regisss/math_qa huggingface dataset:
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 3 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 10 hr , d ) 14 hr , e ) 16 hr
Rationale: "work done by the tank in 1 hour = ( 1 / 2 - 1 / 3 ) = 1 / 14 leak will empty the tank in 14 hrs . answer : d"
Answer: d
Problem: right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x - and y - coordinates of p , q and r are to be integers that satisfy the inequalities - 4 < = x < = 5 and 6 < = y < = 16 . how many different triangles with these properties could be constructed ?
Options: a ) 110 , b ) 1100 , c ) 9900 , d ) 10000 , e ) 12100
Rationale: "we know that p , q , r can only lie on a grid 10 x 11 let ' s start by fixing p ' x - coordinate : we have 10 possible places for it then we choose x - coordinate for r : since pr | | x - axis , r ' s x - coordinate can not coincide with p ' s x - coord , so we have only 9 possible choices left . then , we fix p ' s ( and r ' s too ) y - coordinate : 11 possible choices . finally , after we fixed p and r , q ' s x - coordinate must be the same as p ' s ( because p is the right angle and pr | | x - axis ) , so the only choice is for y - coordinate , and we have 10 possible choices left . so , total number of different triangles : 10 * 9 * 11 * 10 = 9,900 answer : c"
Answer: c
Problem: sand is poured into a box so that the box is being filled at the rate of 3 cubic feet per hour . if the empty rectangular box is 5 feet long , 4 feet wide , and 3 feet deep , approximately how many hours does it take to fill the box ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "the volume the box is : length * width * depth = 5 * 4 * 3 = 60 cubic feet . 60 cubic feet / 3 cubic feet per hour = 20 hours . it will take 20 hours to fill the box . the answer is d ."
Answer: d
Problem: jack and christina are standing 270 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 4 feet per second and christina walks in a straight line toward jack at a constant speed of 5 feet per second . lindy runs at a constant speed of 8 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
Options: a ) 150 , b ) 180 , c ) 210 , d ) 240 , e ) 270
Rationale: "the relative speed of jack and christina is 4 + 5 = 9 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 270 / 7 = 30 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 8 * 30 = 240 feet . answer : d ."
Answer: d
Problem: how many liters of water must be added to 20 liters of milk and water containing 10 % water to make it 50 % water ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "by rule of alligation : 50 % - 10 % = 40 % 100 % - 50 % = 50 % quantity of pure water : quantity of the mixture = 4 : 5 there are 20 liters of mixture , so we need to add 16 liters of pure water . the answer is d ."
Answer: d
Problem: man 1 alone can do a piece of work in 6 days and man 2 alone in 8 days . man 1 and man 2 undertook to do it for rs . 3200 . with the help of man 3 , they completed the work in 3 days . how much is to be paid to man 3 ?
Options: a ) 400 , b ) 200 , c ) 100 , d ) 150 , e ) 500
Rationale: man 3 1 day work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 man 1 : man 2 : man 3 = 1 / 6 : 1 / 8 : 1 / 24 = = > 4 : 3 : 1 man 3 share = 3 * 1 / 24 * 3200 = rs 400 answer a
Answer: a
Problem: in arun ' s opinion , his weight is greater than 65 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 68 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 16.5 kg , b ) 66.5 kg , c ) 26.5 kg , d ) 56.5 kg , e ) 86.5 kg
Rationale: "let arun ' s weight be x kg . according to arun , 65 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 68 . the values satisfying all the above conditions are 66 and 67 . required average = ( 66 + 67 ) / 2 = 66.5 kg answer : b"
Answer: b
Problem: shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 500 as interest . he invested the remaining in a bond that paid compound interest , interest being compounded annually , for the same 2 years at the same rate of interest and received $ 555 as interest . what was the value of his total savings before investing in these two bonds ?
Options: a ) 2,000 , b ) 2,500 , c ) 4,000 , d ) 5,000 , e ) 6,000
Rationale: "so , we know that shawn received 20 % of the amount he invested in a year . we also know that in one year shawn received $ 250 , thus 0.2 x = $ 250 - - > x = $ 1,250 . since , he invested equal sums in his 2 bonds , then his total savings before investing was 2 * $ 1,250 = $ 2,500 . answer : b"
Answer: b
Problem: ramesh purchased a refrigerator for rs . 15500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 34778 , b ) 26888 , c ) 2899 , d ) 17600 , e ) 21725
Rationale: "price at which the tv set is bought = rs . 15,500 discount offered = 20 % marked price = 15500 * 100 / 80 = rs . 19375 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 19375 + 375 = rs . 19750 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 19750 * 110 / 100 = rs . 21725 answer : e"
Answer: e
Problem: how many numbers from 10 to 1000000 are exactly divisible by 9 ?
Options: a ) 900 , b ) 8000 , c ) 1100 , d ) 111110 , e ) 14
Rationale: "10 / 9 = 1 and 1000000 / 9 = 111111 = = > 111111 - 1 = 111110 . answer : d"
Answer: d
Problem: a train running at the speed of 60 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 150 , b ) 872 , c ) 287 , d ) 288 , e ) 212
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 9 = 150 meter answer : a"
Answer: a
Problem: a rectangular plot measuring 30 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 46 m , b ) 66 m , c ) 26 m , d ) 56 m , e ) 32 m
Rationale: "perimeter of the plot = 2 ( 30 + 50 ) = 160 m no of poles = 160 / 5 = 32 m answer : e"
Answer: e
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 4 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 ) 5 / 21
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 4 * x hence , a 1 + a 2 + . . + a 20 + n = 24 x so , the fraction asked = 4 x / 24 x = 1 / 6 ; answer : b ."
Answer: b
Problem: a batsman in his 12 th innings makes a score of 80 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 58
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 80 ∴ x = 58 answer e"
Answer: e
Problem: what is the compound interest on rs . 4500 at 5 % p . a . compounded half - yearly for 3 1 / 2 years .
Options: a ) rs . 859.09 , b ) rs . 349.09 , c ) rs . 449.09 , d ) rs . 749.09 , e ) rs . 849.09
Rationale: "compound interest : a = p ( 1 + r / n ) nt a = 5 , 349.09 c . i . > > 5 , 349.09 - 4500 > > rs . 849.09 answer : e"
Answer: e
Problem: danny can divide his herd into 5 equal parts and also to 6 equal parts , but not to 9 equal parts . what could be the number of cows danny has in his herd ?
Options: a ) 120 , b ) 155 , c ) 180 , d ) 336 , e ) 456
Rationale: danny can divide his herd into 5 equal parts and also to 6 equal parts = > no of cows = multiple of 5 and 6 = multiple of 30 . only option a and c qualify . now 2 nd condition : but not to 9 equal parts : so it should not be a multiple of 9 . answer : a
Answer: a
Problem: a and b can do a work in 8 days , b and c can do it in 12 days ; a , b and c together can finish it in 6 days . a and c together will do it in ?
Options: a ) 8 days , b ) 10 days , c ) 12 days , d ) 7 days , e ) 5 days
Rationale: "a + b + c 1 day work = 1 / 6 a + b 1 day work = 1 / 8 b + c 1 day work = 1 / 12 a + c 1 day work = 2 * 1 / 6 - 1 / 8 + 1 / 12 = 1 / 3 - 5 / 24 = 3 / 24 = 1 / 8 a and c together will do the work in 8 days . answer is a"
Answer: a
Problem: how much is 90 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 29 , b ) 776 , c ) 66 , d ) 16 , e ) 99
Rationale: "( 90 / 100 ) * 40 – ( 4 / 5 ) * 25 36 - 20 = 16 answer : d"
Answer: d
Problem: a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 6 inches , then what is the maximum number of soap boxes that can be placed in each carton ?
Options: a ) 210 , b ) 252 , c ) 250 , d ) 300 , e ) 420
Rationale: "however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 42 * 60 dimensions of the soap = 6 * 6 * 7 placing the 7 inch side along 42 inch side we get 6 soaps in a line and in a similar way 5 along 25 and 6 along 60 we get = 5 x 5 x 10 = 250 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( c )"
Answer: c
Problem: suresh and ramesh started a business investing rs . 24,000 and rs . 40,000 respectively . out of total profit of rs . 19,000 , what is ramesh ' s share ?
Options: a ) s . 7375 , b ) s . 8379 , c ) s . 9875 , d ) s . 10875 , e ) s . 11875
Rationale: explanation : ratio of suresh and ramesh ' s share = 24,000 : 40,000 = 3 : 5 ramesh ' s share = rs . ( 19000 x 5 / 8 ) = rs . 11875 answer : e
Answer: e
Problem: if difference between compound interest and simple interest on a sum at 5 % p . a . for 2 years is rs . 60 , then what is the sum ?
Options: a ) rs . 8000 , b ) rs . 4000 , c ) rs . 5000 , d ) rs . 6000 , e ) rs . 24000
Rationale: "c . i - s . i = 60 si = ( x * 2 * 5 ) / 100 = x / 10 ci = { x * ( 1 + 5 / 100 ) ^ 2 - x } = 41 x / 400 ci - si = 41 x / 400 - x / 10 = 60 x = 24000 answer : e"
Answer: e
Problem: a larger cube has 343 cubic inch as a volume and in the cube there are 343 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 343 smaller cubes and the surface area of the larger cube , in square inch ?
Options: a ) 54 , b ) 64 , c ) 81 , d ) 108 , e ) 1764
Rationale: "volume of larger cube = 343 = 7 ^ 3 side of larger cube = 7 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 7 ^ 2 = 294 surface area of 27 smaller cubes = 343 * 6 * 1 = 2058 difference = 2058 - 294 = 1764 answer : e"
Answer: e
Problem: salesperson a ' s compensation for any week is $ 360 plus 6 percent of the portion of a ' s total sales above $ 1000 for that week . salesperson b ' s compensation for any week is 10 percent of a ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 18,000 , c ) $ 15,00 , d ) $ 4,500 , e ) $ 15,000
Rationale: sometime , setting up an equation is an easy way to go with : 360 + 0.06 ( x - 1000 ) = 0.1 x x = 15,000 ans : e
Answer: e
Problem: if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 3 strokes ?
Options: a ) 15 / 16 , b ) 7 / 8 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "left after 1 st stroke = 1 / 2 left after 2 nd stroke = 1 / 2 * 1 / 2 = 1 / 4 left after 3 rd stroke = 1 / 2 * 1 / 4 = 1 / 8 so removed = 1 - 1 / 8 = 7 / 8 = b"
Answer: b
Problem: if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
Options: a ) 400 , b ) 420 , c ) 480 , d ) 500 , e ) 600
Rationale: "minimum no of mail to be sent for getting 300 responses at 60 % = 300 / 0.6 = 500 option d"
Answer: d
Problem: a person crosses a 1000 m long street in 10 minutes . what is his speed in km per hour ?
Options: a ) 7.1 , b ) 8.2 , c ) 4.6 , d ) 6.0 , e ) 12.8
Rationale: "distance = 1000 meter time = 10 minutes = 10 x 60 seconds = 600 seconds speed = distance / time = 1000 / 600 = 1.67 m / s = 1.67 ã — 18 / 5 km / hr = 6.0 km / hr answer : d"
Answer: d
Problem: how long does a train 110 m long travelling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) 15.8 sec , b ) 14.9 sec , c ) 12.4 sec , d ) 16.8 sec , e ) 11.8 sec
Rationale: "d 16.8 sec d = 110 + 170 = 280 m s = 60 * 5 / 18 = 50 / 3 t = 280 * 3 / 50 = 16.8 sec"
Answer: d
Problem: two trains from opposite directions are to cross each other . the length of two trains are 100 meter and 200 meter respectively . the speed of first train is 100 km / hour and second train 200 km / hour . in how much time will they cross each other ?
Options: a ) 2 second , b ) 3.6 second , c ) 5 second , d ) 5.5 second , e ) 6 second
Rationale: the crossing moment starts when the head of first compartment of two trains meet or touch . the process of crossing each other continues till 100 + 200 meter = 300 meter is covered . the speed will be 100 km / hour + 200 km / hour = 300 km / hour . 300 x 1000 meter covered in 3600 seconds . so , 300 meter covered in 3.6 seconds . answer : b .
Answer: b
Problem: let n be the greatest number that will divide 1305 , 4665 and 6905 , leaving the same remainder in each case . then sum of the digits in n is :
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : n = h . c . f . of ( 4665 - 1305 ) , ( 6905 - 4665 ) and ( 6905 - 1305 ) = h . c . f . of 3360 , 2240 and 5600 = 1120 . sum of digits in n = ( 1 + 1 + 2 + 0 ) = 4 answer is a"
Answer: a
Problem: in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of five metre is left from all sides of the boundary of the garden . what is the length of the garden ?
Options: a ) 32 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 5 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 5 + 5 = 32 meter answer is a .
Answer: a
Problem: 15.06 * 0.000001 = ?
Options: a ) 15060000 , b ) 0.001506 , c ) 0.01506 , d ) 1.506 e - 05 , e ) none of these
Rationale: "explanation : clearly after decimal 8 digits should be there . option d"
Answer: d
Problem: darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 2 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?
Options: a ) 10.5 , b ) 15 , c ) 25.5 , d ) 30 , e ) 23.5
Rationale: "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 2 x = 23.5 minutes answer : e"
Answer: e
Problem: a driver would have reduced the time it took to drive from home to the store by 1 / 4 if the average speed had been increased by 12 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Rationale: "since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 4 would give us : d = ( r ) ( t ) = ( 3 t / 4 ) ( x * r ) x = 4 / 3 since ( 3 t / 4 ) ( 4 r / 3 ) = ( r ) ( t ) = d 4 r / 3 = r + 12 r / 3 = 12 r = 36 the answer is d ."
Answer: d
Problem: a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 300 shares of the company ' s stock ?
Options: a ) $ 92 , b ) $ 96 , c ) $ 156 , d ) $ 120 , e ) $ 240
Rationale: "eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 300 - - > $ 156 answer is c"
Answer: c
Problem: can you find the smallest non fractional number such that if the number gets divided by 6 , we get the remainder of 1 ; if the number gets divided by 7 , we get the remainder of 2 if the number gets divided by 8 , we get the remainder of 3 ; if the number gets divided by 9 , we get the remainder of 4 .
Options: a ) 1006 , b ) 1230 , c ) 1010 , d ) 1200 , e ) 1300
Rationale: a . 1006 as we know lcm of the numbers 6 7 8 & 9 is 1008 so if i divide 1008 by any of the four number , it gives remainder as 0 . now to get reminder as desired , is should be 2 short of 1006 . ( 3 - 1,4 - 2,5 - 3,6 - 4 ) ans : option a
Answer: a
Problem: which is less than 3 ?
Options: a ) 3 , b ) 0.3 , c ) 33 , d ) 3 / 1 , e ) 13
Rationale: "0.3 less than 3 . answer : b"
Answer: b
Problem: the difference of two numbers is 1360 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 269
Rationale: "let the smaller number be x . then larger number = ( x + 1360 ) . x + 1360 = 6 x + 15 5 x = 1345 x = 269 smaller number = 270 . answer e"
Answer: e
Problem: the average of 10 numbers is 23 . if each number is increased by 2 , what will the new average be ?
Options: a ) 36 , b ) 25 , c ) 72 , d ) 29 , e ) 22
Rationale: "sum of the 10 numbers = 230 if each number is increased by 2 , the total increase = 2 * 10 = 20 the new sum = 230 + 20 = 250 the new average = 250 / 10 = 25 . answer : 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 $ 0.50 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.33 , 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 * 0.5 = 3 * x - - > x = $ 0.33 . answer : c ."
Answer: c
Problem: a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party t . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: "s = 100 not ( t and b ) = 35 only t = 20 ( t and b ) / b = 1 / 2 let ( t and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans"
Answer: a
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 85 . how much was lent at 5 % ?
Options: a ) 399 , b ) 700 , c ) 288 , d ) 500 , e ) 211
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 85 5 x / 100 + 90 – 6 x / 100 = 85 x / 100 = 5 = > x = 500 answer : d"
Answer: d
Problem: excluding stoppages , the speed of a train is 30 kmph and including stoppages it is 21 kmph . of how many minutes does the train stop per hour ?
Options: a ) 16 , b ) 17 , c ) 12 , d ) 15 , e ) 18
Rationale: "t = 9 / 30 * 60 = 18 answer : e"
Answer: e
Problem: a man took loan from a bank at the rate of 5 % p . a . s . i . after 13 years he had to pay rs . 1300 interest only for the period . the principal amount borrowed by him was ?
Options: a ) 1750 , b ) 4000 , c ) 3500 , d ) 2000 , e ) 1000
Rationale: "principal = ( 100 * 1300 ) / ( 5 * 13 ) = rs . 2000 answer : d"
Answer: d
Problem: in a games hour 4 different types of players came to the ground ? cricket 15 , hokey 12 , football 13 , softball 15 . how many players are present in the ground ?
Options: a ) 70 , b ) 52 , c ) 55 , d ) 49 , e ) 50
Rationale: "total number of players = 15 + 12 + 13 + 15 = 55 answer is c"
Answer: c
Problem: if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 25 ) which of these integers could be the value of z ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 25 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 26 incorrect c . 2 / 2 = 2 / 3 + 2 / 27 incorrect d . 2 / 3 = 2 / 4 + 2 / 28 incorrect e . 2 / 4 = 2 / 5 + 2 / 30 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case
Answer: e
Problem: the average student age of a certain class which has 45 students is 14 . if one student aged 15 go to another class and the age of the class teacher is included the average changes to 14.66 . what is the age of class teacher ?
Options: a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45
Rationale: sum of ages of class before replacement = 45 x 14 = 630 sum of ages of class without teacher = 630 - 15 = 615 sum of ages of class after replacement = 45 x 14.66 = 660 age of teacher = 660 - 615 = 45 answer : e
Answer: e
Problem: 41 % of 801 – 150.17 = ? – 57 % of 910
Options: a ) 797 , b ) 697 , c ) 687 , d ) 699 , e ) 799
Rationale: "explanation : 328 – 150 = 178 x – 519 = 178 x = 697 answer : option b"
Answer: b
Problem: the area of a square garden is q square feet and the perimeter is p feet . if q = 2 p + 33 , what is the perimeter of the garden in feet ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: "let x be the length of one side of the square garden . x ^ 2 = 8 x + 33 x ^ 2 - 8 x - 33 = 0 ( x - 11 ) ( x + 3 ) = 0 x = 11 , - 3 p = 4 ( 11 ) = 44 the answer is e ."
Answer: e
Problem: the mean of 50 observations was 41 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.2 , b ) 36.1 , c ) 36.5 , d ) 41.5 , e ) none
Rationale: "sol . therefore correct sum = ( 41 × 50 + 48 – 23 ) = 2075 . therefore correct mean = 2075 / 50 = 41.5 . answer d"
Answer: d
Problem: a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning ?
Options: a ) 15 , b ) 88 , c ) 44 , d ) 54 , e ) 23
Rationale: "let the average after 7 th inning = x then average after 16 th inning = x - 3 16 ( x - 3 ) + 87 = 17 x x = 87 - 48 = 39 answer = b"
Answer: b
Problem: in what time will a train 300 meters long cross an electric pole , if its speed is 90 km / hr
Options: a ) 5 seconds , b ) 12 seconds , c ) 3 seconds , d ) 2.5 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 90 * ( 5 / 18 ) = 25 m / sec time = distance / speed = 300 / 25 = 12 seconds answer : b"
Answer: b
Problem: a present value of a machine is $ 1100 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?
Options: a ) $ 900 , b ) $ 891 , c ) $ 915 , d ) $ 715 , e ) $ 795
Rationale: p = $ 1100 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 1100 * 9 / 10 * 9 / 10 = $ 891 answer is b
Answer: b
Problem: vanessa , mike and sarah have missed a total of 17 days of school this year . vanessa and mike have missed 14 days total , and mike and sarah have missed 12 days total . how many days of school did vanessa miss alone ?
Options: a ) 9 , b ) 4 , c ) 5 , d ) 2 , e ) 3
Rationale: vanessa + mike + sarah = 17 v + m = 14 m + s = 12 < < use this formula & plug into the original formula , to get vanessa ' s total v + ( m + s ) = 17 v + 12 = 17 subtract 12 from both sides v = 5 answer : c
Answer: c
Problem: sandy is younger than molly by 16 years . if the ratio of their ages is 7 : 9 , how old is sandy ?
Options: a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70
Rationale: "let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 16 x = 8 sandy is 56 years old . the answer is c ."
Answer: c
Problem: if both 7 ^ 2 and 3 ^ 3 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ?
Options: a ) 99 , b ) 147 , c ) 363 , d ) 1200 , e ) 1625
Rationale: "the number a must include at least 3 * 7 ^ 2 = 147 the answer is b ."
Answer: b
Problem: in a village of 2,600 people , 800 people are over 70 years old and 850 people are female . it is known that 40 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a male or younger than 70 years old ?
Options: a ) 221 / 250 , b ) 199 / 250 , c ) 33 / 50 , d ) 8 / 25 , e ) 209 / 260
Rationale: the number of people younger than 70 years old is 2600 - 800 = 1800 the number of females older than 70 years old is 0.6 * 850 = 510 then the number of males older than 70 years old is 800 - 510 = 290 . the number of people who are either male or younger than 70 is 1800 + 290 = 2090 . p ( a person is younger than 70 or male ) = 2090 / 2600 = 209 / 260 the answer is e .
Answer: e
Problem: a circle graph shows how the budget of a certain company was spent : 60 percent for salaries , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent transportation ?
Options: a ) 18 ° , b ) 36 ° , c ) 54 ° , d ) 72 ° , e ) 90 °
Rationale: "the percent of the budget for transportation is 100 - ( 60 + 9 + 5 + 4 + 2 ) = 20 % 100 % of the circle is 360 degrees . then ( 20 % / 100 % ) * 360 = 72 degrees the answer is d ."
Answer: d
Problem: two trains 140 m and 160 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 ) 7 , b ) 8.2 , c ) 2 , d ) 10.8 , e ) 11.2
Rationale: "answer : option d relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 160 = 300 m . required time = 300 * 9 / 250 = 54 / 5 = 10.8 sec"
Answer: d
Problem: working alone , a can complete a certain kind of job in 6 hours . a and d , working together at their respective rates , can complete one of these jobs in 4 hours . in how many hours can d , working alone , complete one of these jobs ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let total time taken by d to complete the job = d total time taken by a to complete the job = 6 work done by a in an hour 1 / a = 1 / 6 working together a and d can complete the job in 4 hours 1 / a + 1 / d = 1 / 4 = > 1 / d = 1 / 4 - 1 / a = 1 / 4 - 1 / 6 = 1 / 12 = > d = 12 hours answer c"
Answer: c
Problem: ashok secured average of 70 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 50 , b ) 74 , c ) 78 , d ) 80 , e ) none of these
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 70 therefore total marks in 6 subjects = 70 * 6 = 420 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 420 – 370 = 50 answer a"
Answer: a
Problem: population is 23000 . population increases by 10 % every year , then the population after 3 years is ?
Options: a ) 26630 , b ) 26640 , c ) 36623 , d ) 30613 , e ) 26820
Rationale: "population after 1 st year = 23000 * 10 / 100 = 2300 = = = > 23000 + 2000 = 25300 population after 2 nd year = 25300 * 10 / 100 = 2530 = = = > 25300 + 2530 = 27830 population after 3 rd year = 27830 * 10 / 100 = 2783 = = = > 27830 + 2783 = 30613 answer : d"
Answer: d
Problem: a train running at the speed of 72 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 299 meter , c ) 666 meter , d ) 155 meter , e ) 180 meter
Rationale: "speed = 72 * ( 5 / 18 ) m / sec = 20 m / sec length of train ( distance ) = speed * time ( 20 ) * 9 = 180 meter answer : e"
Answer: e
Problem: two numbers are in the ratio of 5 : 7 . if 33 is subtracted from each number , they are in the ratio of 1 : 2 . what are the two numbers ?
Options: a ) 45 , 63 , b ) 50 , 70 , c ) 55 , 77 , d ) 60 , 84 , e ) 65 , 91
Rationale: "( 5 x - 33 ) : ( 7 x - 33 ) = 1 y : 2 y 5 x - 33 = y 7 x - 33 = 2 y 231 - 165 = 10 y - 7 y 66 = 3 y y = 22 5 x - 33 = 22 x = 11 the two numbers are 5 x and 7 x which are 55 and 77 . the answer is c ."
Answer: c
Problem: x and y are positive integers . when x is divided by 12 , the remainder is 5 , and when x is divided by 13 , the remainder is 3 . when y is divided by 14 , the remainder is 5 , and when y is divided by 7 , the remainder is 5 . what is the least possible value of x + y ?
Options: a ) 24 , b ) 12 , c ) 64 , d ) 48 , e ) 25
Rationale: "when x is divided by 12 , the remainder is 5 : so , the possible values of x are : 5 , 17 , 29 , 41 , etc . when x is divided by 13 , the remainder is 3 : so , the possible values of x are : 3 , 16,29 . . . stop . since both lists include 29 , the smallest possible value of x is 29 . when y is divided by 14 , the remainder is 5 : so , the possible values of y are : 5 , 19 , 33,47 etc . when y is divided by 7 , the remainder is 5 : so , the possible values of y are : 5 , 19 . . . stop . since both lists include 19 , the smallest possible value of y is 19 since the smallest possible values of x and y are 29 and 19 respectively , the smallest possible value of x + y is 48 . so , d is the correct answer to the original question ."
Answer: d
Problem: a train running at the speed of 180 km / hr crosses a pole in 7 seconds . what is the length of the train ?
Options: a ) 530 , b ) 305 , c ) 503 , d ) 430 , e ) 350
Rationale: "speed = ( 180 * 5 / 18 ) m / sec = ( 50 ) m / sec length of the train = ( speed x time ) = ( 50 * 7 ) m = 350 m . answer : e"
Answer: e
Problem: the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 432 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 12 , b ) 17 , c ) 18 , d ) 19 , e ) 14
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 432 3 b 2 = 432 b 2 = 144 b = 12 m . answer : option a"
Answer: a
Problem: one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 16 cm 2 . find the lengths of all sides .
Options: a ) 10 and 3 , b ) 9 and 6 , c ) 10 and 7 , d ) 3 and 10 , e ) 10 and 10
Rationale: "let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm 2 , which is 16 cm 2 more than the first area . therefore a 1 + 16 = a 2 x ( x − 3 ) + 16 = ( x + 1 ) ( x − 2 ) x 2 − 3 x + 16 = x 2 + x − 2 x − 2 2 x = 18 x = 9 . so , the sides of the rectangle are 9 cm and ( 9 − 3 ) = 6 cm long . so answer is b ."
Answer: b
Problem: the difference between simple interest and compound interest on rs . 1200 for one year at 10 % per annum reckoned half - yearly is :
Options: a ) rs . 2.50 , b ) rs . 3 , c ) rs . 3.75 , d ) rs . 4 , e ) rs . 5
Rationale: s . i = ( 1000 * 10 * 4 ) / 100 = rs . 400 c . i = 1200 * 1 + 5 / 100 ) 2 – 1200 = 123 . difference = rs . ( 123 - 120 ) = rs . 3 answer : b
Answer: b
Problem: a rectangular tank needs to be coated with insulation . the tank has dimensions of 3 feet , 6 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?
Options: a ) $ 980
b ) $ 1060
c ) $ 1220
d ) $ 1440
e ) $ 1650
Rationale: the total surface area is 2 ( 2 * 3 + 3 * 6 + 2 * 6 ) = 72 square feet the total cost is 72 * $ 20 = $ 1440 the answer is d .
Answer: d
Problem: if a trader sold two cars each at rs . 325475 and gains 13 % on the first and loses 13 % on the second , then his profit or loss percent on the whole is ?
Options: a ) 1.69 % , b ) 1.74 % , c ) 1.84 % , d ) 1.47 % , e ) 1.24 %
Rationale: "sp of each car is rs . 325475 , he gains 13 % on first car and losses 13 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 13 ) ( 13 ) / 100 % = 1.69 % answer : a"
Answer: a
Problem: p , q and r have rs . 5000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) rs . 3000 , b ) rs . 3600 , c ) rs . 2000 , d ) rs . 4000 , e ) none of these
Rationale: "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 5000 - r ) = > 3 r = 10000 - 2 r = > 5 r = 10000 = > r = 2000 . answer : c"
Answer: c
Problem: a cab driver 5 days income was $ 250 , $ 400 , $ 750 , $ 400 , $ 500 . then his average income is ?
Options: a ) $ 440 , b ) $ 450 , c ) $ 460 , d ) $ 470 , e ) $ 480
Rationale: "avg = sum of observations / number of observations avg income = ( 250 + 400 + 750 + 400 + 500 ) / 5 = 460 answer is c"
Answer: c
Problem: 1903 x 1903 = ?
Options: a ) a ) 3623216 , b ) b ) 3624216 , c ) c ) 3624316 , d ) d ) 3621409 , e ) e ) 3625216
Rationale: "1903 x 1903 = ( 1903 ) 2 = ( 1900 + 3 ) 2 = ( 1900 ) 2 + ( 3 ) 2 + ( 2 x 1900 x 3 ) = 3610000 + 9 + 11400 . = 3621409 . d )"
Answer: d
Problem: a man , a woman and a boy can together complete a piece of work in 3 days . if a man alone can do it in 6 days and a boy alone in 9 days , how long will a woman take to complete the work ?
Options: a ) 12 days , b ) 15 days , c ) 16 days , d ) 24 days , e ) 18 days
Rationale: explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 9 ( 1 man + 1 boy ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 9 = 5 / 18 therefore , 1 woman ’ s 1 day ’ s work = 1 / 3 – 5 / 18 = 1 / 18 therefore , the woman alone can finish the work in 18 days . answer : option e
Answer: e
Problem: a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6700 ?
Options: a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6191 , e ) s . 7991
Rationale: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6700 * 6 ) - 34009 ] = rs . ( 40200 - 34009 ) = rs . 6191 . answer : d"
Answer: d
Problem: find the cube root of 804357 ?
Options: a ) 22 , b ) 88 , c ) 93 , d ) 19 , e ) 18
Rationale: "unit digit of the answer is 3 . ( cube of 3 = 27 ) . now omit 357 and find after which cube 804 lies . it is 729 . so our tenth place is 9 . answer = c"
Answer: c
Problem: if p and q are prime numbers , how many divisors does the product p ^ 3 * q ^ 7 have ?
Options: a ) 25 , b ) 30 , c ) 32 , d ) 35 , e ) 40
Rationale: "when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is c . 4 * 8 = 32"
Answer: c
Problem: a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 15 % on conveyance . if his savings at the end of the month is rs . 1200 , then his salary per month in rupees is :
Options: a ) 4000 , b ) 24000 , c ) 8000 , d ) 10000 , e ) none of these
Rationale: "total expenditure = 40 + 25 + 15 + 15 = 95 % saving = ( 100 - 95 ) = 5 % 5 / 100 × salary = 1200 , salary = 24000 rs . answer : b"
Answer: b
Problem: a train , 135 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
Options: a ) 270 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m
Rationale: "explanation : assume the length of the bridge = x meter total distance covered = 135 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 135 + x ) / 30 m / s = > 45 ã — ( 10 / 36 ) = ( 135 + x ) / 30 = > 45 ã — 10 ã — 30 / 36 = 135 + x = > 45 ã — 10 ã — 10 / 12 = 135 + x = > 15 ã — 10 ã — 10 / 4 = 135 + x = > 15 ã — 25 = 135 + x = 375 = > x = 375 - 135 = 240 answer : option e"
Answer: e
Problem: find the ratio between 1 hr 30 minutes and 2 hrs 40 minutes .
Options: a ) 9 : 16 , b ) 5 : 9 , c ) 12 : 17 , d ) 13 : 24 , e ) none of these
Rationale: solution : the ratio = 1 hr 30 min : 2 hr 40 min . 90 min : 160 min = 9 : 16 . answer is a
Answer: a
Problem: a batsman makes a score of 87 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?
Options: a ) 39 , b ) 35 , c ) 42 , d ) 40.5 , e ) 41
Rationale: "explanation : let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 87 = total runs scored in 17 innings = > 16 ( x - 3 ) + 87 = 17 x = > 16 x - 48 + 87 = 17 x = > x = 39 answer : option a"
Answer: a
Problem: mrs . evans gave a test to her freshmen economics class , which has 40 students enrolled and 30 of them answered question 1 correctly . if 29 answered question 2 correctly and 10 did not take the test then how many answered both questions correctly ?
Options: a ) 24 , b ) 27 , c ) 29 , d ) 31 , e ) 33
Rationale: "total number of enrolled students = 40 number of students who did not take test = 10 hence , number of students who took test = 40 - 10 = 30 number of students who answered q 2 correctly = 29 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 29 . number of students who answered both q 1 & q 2 correctly = 29 . answer : c"
Answer: c
Problem: nina has exactly enough money to purchase 5 widgets . if the cost of each widget were reduced by $ 1.25 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?
Options: a ) $ 16.7 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 40
Rationale: "a its is . let price = x ( x - 1.25 ) 8 = 5 x x = 10 / 3 hence total money = 5 * 10 / 3 = 16.7"
Answer: a
Problem: if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 9000 ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 10
Rationale: "required difference = [ 3 ½ % of rs . 9000 ] – [ 3 1 / 3 % of rs . 9000 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 9000 = 1 / 6 % of rs . 9000 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 9000 ] = rs . 15 . answer is c ."
Answer: c
Problem: in a kilometer race , a beats b by 40 meters or 15 seconds . what time does a take to complete the race ?
Options: a ) 277 sec , b ) 285 sec , c ) 267 sec , d ) 167 sec , e ) 276 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 15 ) / 50 = 300 sec . time taken by a = 300 - 15 = 285 sec . answer : b"
Answer: b
Problem: a reduction of 40 % in the price of bananas would enable a man to obtain 67 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1.86 , b ) 2.86 , c ) 4.86 , d ) 3.86 , e ) 5.86
Rationale: "40 * ( 40 / 100 ) = 16 - - - 67 ? - - - 12 = > rs . 2.86 answer : b"
Answer: b
Problem: a waitress ' s income consists of her salary and tips . during one week , her tips were 7 / 4 of her salary . what fraction of her income for the week came from tips ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 2 / 3 , d ) 4 / 9 , e ) 7 / 11
Rationale: "her tips were 7 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 7 / 4 ) ( $ 4 ) = $ 7 so , her total income = $ 4 + $ 7 = $ 11 what fraction of her income for the week came from tips $ 7 / $ 11 = 7 / 11 = e"
Answer: e
Problem: if one cat eats 1.5 rats in 1.5 days , then in howmany days 3 cats will eat 3 rats ? ?
Options: a ) 1 day , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
Rationale: 1 cat - - - - - - 3 / 2 rat - - - - - - - - - 3 / 2 days 1 cat - - - - - - ( 3 / 2 ) * 2 rat - - - - - ( 3 / 2 ) * 2 days ( rat doubled , days doubled ) 1 * 3 cat - - - - - 3 rat - - - - - - - - - - - 3 / 3 = 1 day ( cat * 3 , same rat , days / 3 ) answer : a
Answer: a
Problem: the distance between two cities a and b is 465 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 09 , b ) 07 , c ) 12 , d ) 05 , e ) 03
Rationale: "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 465 therefore , 60 x + 75 ( x - 1 ) = 465 = > x = 3 . so , they meet at ( 8 + 4 ) i . e , 12 noon answer : c )"
Answer: c
Problem: a train 100 m long crosses a platform 125 m long in 10 sec ; find the speed of the train ?
Options: a ) 81 , b ) 77 , c ) 54 , d ) 33 , e ) 99
Rationale: "d = 100 + 125 = 225 t = 10 s = 225 / 10 * 18 / 5 = 81 kmph answer : a"
Answer: a
Problem: calculate the largest 3 digit number which is exactly divisible by 89 ?
Options: a ) 911 , b ) 969 , c ) 979 , d ) 977 , e ) 971
Rationale: "largest 4 digit number is 999 after doing 999 ÷ 89 we get remainder 20 hence largest 3 digit number exactly divisible by 89 = 999 - 20 = 979 c"
Answer: c
Problem: on dividing 83 by a number , the quotient is 9 and the remainder is 2 . find the divisor ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "d = ( d - r ) / q = ( 83 - 2 ) / 9 = 81 / 9 = 9 c )"
Answer: c
Problem: albert invested rs . 1000 in a scheme for 3 years at compound interest rate 10 % p . a . how much amount will albert get on maturity of the fixed deposit ?
Options: a ) s . 1300 , b ) s . 1005 , c ) s . 1031 , d ) s 1331 , e ) s . 1120
Rationale: "amount = [ 1000 * ( 1 + 10 / 100 ) 3 ] = 1000 * 11 / 10 * 11 / 10 * 11 / 10 = rs . 1331 answer : d"
Answer: d
Problem: if a ' s height is 35 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 66.66 % , b ) 66.68 % , c ) 53.84 % , d ) 86.66 % , e ) 66.65 %
Rationale: "excess of b ' s height over a ' s = [ ( 35 / ( 100 - 35 ) ] x 100 % = 53.84 % answer : c )"
Answer: c
Problem: what is 5 / 8 as a percent
Options: a ) 62.5 % , b ) 63 % , c ) 63.5 % , d ) 64.5 % , e ) 65 %
Rationale: "5 / 8 as a percent = ( 5 / 8 ) x 100 = 0.625 x 100 = 62.5 % answer : a i . e . 62.5 %"
Answer: a
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 77.44 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 88 , e ) 97
Rationale: "money collected = ( 77.44 x 100 ) paise = 7744 paise . number of members = square root of 7744 = 88 . answer : option d"
Answer: d
Problem: a library has an average of 510 visitors on sunday and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 288 , b ) 278 , c ) 267 , d ) 285 , e ) 231
Rationale: "since the month begins with a sunday , so there will be five sundays in the month . required average = [ ( 510 * 5 ) + ( 240 * 25 ) ] / 30 = 8550 / 30 = 285 . answer : d"
Answer: d
Problem: some of the 50 % solution of acid was removed and this was replaced with an equal amount of 10 % solution of acid . as a result , a 20 % solution of acid was obtained . what fraction of the original solution was replaced ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 3 / 5 , e ) 4 / 5
Rationale: "let x be the fraction of the original solution that was replaced . 0.5 * ( 1 - x ) + 0.1 ( x ) = 0.2 0.4 x = 0.3 x = 3 / 4 the answer is c ."
Answer: c
Problem: in a park there are two ponds with both brown ducks and green ducks . in the smaller pond there are 30 ducks and in the larger pond there are 50 ducks . if 20 % of the ducks in the smaller pond are green and 12 % of the ducks in the larger pond are green , then what percentage of ducks are green ?
Options: a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %
Rationale: number of ducks in small pond = 30 green ducks in small pond = 20 % of 30 = 6 ducks number of ducks in large pond = 50 green ducks in large pond = 12 % of 50 = 6 ducks total number of ducks = 30 + 50 = 80 total number of green ducks = 6 + 6 = 12 ducks percentage of green ducks = 12 / 80 * 100 = 15 % answer : c
Answer: c
Problem: the h . c . f of two numbers is 17 and their l . c . m is 5134 . if one of the numbers is 289 , then the other is ?
Options: a ) 302 , b ) 304 , c ) 306 , d ) 308 , e ) 310
Rationale: "other number = ( 17 * 5134 ) / 289 = 302 . answer : a"
Answer: a
Problem: a fruit drink is made of orange , watermelon , and grape juice , where 15 percent of the drink is orange juice and 60 percent is watermelon juice . if the drink is made with 35 ounces of grape juice , how many ounces is the drink total ?
Options: a ) 120 , b ) 140 , c ) 160 , d ) 180 , e ) 200
Rationale: "let the total number of ounces in the drink be x . % of orange = 15 % % of watermelon = 60 % % of grape = 100 % - 75 % = 25 % 0.25 x = 35 x = 140 therefore there are a total of 140 ounces in the drink . the answer is b ."
Answer: b
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 8 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4529
b ) s . 4586
c ) s . 7248
d ) s . 4530
e ) s . 4528
Rationale: area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 8 = rs . 7248 answer : c
Answer: c