in weight = x â ˆ ’ 45 = > 20 = x - 45 = > x = 20 + 45 = 65 answer : option b"
Answer: b
Problem: in what time will a train 100 m long cross an electric pole , it its speed be 54 km / hr ?
Options: a ) 2.5 , b ) 2.9 , c ) 6.67 , d ) 2.8 , e ) 2.1
Rationale: "speed = 54 * 5 / 18 = 15 m / sec time taken = 100 / 15 = 6.67 sec . answer : c"
Answer: c
Problem: find the area of a triangle whose sides are 41 cm , 28 cm , 15 cm . also , find the length of the altitude corresponding to the largest side of the triangle .
Options: a ) 4.1 cm
b ) 5.1 cm
c ) 6.1 cm
d ) 7.1 cm
e ) 8.1 cm
Rationale: semi - perimeter of the triangle = ( a + b + c ) / 2 = ( 41 + 28 + 15 ) / 2 = 84 / 2 = 42 cm therefore , area of the triangle = √ ( s ( s - a ) ( s - b ) ( s - c ) ) = √ ( 42 ( 42 - 41 ) ( 42 - 28 ) ( 42 - 15 ) ) cm ² = √ ( 42 × 1 × 27 × 14 ) cm ² = √ ( 3 × 3 × 3 × 3 × 2 × 2 × 7 × 7 ) cm ² = 3 × 3 × 2 × 7 cm ² = 126 cm ² now , area of triangle = 1 / 2 × b × h therefore , h = 2 a / b = ( 2 × 126 ) / 41 = 252 / 41 = 6.1 cm answer : option c
Answer: c
Problem: alex takes a loan of $ 8,000 to buy a used truck at the rate of 6 % simple interest . calculate the annual interest to be paid for the loan amount .
Options: a ) 480 , b ) 520 , c ) 460 , d ) 400 , e ) 520
Rationale: "from the details given in the problem principle = p = $ 8,000 and r = 6 % or 0.06 expressed as a decimal . as the annual interest is to be calculated , the time period t = 1 . plugging these values in the simple interest formula , i = p x t x r = 8,000 x 1 x 0.06 = 480.00 annual interest to be paid = $ 480 answer : a"
Answer: a
Problem: if john covers a certain distance in 1 hr . 24 min . by covering two third of the distance at 4 kmph and the rest at 5 kmph , then find the total distance
Options: a ) 4 km , b ) 6 km , c ) 6.8 km , d ) 7.2 km , e ) none of these
Rationale: explanation : let the total distance be y km . then , ( 2 / 3 ) y / 4 + ( 1 / 3 ) y / 5 = 7 / 5 y / 6 + y / 15 = 7 / 5 7 y = 42 y = 6 km answer b
Answer: b
Problem: in how many ways 4 boys and 3 girls can be seated in a row so that they are alternative ?
Options: a ) 120 , b ) 144 , c ) 160 , d ) 210 , e ) 180
Rationale: "4 boys can be seated in 4 ! three girls can be seated in 3 ! required number = 4 ! 3 ! = 144 answer is b"
Answer: b
Problem: if ( 10 ^ 4 * 3.456789 ) ^ 10 is written as a single term , how many digits would be to the right of the decimal place ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 32 , e ) 48
Rationale: "3.456789 ^ 10 has 6 * 10 = 60 decimal places . 10 ^ 40 moves the decimal place to the right 40 places . ( 10 ^ 4 * 3.456789 ) ^ 10 has 60 - 40 = 20 digits after the decimal point . the answer is c ."
Answer: c
Problem: if each edge of cube increased by 30 % , the percentage increase in
Options: a ) 69 , b ) 72 , c ) 64 , d ) 61 , e ) 75
Rationale: "100 × ( 130 ) / 100 × ( 130 ) / 100 = 169 = > 69 % answer is a ."
Answer: a
Problem: a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 63 liters of drink a to convert it to drink b ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
Rationale: "in 63 liters of drink a , there are 36 liters of milk and 27 liters of juice . with 36 liters of milk , we need a total of 48 liters of juice to make drink b . we need to add 21 liters of juice . the answer is c ."
Answer: c
Problem: what is the remainder when 15487 ^ ( 62177037 ) is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "we need to find the units digit of the number . the units digit of powers of seven repeats 7 , 9 , 3 , and 1 cyclically . since 62177037 has the form 4 a + 1 , the units digit is 7 . then the remainder when dividing by 5 is 2 . the answer is c ."
Answer: c
Problem: james went on a diet 12 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 190 pounds ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: 222 - 198 = 24 pounds lost in 12 months 24 / 12 = 2 , so joe is losing weight at a rate of 2 pounds per month . . . . in approximately how many months will he weigh 190 pounds ? a simple approach is to just list the weights . now : 198 lbs in 1 month : 196 lbs in 2 months : 194 lbs in 3 months : 192 lbs in 4 months : 190 lbs answer : c
Answer: c
Problem: the dimensions of a rectangular solid are 4 inches , 5 inches , and 9 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?
Options: a ) 2 : 5 , b ) 5 : 9 , c ) 5 : 16 , d ) 25 : 7 , e ) 32 : 25
Rationale: answer : b .
Answer: b
Problem: there are cats got together and decided to kill the mice of 999951 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ?
Options: a ) 941,1009 , b ) 993,1007 , c ) 991,1009 , d ) 791,1009 , e ) 931,1009
Rationale: "999951 can be written as 1000000 â € “ 49 = 10002 â € “ 72 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 7 ) * ( 1000 - 7 ) = ( 1007 ) * ( 993 ) given that number of cats is less than number if mice . so number of cats is 993 and number of mice were 1007 answer b"
Answer: b
Problem: a taxi company costs $ 2.75 for the first quarter - mile and 12.5 cents for each additional quarter mile . what is the maximum distance you can travel with $ 6.50 ?
Options: a ) 4 miles , b ) 5 3 / 4 miles , c ) 6 1 / 2 miles , d ) 7 3 / 4 miles , e ) 8 1 / 4 miles
Rationale: use reverse calculation - total cost = fixed cost ( for 1 / 4 miles ) + variable cost ( distance travelled ) or , 6.50 = 2.75 + 0.125 * d or , 3.75 = d / 8 or , d = 30 quarter miles so , total distance = ( 30 + 1 ) quarter miles so , distance = 31 / 4 = > 73 / 4 miles hence answer will be ( d )
Answer: d
Problem: claire has a total of 96 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?
Options: a ) 84 , b ) 50 , c ) 54 , d ) 57 , e ) 60
Rationale: "g + h = 96 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 96 - h or 3 ( 96 - h ) + 4 h = 300 h = 300 - 288 = 12 then g = 96 - 12 = 84 a"
Answer: a
Problem: find 94 × × 97
Options: a ) 93 / 198 , b ) 93 / 12 , c ) 93 / 18 , d ) 93 / 10 , e ) 93 / 11
Rationale: "here both numbers are less than 100 . so they are deficient of - 6 and - 3 compared with 100 . so answer : c"
Answer: c
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 800 m long ?
Options: a ) 266 sec , b ) 200 sec , c ) 776 sec , d ) 166 sec , e ) 997 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2000 m t = d / s t = 2000 / 10 t = 200 sec answer : b"
Answer: b
Problem: at what rate percent of simple interest will a sum of money double itself in 11 years ?
Options: a ) 9.09 % , 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 * 11 ) = 100 / 11 = 9.09 % answer : a"
Answer: a
Problem: if m and n are positive integers and m ^ 2 + n ^ 2 = 137 , what is the value of m ^ 3 + n ^ 3 ?
Options: a ) 72 , b ) 224 , c ) 320 , d ) 512 , e ) 1,395
Rationale: you need to integers which squared are equal 40 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 8 ^ 2 = 64 9 ^ 2 = 81 10 ^ 2 = 100 11 ^ 2 = 121 stop . the integers ca n ' t be greater than 6 or we will score above 137 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 8 ^ 2 = 64 9 ^ 2 = 81 10 ^ 2 = 100 11 ^ 2 = 121 the only pair that matches is 11 ^ 2 + 4 ^ 2 = 137 . so 11 ^ 3 + 4 ^ 3 = 1395 . answer e . )
Answer: e
Problem: if the product of the integers from 1 to n is divisible by 630 , what is the least possible value of n ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
Rationale: "630 = 2 x 3 x 3 x 5 x 7 n must include at least up to the number 7 . the answer is a ."
Answer: a
Problem: a monkey start climbing up a tree 22 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
Options: a ) 15 hrs , b ) 18 hrs , c ) 20 hrs , d ) 17 hrs , e ) 16 hrs
Rationale: "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 19 hrs it wil be 19 ft . bt since the height of the tree is 22 ft , so if the monkey hops up the tree in the next hr i . e 20 th hr then it reaches at the top of the tree . hence it takes 20 hrs for monkey to reach at the top answer : c"
Answer: c
Problem: the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 26 ?
Options: a ) 50 , b ) 52 , c ) 54 , d ) 56 , e ) 58
Rationale: "$ 26 = 4 * $ 6 + $ 2 the number of doughnuts is 4 * 12 + 2 = 50 the answer is a ."
Answer: a
Problem: when you draw 2 dices together , find the probability of getting a total of 6 ?
Options: a ) 3 / 13 , b ) 2 / 31 , c ) 5 / 36 , d ) 7 / 41 , e ) 7 / 43
Rationale: s = { ( 1,1 ) , ( 1,2 ) , ( 1,3 ) , ( 1,4 ) , ( 1,5 ) , ( 1,6 ) , ( 4,1 ) , ( 4,2 ) , ( 4,3 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 2,1 ) , ( 2,2 ) , ( 2,3 ) , ( 2,4 ) , ( 2,5 ) , ( 2,6 ) , ( 5,1 ) , ( 5,2 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 3,1 ) , ( 3,2 ) , ( 3,3 ) , ( 3,4 ) , ( 3,5 ) , ( 3,6 ) , ( 6,1 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) } n ( s ) = 36 set of total of 6 , a = { ( 1,5 ) , ( 5,1 ) , ( 2,4 ) , ( 4,2 ) , ( 3,3 ) } ; n ( a ) = 5 p ( total of 6 ) = n ( a ) n ( s ) n ( a ) n ( s ) = 5 / 36 c
Answer: c
Problem: elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 50 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 24 , e ) $ 28
Rationale: "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 50 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 50 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 50 i . e . x = 26 i . e . fixed monthly charge , y = 26 answer : d"
Answer: d
Problem: a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1300 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) 12028 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 18000
Rationale: [ 1300 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 18000 answer : c
Answer: c
Problem: a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 9000 interest . the principal amount borrowed by him was .
Options: a ) rs 14000 , b ) rs 25000 , c ) rs 16000 , d ) rs 17000 , e ) none of these
Rationale: explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 9000 â ˆ — 100 / 12 â ˆ — 3 = rs 25000 option b
Answer: b
Problem: tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 9 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?
Options: a ) 8 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 5 mph , e ) 0.5 mph
Rationale: "( 1 mph + 9 mph ) / 2 = 5 mph correct option is : d"
Answer: d
Problem: suppose you want to buy 3 loaves of bread that cost $ 2.25 each and a jar of peanut butter that costs $ 2 . a jar of jelly is $ 2.75 , but you don â € ™ t need any jelly . you have $ 14 . how much money will you have left over ?
Options: a ) $ 1.50 , b ) $ 2.50 , c ) $ 5.25 , d ) $ 4.50 , e ) $ 5.50
Rationale: the jelly is extra information . 14.00 â € “ 3 x 2.25 â € “ 2.00 = 14.00 â € “ 6.75 â € “ 2.00 = 5.25 . you have $ 5.25 left . correct answer c
Answer: c
Problem: a batsman scored 110 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 50 % , b ) 40 % , c ) 60 % , d ) 70 % , e ) 45.45 %
Rationale: "number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 110 - ( 60 ) = 50 now , we need to calculate 50 is what percent of 110 . = > 50 / 110 x 100 = 45.45 % answer : e"
Answer: e
Problem: a man can row 3.6 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?
Options: a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.1
Rationale: "speed of boat in still water ( b ) = 3.6 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.2 km / hr . answer : c"
Answer: c
Problem: two cars are traveling in the same direction along the same route . the red car travels at a constant speed of 30 miles per hour , and the black car is traveling at a constant speed of 50 miles per hour . if the red car is 20 miles ahead of the black car , how many hours will it take the black car to overtake the red car ?
Options: a ) 0.1 , b ) 0.6 , c ) 1 , d ) 1.2 , e ) 2
Rationale: "option c 20 + 30 t = 50 t t = 1"
Answer: c
Problem: the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 32,000 locusts ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "- 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 answer : c"
Answer: c
Problem: find the ratio in which rice at rs . 7.10 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg
Options: a ) 2 : 0 , b ) 3 : 4 , c ) 2 : 1 , d ) 2 : 2 , e ) 2 : 8
Rationale: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 80 = 3 : 4 answer : b"
Answer: b
Problem: in an election , candidate a got 75 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate .
Options: a ) 357000 , b ) 357003 , c ) 277677 , d ) 699377 , e ) 267877
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 75 % therefore , the number of valid votes polled in favour of candidate a = 75 % of 476000 = 75 / 100 × 476000 = 35700000 / 100 = 357000 answer : a"
Answer: a
Problem: there is a 40 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 40 cm , how many insects were still left after the race was over ?
Options: a ) 0 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "only the prime numbers greater than 10 and less than 40 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , 31 , and 37 . the total is 8 . the answer is d ."
Answer: d
Problem: the average salary of all the workers in a workshop is $ 1000 . the average salary of 5 technicians is $ 5000 and the average salary of the rest is $ 500 . the total number of workers in the shop is ?
Options: a ) 25 , b ) 20 , c ) 15 , d ) 30 , e ) 18
Rationale: "let the total number of workers be x 1000 x = 5000 * 5 + 500 ( x - 5 ) x = 25 answer is a"
Answer: a
Problem: you have been given a physical balance and 7 weights of 43 , 45 , 30 , 33 , 28 , 37 and 55 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 145 kgs .
Options: a ) 145 , b ) 143 , c ) 147 , d ) 141 , e ) 142
Rationale: 55 + 43 + 45 = 143 answer : b
Answer: b
Problem: united telephone charges a base rate of $ 11.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?
Options: a ) 2 minutes , b ) 10 minutes , c ) 20 minutes , d ) 40 minutes , e ) 60 minutes
Rationale: "lets take number of minutesx . given that , 11 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 20 minutes ans c"
Answer: c
Problem: if the ratio of a to b is 8 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
Options: a ) 8 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6
Rationale: "a : b = 8 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 8 : 15 answer a"
Answer: a
Problem: the least number which when divided by 5 , 67 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is :
Options: a ) 1677 , b ) 1683 , c ) 2523 , d ) 3363 , e ) none of these
Rationale: solution l . c . m . of 5 , 6 , 7 , 8 = 840 . so , required number is of the form 840 k + 3 . least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . so , required number = ( 840 × 2 + 3 ) = 1683 . answer b
Answer: b
Problem: the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 16000 , then find the annual income of a ?
Options: a ) rs . 537600 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these
Rationale: b ' s monthly income = 16000 * 112 / 100 = rs . 17920 b ' s monthly income = 2 parts - - - - > rs . 17920 a ' s monthly income = 5 parts = 5 / 2 * 17920 = rs . 44800 a ' s annual income = rs . 44800 * 12 = rs . 537600 answer : a
Answer: a
Problem: 1 , 13 , 35 , 67 , 109 , ____
Options: a ) 161 , b ) 154 , c ) 216 , d ) 158 , e ) none
Rationale: "1 , 13 , 35 , 67 , 109 , . . . . . 13 = 1 + 12 35 = 13 + 22 67 = 35 + 32 109 = 67 + 42 so 109 + 52 = 161 answer : a"
Answer: a
Problem: two cars start from the opposite places of a main road , 150 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?
Options: a ) 65 , b ) 38 , c ) 20 , d ) 28 , e ) 21
Rationale: answer : a ) 65 km
Answer: a
Problem: a sum of money at simple interest amounts to rs . 820 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 647 , b ) 718 , c ) 654 , d ) 847 , e ) 976
Rationale: "s . i . for 1 year = rs . ( 854 - 820 ) = rs . 34 . s . i . for 3 years = rs . ( 34 x 3 ) = rs . 102 . principal = rs . ( 820 - 102 ) = rs . 718 . answer : b"
Answer: b
Problem: what is the least number . which should be added to 0.0568 to make it a perfect square ?
Options: a ) 0.0004 , b ) 0.0009 , c ) 0.0002 , d ) 0.0003 , e ) 0.0008
Rationale: "0.0568 + 0.0008 = 0.0576 ( 0.24 ) ^ 2 answer : e"
Answer: e
Problem: the average of first five multiples of 5 is :
Options: a ) 9 , b ) 15 , c ) 17 , d ) 8 , e ) 10
Rationale: "explanation : ( 5 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 5 x 15 / 5 = 15 answer : b"
Answer: b