regisss/math_qa huggingface dataset:
Problem: if 80 lamps can be lighted 5 hours per day for 10 days for rs . 21.25 , then the number of lamps which can be lighted 4 hours daily for 30 days for rs . 76.50 , is ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) none of these
Rationale: explanation : ( hrs / day 4 : 5 ) : ( money 21.25 : 76.50 ) : ( days 30 : 10 ) : : 80 : x 4 * 21.25 * 30 * x = 5 * 76.50 * 10 * 80 so x = 120 answer : c
Answer: c
Problem: in a group of ducks and cows , the total number of legs are 20 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 10 , b ) 12 , c ) 13 , d ) 15 , e ) 16
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 20 = > 2 x = 20 = > x = 10 a"
Answer: a
Problem: the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 41 kg , then the weight of b is :
Options: a ) 27 kg , b ) 20 kg , c ) 26 kg , d ) 31 kg , e ) 35 kg
Rationale: "let d sum of a , b , c is 3 * 45 = 135 and sum of a and b s 2 * 40 = 80 sum of b and c is 2 * 41 = 82 hence 80 + 82 - 135 = 27 ans = 27 answer : a"
Answer: a
Problem: i sold a book at a profit of 10 % . had i sold it for $ 100 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 2000 , b ) $ 2500 , c ) $ 3000 , d ) $ 3120 , e ) $ 1540
Rationale: "115 % of cost - 110 % of cost = $ 100 5 % of cost = $ 100 cost = 100 * 100 / 5 = $ 2000 answer is a"
Answer: a
Problem: an inspector rejects 0.08 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) 1200 , b ) 1240 , c ) 1852 , d ) 3200 , e ) 2500
Rationale: "then , 0.08 % of x = 2 ( 8 / 100 ) * ( 1 / 100 ) x = 2 x = ( 2 * 100 * 100 ) / 8 = 2500 answer is e"
Answer: e
Problem: the average age of a class is 15.8 years . the average age of the boys in the class is 16.4 years and that of the girls is 15.4 years . what is the ratio of boys to girls in the class ?
Options: a ) 1 : 2 , b ) 3 : 4 , c ) 2 : 3 , d ) 3 : 2 , e ) none of these
Rationale: "let number of boys = x ; let number of girls = y total numbers of students = x + y ( x + y ) × 15.8 = 16.4 x + 15.4 y 0.6 x = 0.4 y x / y = 0.4 / 0.6 = 2 / 3 answer : c"
Answer: c
Problem: in how many years will a sum of money doubles itself at 25 % per annum on simple interest ?
Options: a ) 4 % , b ) 8 % , c ) 10 % , d ) 12 % , e ) 15 %
Rationale: "p = ( p * 25 * r ) / 100 r = 4 % answer : a"
Answer: a
Problem: log 3 n + log 7 n what is 3 digit number n that will be whole number
Options: a ) 343 , b ) 729 , c ) 829 , d ) 929 , e ) 727
Rationale: no of values n can take is 1 7 ^ 3 = 343 answer : a
Answer: a
Problem: at the a - street fish market a vendor sells fresh caught fish . his store is filled with 2 / 7 bass , 1 / 5 tuna , 1 / 7 trout , and the rest are catfish . if a customer just bought 1 / 7 of all the tuna and 1 / 7 of all the catfish , and a fisherman arrived to restock the bass , doubling the number of bass , what proportion of fish now in the store are trout ?
Options: a ) 30 / 71 , b ) 4 / 7 , c ) 5 / 43 , d ) 1 / 2 , e ) 1 / 5
Rationale: bass = 2 / 7 = 10 / 35 tuna = 1 / 5 = 7 / 35 trout = 1 / 7 = 5 / 35 catfish = 1 - ( 10 / 35 + 7 / 35 + 5 / 35 ) = 13 / 35 purchased : tuna = 7 / 35 - ( 7 / 35 ) ( 1 / 7 ) = 6 / 35 , and catfish = 13 / 35 - ( 13 / 35 ) ( 1 / 7 ) = 12 / 35 stocked : doubling the number of bass ( 2 ) ( 10 / 35 ) = 20 / 35 now : 20 + 6 + 5 + 12 = 43 trout proportion is now 5 / 43 . answer : c
Answer: c
Problem: a and b started a business in partnership investing rs . 20000 and rs . 15000 respectively . after 6 months , c joined them with rs . 20000 . whatwill be b ' s share in total profit of rs . 20000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,000 , e ) s . 7,500
Rationale: a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 20000 x 3 / 10 = rs . 6,000 . d
Answer: d
Problem: the product of two positive integers is 323 and their difference is 2 . what is the smaller number ?
Options: a ) 17 , b ) 18 , c ) 16 , d ) 19 , e ) 14
Rationale: let ' s use trial and error to find the two numbers . 20 * 18 = 360 ( too high ) 19 * 17 = 323 the answer is a .
Answer: a
Problem: an alloy is to contain steel and iron in the ratio 5 : 2 . the iron required to be melted with 35 kg of steel is ?
Options: a ) 12 kg , b ) 14 kg , c ) 15 kg , d ) 20 kg , e ) 18 kg
Rationale: let the required quantity of steel be x kg 5 : 2 : : 35 : x 5 x = 2 * 35 x = 14 kg answer is b
Answer: b
Problem: a man complete a journey in 30 hours . he travels first half of the journey at the rate of 20 km / hr and second half at the rate of 10 km / hr . find the total journey in km .
Options: a ) 220 km , b ) 224 km , c ) 230 km , d ) 400 km , e ) 234 km
Rationale: 0.5 x / 20 + 0.5 x / 10 = 30 - - > x / 20 + x / 10 = 60 - - > 3 x = 20 x 60 - - > x = ( 60 x 20 ) / 3 = 400 km . answer : d
Answer: d
Problem: a man sitting in a train which is traveling at 60 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 52 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 75 kmph
Rationale: "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 60 ) kmph = 52 kmph . answer : a"
Answer: a
Problem: 0.0006 ? = 0.03
Options: a ) 2 , b ) 20 , c ) 0.2 , d ) 0.02 , e ) none of these
Rationale: "explanation : required answer = 0.0006 / 0.03 = 0.06 / 3 = 0.02 . answer : option d"
Answer: d
Problem: a train 125 m long passes a man , running at 4 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 11 , b ) 49 , c ) 88 , d ) 65 , e ) 22
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 4 ) km / hr . x - 4 = 45 = = > x = 49 km / hr . answer : b"
Answer: b
Problem: it would take one machine 9 hours to complete a large production order and another machine 8 hours to complete the same order . how many hours would it take both machines , working simultaneously at their respective constant rates , to complete the order ?
Options: a ) 72 / 17 , b ) 17 / 72 , c ) 14 / 24 , d ) 24 / 56 , e ) 34 / 56
Rationale: the rate of the first machine is 1 / 9 job per hour ; the rate of the second machine is 1 / 8 job per hour ; thus , the combined rate of the machines is 1 / 9 + 1 / 8 = 17 / 72 job per hour , which means that it takes 1 / ( 17 / 72 ) = 72 / 17 hours both machines to do the job . answer : a .
Answer: a
Problem: 3034 − ( 1002 ÷ 20.04 ) = ?
Options: a ) 1964 , b ) 1984 , c ) 2964 , d ) 2984 , e ) none of these
Rationale: "explanation : = 3034 − ( 1002 / 2004 × 100 ) = 3034 − 50 = 2984 option d"
Answer: d
Problem: a number is doubled and 9 is added . if the resultant is trebled , it becomes 57 . what is that number ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 7 , e ) 4
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 57 2 x = 10 = > x = 5 answer : a"
Answer: a
Problem: a room is 5 meters 76 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 12 , b ) 15 , c ) 17 , d ) 137 , e ) 147
Rationale: "let us calculate both the length and width of the room in centimeters . length = 5 meters and 76 centimeters = 576 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 576 and 432 = 144 thus , the number of square tiles required = ( 576 x 432 ) / ( 144 x 144 ) = 4 x 3 = 12 answer : b"
Answer: b
Problem: a train sets off at 2 : 00 pm at the speed of 70 km / h . another train starts at 3 : 00 pm in the same direction at the rate of 80 km / h . at what time will the second train catch the first train ?
Options: a ) 10 : 00 , b ) 10 : 30 , c ) 11 : 00 , d ) 11 : 30 , e ) 12 : 00
Rationale: in one hour the first train travels 70 km . the second train catches the first train at a rate of 80 km / h - 70 km / h = 10 km / h . the second train will catch the first train in 70 / 10 = 7 hours , so at 10 : 00 pm . the answer is a .
Answer: a
Problem: a boat can travel with a speed of 15 km / hr in still water . if the speed of the stream is 5 km / hr . find the time taken by the boat to go 68 km downstream ?
Options: a ) 2 hours , b ) 3 hours , c ) 4 hours , d ) 3 hours 24 minutes , e ) none
Rationale: "solution speed downstream = ( 15 + 5 ) km / hr = 20 km / hr . time taken to travel 68 km downstream = ( 68 / 20 ) hrs = 3 hrs 24 minutes . answer d"
Answer: d
Problem: mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 9 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "if n = 10 mark sold 1 box and ann sold 8 boxes total 9 < 10 answer : b"
Answer: b
Problem: 135 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 12 liters , b ) 32 liters , c ) 41 liters , d ) 54 liters , e ) 34 liters
Rationale: "milk = 3 / 5 * 135 = 81 liters water = 54 liters 81 : ( 54 + p ) = 3 : 4 162 + 3 p = 324 = > p = 54 54 liters of water are to be added for the ratio become 3 : 4 . answer : d"
Answer: d
Problem: 17 times a positive integer is more than its square by 60 , then the positive integer is
Options: a ) 13 , b ) 10 , c ) 11 , d ) 5 , e ) 14
Rationale: "explanation : let the number be x . then , 17 x = x 2 + 60 = > x 2 - 17 x + 60 = 0 = > ( x - 12 ) ( x - 5 ) = 0 = > x = 5 or 12 answer : option d"
Answer: d
Problem: a certain junior class has 1000 students and a certain senior class has 800 students . among these students , there are 40 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 ) 3 / 40000 , b ) 1 / 3600 , c ) 1 / 20000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "let ' s see pick 40 / 1000 first then we can only pick 1 other pair from the 800 so total will be 40 / 800 * 1000 simplify and you get 1 / 20000 answer is c"
Answer: c
Problem: a card is drawn from a pack of 52 cards . the probability of getting a queen of club or a king of heart is
Options: a ) 1 / 13 , b ) 2 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) 1 / 23
Rationale: "explanation : total number of cases = 52 favourable cases = 2 probability = 2 / 56 = 1 / 26 answer is c"
Answer: c
Problem: frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 480 square feet . how many feet offence does frank use ?
Options: a ) 14
b ) 47
c ) 54
d ) 180
e ) 64
Rationale: area = length x breadth 480 = 40 x breadth so , breadth = 12 units fencing required is - breadth + breadth + length 12 + 12 + 40 = > 64 feet answer must be ( e ) 64
Answer: e
Problem: the height of the wall is 6 times its width and length of the wall is 7 times its height . if the volume of the wall be 6804 cu . m . its width is
Options: a ) 3 m , b ) 5 m , c ) 6 m , d ) 7 m , e ) 8 m
Rationale: "explanation : let width = x then , height = 6 x and length = 42 x 42 x ã — 6 x ã — x = 6804 x = 3 answer : a"
Answer: a
Problem: 90 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 66 , b ) 35 , c ) 42 , d ) 27 , e ) 11
Rationale: x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 90 = 35 answer : b
Answer: b
Problem: a train running at 1 / 3 of its own speed reached a place in 9 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 8 hrs , b ) 10 hrs , c ) 12 hrs , d ) 15 hrs , e ) 6 hrs
Rationale: "time taken if run its own speed = 1 / 3 * 9 = 3 hrs time saved = 9 - 3 = 6 hrs answer : e"
Answer: e
Problem: the radius of a semi circle is 7 cm then its perimeter is ?
Options: a ) 32.8 , b ) 36 , c ) 32.1 , d ) 32.2 , e ) 32.9
Rationale: "radius = 7 cm then diameter = 14 cm 1 / 2 * 22 / 7 * 14 + 14 = 36 answer : b"
Answer: b
Problem: two persons raj and ramu started working for a company in similar jobs on january 1 , 1991 . raj ' s initial monthly salary was rs 400 , which increases by rs 40 after every year . ramu ' s initial monthly salary was rs 500 which increases by rs 20 after every 6 months . if these arrangements continue till december 31 , 200 . find the total salary they received during that period .
Options: a ) rs 108000 , b ) rs 144000 , c ) rs 132000 , d ) rs 152400 , e ) none of these
Rationale: explanation : raj ' s salary as on 1 jan 1991 is rs 400 per month . his increment in his month salary is rs 40 per annum his total salary from 1 jan 1991 to 31 st dec 2000 i . e . in ten years = > 12 [ 2 ( 400 ) + ( 10 − 1 ) 40 ] × 10 / 2 . = > rs 69600 . ramu ' s salary as on jan 1 st 1991 is rs 550 and his half yearly increment in his month salary is rs 20 . his total salary from 1 jan 1991 to dec 31 , 2000 = > 6 [ 2 ( 500 ) + ( 20 − 1 ) 20 ] × 20 / 2 . = > rs 82000 . total salary of raj and ramu in the ten year period : = > rs . 69600 + rs . 82800 . = > rs 1 , 52400 . answer : d
Answer: d
Problem: at a certain college , 80 percent of the total number of students are freshmen . if 60 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 50 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?
Options: a ) 25 % , b ) 20 % , c ) 22 % , d ) 21 % , e ) 24 %
Rationale: let ' s say there is a total of 100 students at this college . 80 percent of the total number of students are freshmen . # of freshmen = 80 % of 100 = 80 60 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 60 % of 80 = 48 . . . and , of these , 50 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 50 % of 48 = 24 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 24 / 100 = 24 % answer : e
Answer: e
Problem: difference of two numbers is 1670 . if 7.5 % of the number is 12.5 % of the other number , find the number ?
Options: a ) 2660 , 1000 , b ) 3660 , 2000 , c ) 3000 , 4160 , d ) 2490 , 4150 , e ) 2505 , 4175
Rationale: "let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1670 5 * y / 3 – y = 1670 2 * y / 3 = 1670 y = [ ( 1670 * 3 ) / 2 ] = 2505 . one number = 2505 , second number = 5 * y / 3 = 4175 . answer e ."
Answer: e
Problem: the ratio of flour to water to sugar in a recipe is 11 : 8 : 1 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 4 cups of water , how much sugar is required ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: "the ratio of flour to water is 22 : 8 = 11 : 4 . the ratio of flour to sugar is 5.5 : 1 = 11 : 2 . the new ratio of flour to water to sugar is 11 : 4 : 2 if we need 4 cups of water , then we need 2 cups of sugar . the answer is d ."
Answer: d
Problem: craig sells major appliances . for each appliance he sells , craig receives a commission of $ 50 plus 10 percent of the selling price . during one particular week craig sold 6 appliances for selling prices totaling $ 3620 . what was the total of craig ' s commissions for that week ?
Options: a ) $ 412 , b ) $ 526 , c ) $ 585 , d ) $ 605 , e ) $ 662
Rationale: craig receives a commission of $ 50 on each appliance plus a 10 % commission on total sales , thus his commission was 6 * 50 + 0.1 * 3620 = 662 . answer : e .
Answer: e
Problem: if 8 ^ x = 2 ^ 9 , what is x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 2 ^ 3 x = 2 ^ 9 3 x = 9 , therefore x = 3 answer b
Answer: b
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 3 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 3 / 23
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 3 * x hence , a 1 + a 2 + . . + a 20 + n = 23 x so , the fraction asked = 3 x / 23 x = 3 / 23 answer e"
Answer: e
Problem: i chose a number and divide it by 8 . then i subtracted 100 from the result and got 6 . what was the number i chose ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 848
Rationale: "solution : let x be the number i chose , then x / 8 â ˆ ’ 100 = 6 x / 8 = 106 x = 848 answer e"
Answer: e
Problem: the population of a bacteria colony doubles every day . if it was started 7 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 128 , b ) 256 , c ) 512 , d ) 1024 , e ) 2048
Rationale: 2 ^ 7 ( 2 ) = 2 ^ 8 = 256 the answer is b .
Answer: b
Problem: light glows for every 32 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 180 times , b ) 381 times , c ) 155 times , d ) 392 times , e ) 150 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 32 ) = 15582 times . answer : c"
Answer: c
Problem: if the height of a right cone c is 3 and the diameter of the base of c is 8 , what is the distance from the apex of c to any point on the circumference of the base of c ?
Options: a ) 3 √ 2
b ) 5
c ) 5 √ 2
d ) √ ( 67 )
e ) √ ( 73 )
Rationale: height of cone = 3 radius of base = 4 so the distance from the apex of c to any point on the circumference of the base of c will be a right angled triangle hence the distance is sqrt ( 3 ^ 2 + 4 ^ 2 ) = 5 answer : b
Answer: b
Problem: a can copy 50 papers in 10 hrs , while a & b can copy 70 papers in 10 hrs . how many hours are required for b to copy 26 papers ?
Options: a ) 11 hours , b ) 12 hours , c ) 13 hours , d ) 14 hours , e ) 18 hours
Rationale: a can copy 50 papers in 10 hrs , while a & b can copy 70 papers in 10 hrs . it means b can copy 20 papers in 10 hrs . then time taken by b to copy 26 papers = 26 * 10 / 20 = 13 hours answer : c
Answer: c
Problem: 45 % of 816 - 23 % of ? = 240.7
Options: a ) 330 , b ) 440 , c ) 240 , d ) 550 , e ) 230
Rationale: "d 550 ( 816 * 45 ) / 100 - ( ? * 23 ) / 100 = 240.7 = > 367.2 - ( ? * 23 ) / 100 = 240.7 = > ( ? * 23 ) / 100 = 367.2 - 240.7 = > ? = ( 126.5 * 100 ) / 23 = 550"
Answer: d
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 121 hours and 100 hours respectively . the ratio of their speeds is :
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) none of these
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 100 : â ˆ š 121 = 10 : 11 . answer e"
Answer: e
Problem: shanmukham buys good worth rs . 6650 . he gets a rebate of 6 % on it . after getting the rebate , he pays sales tax @ 10 % . find the amount he will have to pay for the goods
Options: a ) 6999.2 , b ) 6876.1 , c ) 6654 , d ) 7000 , e ) none of these
Rationale: explanation : rebate = 6 % of rs . 6650 = rs . 6 / 100 x 6650 = rs . 399 . sales tax = 10 % of rs . ( 6650 399 ) = rs . 10 / 100 x 6251 = rs . 625.10 final amount = rs . ( 6251 + 625.10 ) = rs . 6876.10 answer : b
Answer: b
Problem: the maximum numbers of students among them 781 pens and 710 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
Options: a ) 71 , b ) 910 , c ) 1001 , d ) 1911 , e ) none
Rationale: "olution required number of students . = h . c . f of 781 and 710 . â € ¹ = â € º 71 . answer a"
Answer: a
Problem: what is the measure of the radius of the circle inscribed in a triangle whose sides measure 8 , 15 and 27 units ?
Options: a ) 8.5 units , b ) 6 units , c ) 3 units , d ) 5 units , e ) 2 units
Rationale: "sides are 8 , 15 and 27 . . . thus it is right angle triangle since 27 ^ 2 = 8 ^ 2 + 15 ^ 2 therefore , area = 1 / 2 * 15 * 8 = 60 we have to find in - radius therefore , area of triangle = s * r . . . . where s = semi - perimeter and r = in - radius now s = semi - perimeter = 27 + 15 + 8 / 2 = 30 thus , 60 = 30 * r and hence r = in - radius = 2 option e"
Answer: e
Problem: 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 3 years hence ?
Options: a ) 58 , b ) 59 , c ) 62 , d ) 66 , e ) 74
Rationale: explanation : a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 3 years , their ages will be 43 and 23 . sum of their ages = 43 + 23 = 66 . d )
Answer: d
Problem: two trains 120 m and 190 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 11.6 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 20.8 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 120 + 190 = 310 m . required time = 310 * 9 / 250 = 11.6 = 11.6 sec . answer : b"
Answer: b
Problem: krishan and nandan jointly started a business . krishan invested 4 times as nandan did and invested his money for trible time as compared to nandan . if the gain is proportional to the money invested and the time for which the money is invested and the total gain was rs . 26000 , find the nandan ' s earning .
Options: a ) 4000 , b ) 1000 , c ) 5000 , d ) 3000 , e ) 2000
Rationale: 4 : 1 3 : 1 - - - - - - 12 : 1 13 - - - - - rs . 26000 1 - - - - - ? = > rs . 26000 / 13 = rs . 2000 answer : e
Answer: e
Problem: what is the 21 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 ( 3 rd , 6 th , 9 th , . . . ) to the right of the decimal point is 7 , thus 21 st digit to the right of the decimal point is also 7 . answer : d ."
Answer: d
Problem: two brothers ram and ravi appeared for an exam . the probability of selection of ram is 2 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 2 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 5 / 7 , e ) 7 / 5
Rationale: "let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 2 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 2 / 7 x 1 / 5 = 2 / 35 answer : a"
Answer: a
Problem: if a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet , what is the length of each of the longer sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 104 and a perimeter of 42 . we ' re asked for the length of one of the longer sides of the rectangle . since the answers are all integers , and the area is 104 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 104 , so the correct answer is probably a or c . let ' s test answer c : 8 if . . . the shorter side = 8 . . . the area = 104 . . . . 104 / 8 = 13 = the longer side perimeter = 8 + 8 + 13 + 13 = 42 d"
Answer: d
Problem: a cricket bat is sold for $ 900 , making a profit of $ 75 . the profit percentage would be
Options: a ) 9 % , b ) 12 % , c ) 10 % , d ) 36 % , e ) 40 %
Rationale: "75 / ( 900 - 75 ) = 75 / 825 = 0.9 bit more than 9 % . answer : a"
Answer: a
Problem: if 4 ^ ( 2 x + 2 ) = 16 ^ ( 3 x − 1 ) , what is the value of x ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: 2 ^ ( 4 x + 4 ) = 2 ^ ( 12 x - 4 ) 4 x + 4 = 12 x − 4 x = 1 answer b
Answer: b
Problem: the product of three consecutive numbers is 720 . then the sum of the smallest two numbers is ?
Options: a ) 11 , b ) 15 , c ) 17 , d ) 38 , e ) 56
Rationale: "product of three numbers = 720 720 = 8 * 9 * 10 so , the three numbers are 8 , 9 and 10 . and sum of smallest of these two = 8 + 9 = 17 . answer : option c"
Answer: c
Problem: you collect pens . suppose you start out with 25 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 75 , e ) 43
Rationale: "solution start with 25 pens . mike gives you 22 pens : 25 + 22 = 47 pens . cindy doubles the number of pens you have : 47 ã — 2 = 94 pens . sharon takes 19 pens from you : 94 - 19 = 75 pens . so you have 75 at the end . correct answer : d"
Answer: d
Problem: the population of a town increased from 1 , 45,000 to 2 , 30,500 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 5.8 % , c ) 6.8 % , d ) 8.75 % , e ) none
Rationale: "explanation : increase in 10 years = ( 230500 - 145000 ) = 85500 . increase % = ( 85500 / 145000 x 100 ) % = 58 % . required average = ( 58 / 10 ) % = 5.8 % . answer : option b"
Answer: b
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 1 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: "standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 1 . so , x = 65 / 4 ounces . water = ( 60 / 65 ) * ( 65 / 4 ) = 15 ounces . ans a"
Answer: a
Problem: in a certain animal shelter , the ratio of the number of dogs to the number of cats is 15 to 7 . if 8 additional cats were to be taken in by the shelter , the ratio of the number of dogs to the number of cats would be 15 to 11 . how many dogs are in the shelter ?
Options: a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 60
Rationale: "this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of dogs to the number of cats is 15 : 7 . we ' re then told that 8 more cats are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of dogs . algebraically , since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 18 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 8 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 8 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 8 ) ( 1 ) 11 x = 7 x + 8 4 x = 8 x = 2 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 2 ) = 30 final answer : c"
Answer: c
Problem: the number 523 fbc is divisible by 7 , 89 . then what is the value of f * b * c
Options: a ) 504 , b ) 532 , c ) 210 , d ) 180 , e ) 280
Rationale: lcm of 7 , 8 and 9 is 504 , thus 523 fbc must be divisible by 504 . 523 fbc = 523000 + fbc 523000 divided by 504 gives a remainder of 352 . hence , 352 + fbc = k * 504 . k = 1 fbc = 152 - - > f * b * c = 10 k = 2 fbc = 656 - - > f * b * c = 180 as fbc is three digit number k can not be more than 2 . two answers ? well only one is listed in answer choices , so d . answer : d .
Answer: d
Problem: the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 1.50 + 0.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 2 wheels on each of its other axles ?
Options: a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00
Rationale: "number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 2 = 8 total number of axles = 9 t = 1.50 + 0.50 ( 9 − 2 ) = 1.50 + . 5 * 7 = 1.5 + 1.5 = 5 $ answer e"
Answer: e
Problem: indu gave bindu rs . 5000 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 8 , b ) 2 , c ) 9 , d ) 5 , e ) 1
Rationale: "5000 = d ( 100 / 4 ) 2 d = 8 answer : a"
Answer: a
Problem: a sum of money at simple interest amounts to $ 700 in 3 years and to $ 764 in 4 years . the sum is :
Options: a ) $ 508 , b ) $ 698 , c ) $ 398 , d ) $ 549 , e ) $ 675
Rationale: "a $ 508 s . i . for 1 year = $ ( 764 - 700 ) = $ 64 . s . i . for 3 years = $ ( 64 x 3 ) = $ 192 . principal = $ ( 700 - 192 ) = $ 508 ."
Answer: a
Problem: how many factors does 34 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 20 , d ) 25 , e ) 26
Rationale: "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 5 * 4 = 20 answer c ."
Answer: c
Problem: how many positive integers between 1 and 100 are there such that they are multiples of 15 ?
Options: a ) 5 , b ) 4 , c ) 7 , d ) 1 , e ) 6
Rationale: "multiples of 15 = 15 , 30,45 , - - - - - 90 number of multiples of 15 = > 90 - 15 / 15 + 1 = 6 answer is e"
Answer: e
Problem: a man walking at a rate of 10 km / hr crosses a bridge in 3 minutes . the length of the bridge is ?
Options: a ) 500 , b ) 650 , c ) 250 , d ) 111 , e ) 236
Rationale: "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 5 minutes = 50 / 18 * 5 * 60 = 500 m answer is a"
Answer: a
Problem: how many paying stones , each measuring 3 * 2 m are required to pave a rectangular court yard 15 m long and 6 m board ?
Options: a ) 99 , b ) 18 , c ) 26 , d ) 15 , e ) 12
Rationale: "15 * 6 = 3 * 2 * x = > x = 15 answer : d"
Answer: d
Problem: on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction w of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is w = 2 / 14 = 1 / 7 . answer : e
Answer: e
Problem: what number has a 15 : 1 ratio to the number 10 ?
Options: a ) 130 , b ) 100 , c ) 200 , d ) 150 , e ) 120
Rationale: "15 : 1 = x : 10 x = 10 * 15 x = 150 answer : d"
Answer: d
Problem: if a and b are positive integers and ( 2 ^ a ) ^ b = 2 ^ 7 , what is the value of 2 ^ a * 2 ^ b ?
Options: a ) 16 , b ) 32 , c ) 64 , d ) 256 , e ) 128
Rationale: "2 ^ ab = 2 ^ 7 therefore ab = 7 either a = 1 or 7 or b = 7 or 1 therefore 2 ^ a * 2 ^ b = 2 ^ ( a + b ) = 2 ^ 8 = 256 d"
Answer: d
Problem: a man is 30 years older than his son . in four years , his age will be twice the age of his son . the present age of this son is
Options: a ) 22 years , b ) 23 years , c ) 24 years , d ) 25 years , e ) 26 years
Rationale: "explanation : let ' s son age is x , then father age is x + 30 . = > 2 ( x + 4 ) = ( x + 30 + 4 ) = > 2 x + 8 = x + 34 = > x = 26 years answer : option e"
Answer: e
Problem: the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 17 terms of the arithmetic progression ?
Options: a ) 300 , b ) 120 , c ) 150 , d ) 170 , e ) 270
Rationale: "n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 17 . . . we get 17 / 2 [ 2 a + 14 d ] = 17 [ a + 7 d ] = 17 * 10 = 170 . . . answer is d . . ."
Answer: d
Problem: a man invests rs . 4,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 1500 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : interest on rs . 4000 at 5 % per annum = ( 4000 × 5 × 1 ) / 100 = rs . 200 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 4000 + x ) × 6 × 1 / 100 . = > 200 + 2 x / 25 = ( 4000 + x ) × 6 × 1 / 100 . = > 20000 + 8 x = ( 4000 + x ) × 6 . = > 20000 + 8 x = 24000 + 6 x . = > 2 x = 4000 . = > x = 2000 . answer : d"
Answer: d
Problem: a cab driver 5 days income was $ 400 , $ 250 , $ 650 , $ 400 , $ 500 . then his average income is ?
Options: a ) $ 400 , b ) $ 420 , c ) $ 440 , d ) $ 460 , e ) $ 480
Rationale: "avg = sum of observations / number of observations avg income = ( 400 + 250 + 650 + 400 + 500 ) / 5 = 440 answer is c"
Answer: c
Problem: calculate the time it will take for a train that is 120 meter long to pass a bridge of 160 meter length , if the speed of the train is 40 km / hour ?
Options: a ) 21.2 seconds , b ) 25.2 seconds , c ) 29.2 seconds , d ) 35.2 seconds , e ) 11.2 seconds
Rationale: speed = 40 km / hr = 40 * ( 5 / 18 ) m / sec = 11.1111 m / sec total distance = 120 + 160 = 280 meter time = distance / speed = 280 * ( 1 / 11.1111 ) = 25.2 seconds answer : b
Answer: b
Problem: the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 540 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1290 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 540 × 100 ) / ( 6 × 12 ) = ( 90 × 100 ) / 12 = ( 15 × 100 ) 2 / = rs . 750 bg = bd – td = > 540 = bd - 750 = > bd = 540 + 750 = 1290 answer : option d"
Answer: d
Problem: if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 246 m , what is its area ?
Options: a ) 2510 , b ) 3650 , c ) 2530 , d ) 2515 , e ) 2520
Rationale: "length = breadth + 23 . therefore , 4 × breadth + 2 × 23 = 246 m ⇒ breadth = 50 m length = 50 + 23 = 73 m area = 73 × 50 = 3650 m 2 answer is b ."
Answer: b
Problem: a and b can together finish a work in 30 days . they worked together for 20 days and then b left . after another 20 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 40 , b ) 50 , c ) 54 , d ) 60 , e ) none of these
Rationale: "( a + b ) ' s 20 days work = ( 1 / 30 * 20 ) = 2 / 3 . remaining work = ( 1 - 2 / 3 ) = 1 / 3 . now , 1 / 3 work is done by a in 20 days . whole work will be done by a in ( 20 * 3 ) = 60 days . correct option : d"
Answer: d
Problem: how many numbers between 190 and 580 are divisible by 4,5 and 6 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: every such number must be divisible by l . c . m of 4 , 5,6 i . e , 60 . such numbers are 240,300 , 360,420 , 480,540 . clearly , there are 6 such numbers answer : a
Answer: a
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 24 sec . what is the length of the platform ?
Options: a ) 389 m , b ) 350 m , c ) 187.5 m , d ) 299 m , e ) 219.5 m
Rationale: "speed = 300 / 24 = 25 / 2 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 25 / 2 = > x = 187.5 m . answer : c"
Answer: c
Problem: what percent is 3 % of 5 % ?
Options: a ) 60 % , b ) 50 % , c ) 75 % , d ) 45 % , e ) 30 %
Rationale: "required percentage = 3 % / 5 % * 100 = 3 / 5 * 100 = 60 % answer is a"
Answer: a
Problem: when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum t of all possible 2 - digit remainders for x / y ?
Options: a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784
Rationale: "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . t = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616 . b"
Answer: b
Problem: perimeter of an equilateral and isosceles is 45 and 40 respectively . at least one of the sides of isosceles is equal to the equilateral . what ' s the base of isosceles triangle ?
Options: a ) 7
b ) 8
c ) 9
d ) 10
e ) 11
Rationale: 10 units as other 2 sides will be 15,15 units . answer : d
Answer: d
Problem: kamal obtained 76 , 60 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 74 , d ) 75 , e ) none
Rationale: "sol . average = 76 + 60 + 82 + 67 + 85 / 5 ) = ( 375 / 5 ) = 74 . answer c"
Answer: c
Problem: a train covers a distance of 12 km in 10 min . if it takes 16 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 320 m , b ) 188 m , c ) 120 m , d ) 178 m , e ) 189 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 16 = 320 m . answer : a"
Answer: a
Problem: if 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days . compare the daily work done by a man with that of a boy .
Options: a ) 2 : 9 , b ) 2 : 1 , c ) 2 : 7 , d ) 2 : 5 , e ) 2 : 2
Rationale: "12 m + 16 b - - - - - 5 days 13 m + 24 b - - - - - - - 4 days 60 m + 80 b = 52 m + 96 b 8 m = 16 b = > 1 m = 2 b m : b = 2 : 1 answer : b"
Answer: b
Problem: what least value should be replaced by * in 223 * 431 so the number become divisible by 9
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : trick : number is divisible by 9 , if sum of all digits is divisible by 9 , so ( 2 + 2 + 3 + * + 4 + 3 + 1 ) = 15 + * should be divisible by 9 , 15 + 3 will be divisible by 9 , so that least number is 3 . answer : option a"
Answer: a
Problem: the cost price of a radio is rs . 1340 and it was sold for rs . 1210 , find the loss % ?
Options: a ) 18 % , b ) 9 % , c ) 22 % , d ) 24 % , e ) 21
Rationale: "1340 - - - - 130 100 - - - - ? = > 9 % answer : b"
Answer: b
Problem: the probability that a number selected at random from the first 50 natural numbers is a composite number is ?
Options: a ) 17 / 65 , b ) 17 / 25 , c ) 17 / 28 , d ) 17 / 65 , e ) 17 / 39
Rationale: "the number of exhaustive events = ⁵ ⁰ c ₁ = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . required probability = 34 / 50 = 17 / 25 . answer : b"
Answer: b
Problem: if x : y = 4 : 7 , find the value of ( 6 x + 2 y ) : ( 5 x – y )
Options: a ) 7 : 13 , b ) 38 : 7 , c ) 3 : 13 , d ) 2 : 3 , e ) 38 : 13
Rationale: explanation : given : x / y = 4 / 7 ( 6 x + 2 y ) : ( 5 x – y ) = ( 6 * 4 + 2 * 7 ) : ( 5 * 4 – 7 ) 38 : 13 answer : e
Answer: e
Problem: ritesh and co . generated revenue of rs . 2,500 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: "explanation : given , ritesh and co . generated revenue of rs . 2,500 in 2006 and that this was 12.5 % of the gross revenue . hence , if 2500 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 2500 . = > 20,000 . hence , the total revenue by end of 2007 is rs . 10,000 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 20000 ) × 100 . = > 12.5 % . answer : a"
Answer: a
Problem: according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 15 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 50 , d ) 20 , e ) 100
Rationale: "orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 15 oz can = 300 oz / 15 oz = 20 answer d , 20 cans"
Answer: d
Problem: the difference between compound interest and simple interest on an amount of $ 15,000 for 2 years is $ 96 . what is the rate of interest per annum ?
Options: a ) 6 % , b ) 7 % , c ) 9 % , d ) 8 % , e ) 5 %
Rationale: "[ 15000 x ( 1 + r / 100 ) ^ 2 - 15000 ] - [ ( 15000 x r x 2 ) / 100 ] = 96 = = > 15000 [ ( 1 + r / 100 ) ^ 2 - 1 - 2 r / 100 ] = 96 = = > 15000 [ ( ( 100 + r ) ^ 2 - 10000 - ( 200 x r ) ) / 10000 ] = 96 = = > r ^ 2 = ( 96 x 2 ) / 3 = 64 = = > r = 8 . rate = 8 % answer d ) 8 %"
Answer: d
Problem: if x + y = 14 , x - y = 60 , for integers of x and y , x = ?
Options: a ) 37 , b ) 35 , c ) 25 , d ) 20 , e ) 42
Rationale: "x + y = 14 x - y = 60 2 x = 74 x = 37 answer is a"
Answer: a
Problem: if in a race of 100 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
Options: a ) 20 m , b ) 16 m , c ) 11 m , d ) 10 m , e ) 15 m
Rationale: "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 100 * 5 ) / 25 = 20 m hence , a beats b by 20 m . answer a"
Answer: a
Problem: the speed of a car is 90 km in the first hour and 30 km in the second hour . what is the average speed of the car ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 75 kmph , d ) 85 kmph , e ) 90 kmph
Rationale: "explanation : s = ( 90 + 30 ) / 2 = 60 kmph b )"
Answer: b
Problem: suzie ’ s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 580 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 800 . how much more do pairs of boots cost than pairs of shoes at suzie ’ s discount footwear ?
Options: a ) $ 10.50 , b ) $ 12.50 , c ) $ 11.50 , d ) $ 16.50 , e ) $ 9.50
Rationale: "let x be pair of shoes and y be pair of boots . 22 x + 16 y = 580 . . . eq 1 8 x + 32 y = 800 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 1160 8 x = 800 . 36 x = 360 = > x = 10 . sub x in eq 2 . . . . we get 80 + 32 y = 800 . . . then we get 32 y = 720 then y = 22.50 differenece between x and y is 12.50 answer : b"
Answer: b
Problem: the speed of a boat in still water in 65 km / hr and the rate of current is 15 km / hr . the distance travelled downstream in 25 minutes is :
Options: a ) 55.55 km , b ) 44.44 km , c ) 33.33 km , d ) 22.22 km , e ) 11.11 km
Rationale: "explanation : speed downstream = ( 65 + 15 ) = 80 kmph time = 25 minutes = 25 / 60 hour = 5 / 12 hour distance travelled = time × speed = ( 2 / 5 ) × 80 = 33.33 km answer : option c"
Answer: c
Problem: ( √ 27 + √ 243 ) / √ 48 = ?
Options: a ) 2 √ 2 , b ) 2 √ 3 , c ) 3 √ 2 , d ) 3 √ 3 , e ) 3
Rationale: "( √ 27 + √ 243 ) / √ 48 = ( 3 √ 3 + 9 √ 3 ) / 4 √ 3 = 12 √ 3 / 4 √ 3 = 3 . hence , the correct answer is e ."
Answer: e
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 2887 , b ) 444 , c ) 877 , d ) 278 , e ) 178
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 16 + 21 = 37 t = 12 d = 37 * 12 = 444 answer : b"
Answer: b
Problem: the volume of a cube is 1728 cc . find its surface ?
Options: a ) 864
b ) 209
c ) 278
d ) 276
e ) 280
Rationale: a 3 = 1728 = > a = 12 6 a 2 = 6 * 12 * 12 = 864 answer : a
Answer: a
Problem: you hold some gold in a vault as an investment . over the past year the price of gold increases by 50 % . in order to keep your gold in the vault , you must pay 8 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 35 % , b ) 36 % , c ) 37 % , d ) 38 % , e ) 40 %
Rationale: "( 100 % + 50 % ) * ( 100 % - 8 % ) = 150 * 0.92 = 138 % an increase of 38 % your gold holdings have increased in value by 38 % . the answer is d"
Answer: d
Problem: 18 litres of mixture contains 20 % alcohol and the rest water . if 3 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 16.67 % , b ) 17.14 % , c ) 18.3 % , d ) 19.75 % , e ) 21.23 %
Rationale: "alcohol in the 18 litres of mix . = 20 % of 18 litres = ( 20 * 18 / 100 ) = 3.6 litres water in it = 18 - 3.6 = 14.4 litres new quantity of mix . = 18 + 3 = 21 litres quantity of alcohol in it = 3.6 litres percentage of alcohol in new mix . = 3.6 * 100 / 21 = 17.14 % answer is b"
Answer: b
Problem: two isosceles triangles have equal vertical angles and their areas are in the ratio 4 : 9 . find the ratio of their corresponding heights .
Options: a ) 4 / 5
b ) 5 / 4
c ) 3 / 2
d ) 5 / 7
e ) 2 / 3
Rationale: we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 4 / 9 - - > height / height = 2 / 3 . answer : e .
Answer: e
Problem: in a certain company , the ratio of male to female employees is 7 : 8 . if 3 more men were hired , this ratio would increase to 8 : 9 . how many male employees are there in the company ?
Options: a ) 6 , b ) 21 , c ) 27 , d ) 189 , e ) 192
Rationale: another approach is to use two variables . let m = present number of males let f = present number of females the ratio of male to female employees is 7 : 8 so , m / f = 7 / 8 cross multiply to get 7 f = 8 m if 3 more men were hired , this ratio would increase to 8 : 9 so , ( m + 3 ) / f = 8 / 9 cross multiply to get 9 ( m + 3 ) = 8 f expand : 9 m + 27 = 8 f we now have a system of two equations and two variables : 7 f = 8 m 9 m + 27 = 8 f solve to get : m = 189 and f = 216 answer : d
Answer: d
Problem: a guy was asked to specify his age in years . he said , “ take my age 5 years hence , multiply it by 5 and subtract 5 times of my age 5 years ago and you will know my age . ” what was the age of that guy ?
Options: a ) 18 , b ) 15 , c ) 33 , d ) 39 , e ) 50
Rationale: current age of the guy = a years . then , 5 ( a + 5 ) – 5 ( a – 5 ) = a ( 5 a + 25 ) – ( 5 a – 25 ) = a a = 50 e
Answer: e
Problem: of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 17 boys and 43 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?
Options: a ) 5 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 17 boys . so 17 - 6 - 6 = 5 boys must be neither happy nor sad . answer ( a )"
Answer: a