regisss/math_qa huggingface dataset:
Problem: a work crew of 6 men takes 8 days to complete one - half of a job . if 9 men are then added to the crew and the men continue to work at the same rate , how many days will it take the enlarged crew to do the rest of the job ?
Options: a ) 2 , b ) 3 , c ) 3 1 / 5 , d ) 4 , e ) 4 4 / 5
Rationale: "suppose 1 man can do work in x days . . so 4 men will do in . . 6 / x = 1 / 8 * 1 / 2 as half job is done x = 96 now 9 more are added then 15 / 96 = 1 / 2 * 1 / d for remaining half job d = 3 1 / 5 number of days c"
Answer: c
Problem: what is the dividend . divisor 17 , the quotient is 8 and the remainder is 5
Options: a ) a ) 145 , b ) b ) 141 , c ) c ) 150 , d ) d ) 153 , e ) e ) 158
Rationale: "d = d * q + r d = 17 * 8 + 5 d = 136 + 5 d = 141 answer : b"
Answer: b
Problem: a searchlight on top of the watch - tower makes 3 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 15 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "3 revolutions per minute = 1 revolution every 20 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 20 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 15 seconds ) = 1 - p ( man in dark for max of 15 seconds ) = 1 - 15 / 20 = 1 - 3 / 4 = 1 / 4 or the other way would be : p ( man in dark for at least 5 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 20 seconds because that is the max . in this approach it would be 5 / 20 seconds = 1 / 4 . answer is a"
Answer: a
Problem: john and amanda stand at opposite ends of a straight road and start running towards each other at the same moment . their rates are randomly selected in advance so that john runs at a constant rate of 3 , 4 , or 5 miles per hour and amanda runs at a constant rate of 3 , 4 , 5 , 6 , or 7 miles per hour . what is the probability that john has traveled farther than amanda by the time they meet ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 2 / 15 , e ) 4 / 15
Rationale: john will run farther if he runs at 5 mph and amanda runs at 4 mph or 3 mph . in this case , p ( john runs farther ) = 1 / 3 * 2 / 5 = 2 / 15 john will run farther if he runs at 4 mph and amanda runs at 3 mph . in this case , p ( john runs farther ) = 1 / 3 * 1 / 5 = 1 / 15 p ( john runs farther ) = 2 / 15 + 1 / 15 = 3 / 15 = 1 / 5 the answer is c .
Answer: c
Problem: the average of numbers 0.64205 , 0.64203 , 0.64202 and 0.64201 is ?
Options: a ) 0.64202 , b ) 0.64204 , c ) 0.642022 , d ) 0.642028 , e ) none
Rationale: "answer average = ( 0.64205 + 0.64203 + 0.64202 + 0.64201 ) / 4 = 2.56811 / 4 = 0.642028 correct option : d"
Answer: d
Problem: two bullet train s 140 m and 210 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 15.8 sec . , b ) 12.6 sec . , c ) 11.8 sec . , d ) 10.8 sec . , e ) 08.8 sec .
Rationale: "relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 210 ) m = 350 m . required time = 350 x 9 / 250 = 54 / 5 = 12.6 sec . answer b"
Answer: b
Problem: 4 friends are pooling their money for pizza . emma has 8 dollars . daya has 25 % more money than emma , jeff has 2 / 5 of the money daya has , and brenda has 4 more dollars than jeff . how much money does brenda have ?
Options: a ) 14 , b ) 6 , c ) 7 , d ) 8 , e ) 10
Rationale: d 8 emma has 8 dollars . daya has 25 % more dollars than emma . daya = 8 + 8 x 25 % = 8 + 8 x . 25 = 8 + 2 = 10 jeff has 2 / 5 of what daya has . = 10 x 2 / 5 = 4 brenda has 4 more dollars than jeff . = 4 + 4 = 8 brenda has 8 dollars . the correct answer is d .
Answer: d
Problem: in one alloy there is 12 % chromium while in another alloy it is 8 % . 35 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 8.8 % , b ) 9.75 % , c ) 9.2 % , d ) 8.6 % , e ) 8.4 %
Rationale: "the amount of chromium in the new 35 + 45 = 80 kg alloy is 0.12 * 35 + 0.08 * 45 = 7.8 kg , so the percentage is 7.8 / 80 * 100 = 9.75 % . answer : b ."
Answer: b
Problem: mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 26 miles , how many miles was mike ' s ride ?
Options: a ) 20 , b ) 30 , c ) 36 , d ) 46 , e ) 54
Rationale: "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 26 ) = $ 14 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 14 0.25 * x = 11.5 x = 46 miles the answer is d ."
Answer: d
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.91 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 15 %
Rationale: "let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.91 9.9 - 45 x + 36 x = 8.91 9 x = 0.99 x = 0.11 the answer is c ."
Answer: c
Problem: find the simple interest on $ 10000 at 4 % per annum for 12 months ?
Options: a ) $ 400 , b ) $ 500 , c ) $ 650 , d ) $ 710 , e ) $ 1000
Rationale: "p = $ 10000 r = 4 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 4 * 1 / 100 = $ 400 answer is a"
Answer: a
Problem: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 3 m 3 , then the rise in the water level in the tank will be :
Options: a ) 20 cm , b ) 25 cm , c ) 35 cm , d ) 18.75 cm , e ) none of these
Rationale: "explanation : total volume of water displaced = ( 3 x 50 ) m 3 = 150 m 3 rise in water level = 150 / 40 ã — 20 = 0.1875 m = 18.75 cm answer : d"
Answer: d
Problem: a contractor undertakes to built a walls in 50 days . he employs 40 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?
Options: a ) 60 , b ) 30 , c ) 35 , d ) 20 , e ) none of these
Rationale: "40 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 40 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 40 × 25 × 0.6 / 25 × 0.4 = 60 men answera"
Answer: a
Problem: the average weight of 6 person ' s increases by 4.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?
Options: a ) 160 kg , b ) 175 kg , c ) 180 kg , d ) 102 kg , e ) 190 kg
Rationale: "total weight increased = ( 6 x 4.5 ) kg = 27 kg . weight of new person = ( 75 + 27 ) kg = 102 kg option d"
Answer: d
Problem: a thief goes away with a santro car at a speed of 40 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start ?
Options: a ) a ) 2 , b ) b ) 5 , c ) c ) 7 , d ) d ) 5 , e ) e ) 1
Rationale: "explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 60 40 d = 20 rs = 60 – 40 = 20 t = 20 / 10 = 1 hours answer : option e"
Answer: e
Problem: sandy buys an old scooter for $ 900 and spends $ 300 on its repairs . if sandy sells the scooter for $ 1500 , what is the gain percent ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "selling price / total cost = 1500 / 1200 = 1.25 the gain percent is 25 % . the answer is d ."
Answer: d
Problem: a , b , c , d , e are the 5 electronic shops in the naza market , which have 20 , 30 , 60 , 80 and 50 t . v . sets with them respectively , then the average number of t . v . sets in each shop is
Options: a ) 24 , b ) 48 , c ) 50 , d ) 60 , e ) none
Rationale: answer average number of t . v . sets = ( 20 + 30 + 60 + 80 + 50 ) / 5 = 48 correct option : b
Answer: b
Problem: a no . when divided by 281 gives a remainder 160 , what remainder will be obtainedby dividingthe same no . 21 ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "281 + 160 = 441 / 21 = 21 ( remainder ) a"
Answer: a
Problem: in the rectangular coordinate system , points ( 16 , 0 ) and ( – 16 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) none of the above
Rationale: "d it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 16 d"
Answer: d
Problem: the speed of a railway engine is 74 km per hour when no compartment is attached , and the reduction in speed is directly proportional to the square root of the number of compartments attached . if the speed of the train carried by this engine is 24 km per hour when 9 compartments are attached , the maximum number of compartments that can be carried by the engine is :
Options: a ) 49 , b ) 18 , c ) 16 , d ) 17 , e ) 19
Rationale: "the reduction in speed is directly proportional to the square root of the number of compartments attached doesreductionmean amount subtracted ? or percentage decrease ? there are at least two interpretations , and the wording does not provide a clear interpretation between them . evidently what the question intends is the subtraction interpretation . what is subtracted from the speed is directly proportional to the square root of the number of compartments attached . in other words , if s = speed , and n = number of compartments , then s = 74 - k * sqrt ( n ) wherekis a constant of the proportionality . in general , if a is directly proportional to b , we can write a = k * b and solve for k . if n = 9 , then s = 24 24 = 74 - k * sqrt ( 9 ) = 74 - 3 k k = 16.67 now , we need to know : what value of n makes s go to zero ? 0 = 74 - 16.67 * sqrt ( n ) 16.67 * sqrt ( n ) = 74 sqrt ( n ) = 4.44 n = 4.44 ^ 2 > 19 with 20 compartments , the train does not budge . therefore , it would budge if there were one fewer cars . thus , 19 is the maximum number of cars the engine can pull and still move . e"
Answer: e
Problem: the sum of even numbers between 1 and 31 is
Options: a ) 16 , b ) 128 , c ) 240 , d ) 512 , e ) none
Rationale: "solution required numbers are 2 , 4 , 6 , . . 30 . this is an a . p containing 15 terms . required sum = n / 2 ( first term + last term ) ‹ = › 15 / 2 ( 2 + 30 ) ‹ = › 240 . answer c"
Answer: c
Problem: find value for x from below equation ? x + 1 = - 3
Options: a ) 1 , b ) - 4 , c ) - 1 , d ) 2 , e ) 3
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = - 3 - 1 2 . simplify both sides : x = - 4 b"
Answer: b
Problem: if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 50 , what is the value of c â ˆ ’ a ?
Options: a ) 25 , b ) 10 , c ) 90 , d ) 14 , e ) it can not be determined from the information given
Rationale: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 100 - - 2 subtracting 1 from 2 we have c - a = 10 ; answer : b"
Answer: b
Problem: a certain plant was 11 feet long on the day it was plantedthe length grows by a constant amount everyday ( inc . the first day it was planted ) . if this plant grew by 30 % b / w the 4 th day and 10 th day after it was planted , how many feet per day does the plant grow
Options: a ) a ) 2 , b ) b ) 4.5 , c ) c ) 0.69 , d ) d ) 5.5 , e ) e ) 3
Rationale: if the plant is 11 feet tall when it is planted , it will be 11 + k feet tall at the end of the day ( where k is the constant length it grows by every day ) . similarly , at the end of the 4 th day the plant must be 11 + 4 k feet tall and at the end of the 10 th day it must be 11 + 10 k feet tall . therefore 6 k = 0.3 ( 11 + 4 k ) = > k = 0.69 therefore the plant grows by 0.69 feet every day . option ( c )
Answer: c
Problem: 6,61 , 212,507 , _ ?
Options: a ) 974 , b ) 994 , c ) 954 , d ) 845 , e ) 754
Rationale: "( 2 ) 3 - 2 = 6 ( 4 ) ^ 3 - 3 = 61 ( 6 ) ^ 3 - 4 = 212 ( 8 ) ^ 3 - 5 = 507 ( 10 ) ^ 3 - 6 = 994 answer : b"
Answer: b
Problem: john and steve are speed walkers in a race . john is 14 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
Options: a ) 13 seconds , b ) 17 seconds , c ) 26 seconds , d ) 32 seconds , e ) 51 seconds
Rationale: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 14 + 2 - - - > 0.5 t = 16 - - - > t = 32 seconds . d is the correct answer ."
Answer: d
Problem: the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing theaverage by 4 year . find what was theoriginal strength of class ?
Options: a ) 11 , b ) 12 , c ) 17 , d ) 19 , e ) 21
Rationale: "let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 ⇒ 40 y + 384 = 36 y + 432 ⇒ 4 y = 48 ∴ y = 12 b"
Answer: b
Problem: running at the same constant rate , 5 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1,800 , c ) 2,160 , d ) 10,800 , e ) 64,800
Rationale: "5 machines produce 270 bottles per minute ; 1 machine produces 270 / 5 = 54 bottles per minute ; 10 machines produce 54 * 10 = 540 bottles per minute ; in 4 minutes 10 machines produce 540 * 4 = 2,160 bottles . answer : c ."
Answer: c
Problem: the radius of the wheel of a bus is 100 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 175 , b ) 250 , c ) 300 , d ) 330 , e ) none of these
Rationale: "radius of the wheel of bus = 100 cm . then , circumference of wheel = 2 ï € r = 200 ï € = 628.57 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 440 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 628.57 = 175 answer a"
Answer: a
Problem: what is the smallest positive integer x , such that 1944 x is a perfect cube ?
Options: a ) 4 , b ) 3 , c ) 8 , d ) 12 , e ) 18
Rationale: "take out the factors of 1944 that will come 2 ^ 3 * 3 ^ 3 * 3 ^ 2 . for perfect cube you need every no . raise to the power 3 . for 1944 to be a perfect cube , need 1 3 that means = 3 b is the answer ."
Answer: b
Problem: if n is an integer and 101 n ^ 2 is less than or equal to 6400 , what is the greatest possible value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: 101 * n ^ 2 < = 6400 n ^ 2 < = 6400 / 101 which will be less than 81 since 6400 / 100 = 64 which is the square of 9 next closest value of n where n ^ 2 < = 64 is 7 ans a
Answer: a
Problem: a number whose fifth part increased by 5 is equal to its fourth part diminished by 5 is ?
Options: a ) 160 , b ) 180 , c ) 200 , d ) 220 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 5 = ( n / 4 ) - 5 ⇒ ( n / 4 ) - ( n / 5 ) = 10 ⇒ ( 5 n - 4 n ) / 20 = 10 ∴ n = 200 option : c"
Answer: c
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 390 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) 60 sec
Rationale: "explanation : speed = 45 km / hr = 45 × ( 10 / 36 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 390 = 750 meter time taken to cross the platform = 750 / ( 25 / 2 ) = 750 × 2 / 25 = 60 seconds answer : option e"
Answer: e
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 500 more than d , what is a ' s share ?
Options: a ) rs . 2500 , b ) rs . 1000 , c ) rs . 1500 , d ) rs . 2000 , e ) none
Rationale: sol . let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 500 ⇔ x = 500 . ∴ a ' s share = rs . 5 x = rs . ( 5 x 500 ) = rs . 2500 . answer a
Answer: a
Problem: a certain high school has 500 students . of these students , 50 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?
Options: a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470
Rationale: "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 50 y = 20 z = 10 so , we have 50 students taking music , 20 taking art and 10 taking both music and art . 40 student taking just music 10 student taking just art 10 student taking both music and art total = 60 students we ' re asked for the total number of students who are taking neither course . that is 500 - 60 = 440 . b"
Answer: b
Problem: praveen starts business with rs . 3920 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?
Options: a ) s . 10080 , b ) s . 8000 , c ) s . 8500 , d ) s . 9000 , e ) s . 6000
Rationale: "let hari ’ s capital be rs . x . then , 3920 * 12 / 7 x = 2 / 3 = > 14 x = 141120 = > x = 10080 . answer : a"
Answer: a
Problem: the ratio between b and y is 7 / 9 ; b and y are increased by 4 , what is the ratio between the new values of b and y ?
Options: a ) 7 / 9 , b ) 14 / 9 , c ) 7 / 18 , d ) 11 / 13 , e ) it can not be determined
Rationale: ratio = 7 k / 9 k = 7 / 9 , 14 / 18 , etc . b and y are increased by 4 - - > ( 7 k + 4 ) / ( 9 k + 4 ) new ratio can be 11 / 13 , 18 / 22 , etc . answer : e
Answer: e
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 ) 2 , b ) 7 , c ) 3 , d ) 0 , e ) 8
Rationale: "explanation : s . i = rs . ( 1200 x 10 x 1 / 100 ) = rs . 120 . c . i = rs [ ( 1200 x 1 + 5 / 100 ) ² - 1200 ] = rs . 123 . difference = rs . [ 123 - 120 ] = rs . 3 . answer : b"
Answer: b
Problem: a woman can do a piece of work in 40 days . man is 25 % more efficient than woman . in how many days a man can do the same piece of work ?
Options: a ) 32 days , b ) 36 days , c ) 38 days , d ) 40 days , e ) 53 days
Rationale: the ratio of the efficiencies of a woman and man = 100 : 125 = 4 : 5 the ratio of the days taken by woman and man to finish the work = 5 : 4 woman takes 32 days to finish the work . = > 5 parts = 40 the number of days taken by man to finish the work = 4 parts = 40 / 5 x 4 = 32 days a
Answer: a
Problem: if a ^ 2 + b ^ 2 = 144 and ab ≠ 0 , then the greatest possible value for b is between
Options: a ) 16 and 13 , b ) 12 and 3 , c ) 11 and 4 , d ) 10 and 5 , e ) 9 and 6
Rationale: since a ≠ 0 , greatest possible value for b will be less than 12 but closer to it . so it lies between 11 and 12 answer : b
Answer: b
Problem: the ratio between the present ages of a and b is 3.5 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
Options: a ) 14 : 4 , b ) 13 : 0 , c ) 15 : 11 , d ) 13 : 12 , e ) 13 : 17
Rationale: "let the present ages of a and b be 3.5 x and 3 x years respectively . then , ( 3.5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 0.5 x = 8 = > x = 16 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 60 : 44 = 15 : 11 . answer : c"
Answer: c
Problem: ram , who is half as efficient as krish , will take 21 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?
Options: a ) 16 days , b ) 12 days , c ) 8 days , d ) 7 days , e ) 18 days
Rationale: "number of days taken by ram to complete task = 21 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 24 days is 21 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 21 w / 3 w = 7 days answer d"
Answer: d
Problem: calculate the l . c . m of 7 / 10 , 8 / 9 , 3 / 8 , 5 / 12 is :
Options: a ) 840 , b ) 70 , c ) 740 , d ) 140 , e ) 940
Rationale: required l . c . m = l . c . m . of 7 , 8 , 3 , 5 / h . c . f . of 10 , 9 , 8 , 12 = 840 / 1 = 840 answer is a
Answer: a
Problem: a circular mat with diameter 18 inches is placed on a square tabletop , each of whose sides is 24 inches long . which of the following is closest to the fraction of the tabletop covered by the mat ?
Options: a ) 5 / 12
b ) 3 / 5
c ) 1 / 2
d ) 3 / 8
e ) 5 / 6
Rationale: so we are looking for the area of the cloth over the area of the table area of the cloth = ( pi ) ( r ) ^ 2 which is about ( 3 ) ( 9 ) ( 9 ) area of the table = ( 24 ) ( 24 ) so the quick way to estimate is looking at the fraction like this : ( 3 / 24 ) ( 81 / 24 ) i hope this is easy to follow , so with some simplification i get ( 1 / 8 ) ( 3 ) = ( 3 / 8 ) answer is d
Answer: d
Problem: a man swims downstream 36 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 2 , e ) 4
Rationale: "36 - - - 3 ds = 12 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 12 + 6 ) / 2 = 9 answer : c"
Answer: c
Problem: the cash realised on selling a 14 % stock is rs . 109.25 , brokerage being 1 / 4 % is ?
Options: a ) 366 , b ) 106 , c ) 102 , d ) 109 , e ) 122
Rationale: "cash realised = rs . ( 109.25 - 0.25 ) = rs . 109 . answer : d"
Answer: d
Problem: the price of maruti car rises by 30 percent while the sales of the car come down by 20 % . what is the percentage change in the total revenue ?
Options: a ) - 4 % , b ) - 2 % , c ) + 4 % , d ) + 2 % , e ) none of these
Rationale: solution : let initial price of maruti car be rs . 100 . as price increases 30 % , price of car will become , ( 100 + 30 % of 100 ) = rs . 130 . due to increase in price , sales is down by 20 % . it means , it is going make 20 % less revenue as expected after increment of price . so , new revenue = ( 130 - 20 % of 130 ) = rs . 104 . the initial revenue was rs . 100 which becomes rs . 104 at the end . it means there is 4 % increment in the total revenue . mind calculation method : 100 = = 30 % ↑ ( price effect ) = = > 130 = = 20 % ↓ ( sales effects ) = = > 104 . hence , 4 % rises . answer : option c
Answer: c
Problem: if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 21 ( q + 1 ) , what is the least possible value of p + q ?
Options: a ) 36 , b ) 42 , c ) 44 , d ) 46 , e ) none
Rationale: "17 ( p + 1 ) = 21 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 21 / 17 - - > the least positive value of p + 1 is 21 , so the least value of p is 20 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 20 + 16 = 36 . answer : a ."
Answer: a
Problem: the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 60 percent of b , what is the value of m / x ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 4 , d ) 3 / 2 , e ) 2 / 3
Rationale: "a / b = 4 / 5 m / x = ( 2 / 5 ) * 5 / ( 5 / 4 ) * 4 = 2 / 5 the answer is b ."
Answer: b
Problem: two numbers are in the ratio 3 : 4 . if their l . c . m . is 84 . what is sum of the numbers ?
Options: a ) 49 , b ) 56 , c ) 76 , d ) 84 , e ) 85
Rationale: "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 84 = > 12 x = 84 = > x = 84 / 12 = 7 sum of the numbers = 3 x + 4 x = 7 x = 7 x 7 = 49 answer : option a"
Answer: a
Problem: three rugs have a combined area of 212 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?
Options: a ) 18 square meters , b ) 20 square meters , c ) 24 square meters , d ) 28 square meters , e ) 30 square meters
Rationale: "total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 212 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 24 . answer : c ."
Answer: c
Problem: when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction q of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?
Options: a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14
Rationale: "if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus q = 11 / 14 of the remaining votes must be against . answer : a ."
Answer: a
Problem: for 2 consecutive yrs , my incomes are in the ratio of 4 : 7 and expenses in the ratio of 3 : 5 . if my income in the 2 nd yr is rs . 42000 & my expenses in the first yr in rs . 20000 , my total savings for the two - year is
Options: a ) s . 8000 , b ) s . 9000 , c ) s . 9900 , d ) s . 9990 , e ) s . 11000
Rationale: "sol . income in first year = * x 42000 = rs . 24000 expenses in second year = \ x 21000 = rs . 35000 total savings = total income - total expenses = ( 42000 + 24000 ) - ( 20000 + 35000 ) = 66000 - 55000 = rs . 11000 e"
Answer: e
Problem: tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 12 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 156 , b ) 146 , c ) 158 , d ) 187 , e ) 160
Rationale: "a 156 sum = ( n x n ) + n hence , 12 x 12 = 144 + 12 = 156"
Answer: a
Problem: during a certain season , a team won 70 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
Options: a ) 180 , b ) 170 , c ) 156 , d ) 150 , e ) 100
Rationale: "we are first given that a team won 70 percent of its first 100 games . this means the team won 0.7 x 100 = 70 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 70 + 0.5 t – 50 = 0.7 t 20 = 0.2 t 200 = 2 t 100 = t answer is e ."
Answer: e
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is six times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 54 : 8
Rationale: "water : soap = 3 : 2 soap : salt = 18 : 2 = > for 18 soap , salt = 2 = > for 2 soap , salt = ( 2 / 18 ) * 2 = 2 / 9 so , water : soap : salt = 3 : 2 : 2 / 9 = 54 : 36 : 4 after open container , water : soap : salt = 27 : 36 : 4 so , water : salt = 27 : 4 = 54 : 8 e"
Answer: e
Problem: if x 2 + kx - 3 , is divisible by ( x - 1 ) , what is the value of k
Options: a ) - 1 , b ) 1 , c ) 2 , d ) - 1 , e ) 0
Rationale: explanation : if x 2 + kx - 3 is divisible by ( x - 1 ) then x = 1 ( 1 ) 2 + 1 ( k ) - 3 = 0 1 + k - 3 = 0 k = 2 answer : option c
Answer: c
Problem: if ( x - 10 ) ( y - 5 ) ( z - 2 ) = 1000 then what is the least value of x + y + z ? if x , y , z are all integer no .
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: ( x - 10 ) ( y - 5 ) ( z - 2 ) = 1000 put x = 0 y = - 5 z = 12 then ( 0 - 10 ) ( - 5 - 5 ) ( 12 - 2 ) = 1000 ( - 10 ) ( - 10 ) ( 10 ) = 1000 1000 = 1000 answer : a
Answer: a
Problem: 0.002 x 0.4 = ?
Options: a ) 8.0 , b ) 0.008 , c ) 0.08 , d ) 0.8 , e ) 0.0008
Rationale: "2 x 4 = 8 . sum of decimal places = 4 0.002 x 0.4 = 0.0008 answer : option e"
Answer: e
Problem: for what value of x , is | x – 2 | + | x + 5 | + | x | = 17 ?
Options: a ) 0 , b ) 3 , c ) - 3 , d ) 5 , e ) - 5
Rationale: "for what value of x , is | x – 2 | + | x + 5 | + | x | = 17 ? it ' s easiest just to plug in answer choices : ( d ) : 5 | x – 2 | + | x + 5 | + | x | = 17 ? | 5 - 3 | + | 5 + 5 | + | 5 | = 17 ? | 2 | + | 10 | + | 5 | = 17 ( d )"
Answer: d
Problem: a can run 4 times as fast as b and gives b a start of 60 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 70 m , b ) 60 m , c ) 80 m , d ) 65 m , e ) 75 m
Rationale: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 60 m he gains 60 * ( 4 / 3 ) i . e 80 m answer : c"
Answer: c
Problem: a train 175 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 22 sec , b ) 16 sec , c ) 17 sec , d ) 88 sec , e ) 10 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 175 * 2 / 35 = 10 sec answer : e"
Answer: e
Problem: an 80 - liter solution of cool - drink is made from 10 % jasmine water . if 8 liters of jasmine and 12 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 12 % , b ) 14 % , c ) 16 % , d ) 18 % , e ) 20 %
Rationale: "the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.1 ( 80 ) + 8 ) / 100 = 16 / 100 = 16 % the answer is c ."
Answer: c
Problem: what is the sum of all the multiples of 10 between 0 and 99 ?
Options: a ) 500 , b ) 620 , c ) 450 , d ) 340 , e ) 440
Rationale: "the multiples of 10 between 0 and 99 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , and 90 . if these are all added together , the result is 450 . final answer : c"
Answer: c
Problem: the length of rectangle is thrice its breadth and its perimeter is 120 m , find the area of the rectangle ?
Options: a ) 432 sq m , b ) 356 sq m , c ) 452 sq m , d ) 428 sq m , e ) 675 sq m
Rationale: "2 ( 3 x + x ) = 120 l = 45 b = 15 lb = 45 * 15 = 675 answer : e"
Answer: e
Problem: an article is bought for rs . 805 and sold for rs . 900 , find the gain percent ?
Options: a ) 12.8 % , b ) 17.8 % , c ) 15.8 % , d ) 11.8 % , e ) 14.8 %
Rationale: "805 - - - - 95 100 - - - - ? = > 11.8 % answer : d"
Answer: d
Problem: at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 164.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
Options: a ) $ 21 , b ) $ 27 , c ) $ 31 , d ) $ 41 , e ) it can not be determined
Rationale: "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 164.5 subtracting the first equation from the second gives us b + 3 s = 44.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 31 . in any case , there is no necessity to know each item ' s price , just the sum . answer : c"
Answer: c
Problem: 65 % of x = 20 % of 682.50 . find the value of x ?
Options: a ) 100 , b ) 210 , c ) 150 , d ) 180 , e ) 199
Rationale: "65 % of x = 20 % of 682.50 then , 65 / 100 * x = 20 / 100 * 6825 / 10 x = 210 answer is b"
Answer: b
Problem: a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 200 that is both a prime and a palindrome . what is the sum of the digits of p ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "given that p is smallest integer greater than 200 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 answer : e"
Answer: e
Problem: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 120 kilometers ?
Options: a ) 4.5 , b ) 5.5 , c ) 6.5 , d ) 3 , e ) 8.5
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 120 kilometers ? 120 ÷ 40 = 3 × 1 gallon = 3 gallons correct answer d"
Answer: d
Problem: a ranch has both horses and ponies . exactly 5 / 7 of the ponies have horseshoes , and exactly 2 / 3 of the ponies with horseshoes are from iceland . if there are 4 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
Options: a ) 34 , b ) 38 , c ) 42 , d ) 46 , e ) 50
Rationale: "5 / 7 * p are ponies with horseshoes , so p is a multiple of 7 . 2 / 3 * 5 / 7 * p = 10 / 21 * p are icelandic ponies with horseshoes , so p is a multiple of 21 . the minimum value of p is 21 . then h = p + 4 = 25 . the minimum number of horses and ponies is 46 . the answer is d ."
Answer: d
Problem: a fruit seller had some oranges . he sells 40 % oranges and still has 420 oranges . how many oranges he had originally ?
Options: a ) 420 , b ) 700 , c ) 220 , d ) 400 , e ) none of these
Rationale: "explanation : he sells 40 % of oranges and still there are 420 oranges remaining = > 60 % of oranges = 420 ⇒ ( 60 × total oranges ) / 100 = 420 ⇒ total oranges / 100 = 7 ⇒ total oranges = 7 × 100 = 700 answer : option b"
Answer: b
Problem: if x ^ 2 + y ^ 2 = 16 and xy = 3 , then ( x − y ) ^ 2 =
Options: a ) 8 , b ) 11 , c ) 10 , d ) 17 , e ) 20
Rationale: "but you can not take xy + 3 to mean xy = - 3 . . only if xy + 3 = 0 , it will mean xy = - 3 . . rest your solution is perfect and you will get your correct answer as 16 - 2 * 3 = 10 . . answer c"
Answer: c
Problem: on the first day of her vacation , louisa traveled 160 miles . on the second day , traveling at the same average speed , she traveled 280 miles . if the 160 - mile trip took 3 hours less than the 280 - mile trip , what was the average speed , in miles per hour ?
Options: a ) 40 , b ) 45 , c ) 46 , d ) 48 , e ) 50
Rationale: ( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 160 / t = 280 / ( t + 3 ) - - > 4 / t = 7 / ( t + 3 ) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > ( rate ) = 160 / 4 = 40 answer : a
Answer: a
Problem: evaluate : | 5 - 8 ( 3 - 12 ) | - | 5 - 11 | = ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 71 , e ) 80
Rationale: "according to order of operations , inner brackets first . hence | 5 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 5 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 5 + 72 | - | 5 - 11 | = | 77 | - | - 6 | = 77 - 6 = 71 correct answer d ) 71"
Answer: d
Problem: a 10 % stock yielding 8 % is quoted at ?
Options: a ) 125 , b ) 170 , c ) 175 , d ) 180 , e ) 185
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 10 , money invested = 100 × 10 / 8 = rs . 125 ie , market value of the stock = rs . 125 answer is a ."
Answer: a
Problem: what is the sum of natural numbers between 30 and 100
Options: a ) 4615 , b ) 4860 , c ) 5000 , d ) 5500 , e ) 5550
Rationale: "a = first number l = last number sn = n / 2 [ a + l ] between 30 and 100 numbers = 71 = > 100 - 30 = 70 + 1 = 71 sn = 71 / 2 ã — 130 = 71 ã — 65 = 4615 answer : a"
Answer: a
Problem: what is the least value of x . so that 4 x 569 is divisible by 3 ?
Options: a ) 2 , b ) 5 , c ) 1 , d ) 0 , e ) 7
Rationale: "the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 4 + x + 5 + 6 + 9 = 24 + x least value of x may be 0 therefore 24 + 0 = 24 is divisible by 3 . d"
Answer: d
Problem: if a trader sold two cars each at rs . 325475 and gains 12 % on the first and loses 12 % on the second , then his profit or loss percent on the whole is ?
Options: a ) 1.44 % , b ) 1.43 % , c ) 1.34 % , d ) 4.44 % , e ) 1.74 %
Rationale: sp of each car is rs . 325475 , he gains 12 % on first car and losses 12 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 12 ) ( 12 ) / 100 % = 1.44 % answer : a
Answer: a
Problem: i flew my tiny seaplane to visit my mother . on the flight up , i flew at 96 mph . on the way home , i flew 88 mph . what was my average speed for the trip ?
Options: a ) 198 mph , b ) 110 mph , c ) 92 mph , d ) 100 mph , e ) 99 mph
Rationale: "( 96 mph + 88 mph ) / 2 = 92 mph correct answer is : c"
Answer: c
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 20 cm ?
Options: a ) 827 cm 2 , b ) 380 cm 2 , c ) 285 cm 2 , d ) 178 cm 2 , e ) 176 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 20 ) = 380 cm 2 answer : b"
Answer: b
Problem: if x < y < z and y - x > 11 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 15
Rationale: "we have : 1 ) x < y < z 2 ) y - x > 11 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 11 , the least value for y - x must be 13 , the least value for x must be 2 , and , thus , the least possible value for y must be 15 ( y - 2 = 13 , y = 15 ) 2 < 15 < z , since z is odd , the least possible value for z is 17 z - x = 17 - 2 = 15 answer e"
Answer: e
Problem: find k if 24 / k = 4 .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3
Rationale: "since 24 / k = 4 and 24 / 6 = 4 , then k = 6 correct answer a"
Answer: a
Problem: a merchandise feedback online portal accords ‘ ratings ’ to a product by recording the percentage of customers who have reported their views as either ‘ satisfied ’ or ‘ unsatisfied ’ only . the portal rounds off the exact percentage value calculated to the closest integral value . if the percentage of unsatisfied customers as recorded by the portal is 57 % , what is the least possible number of people that could have reported their views as ‘ satisfied ’ ?
Options: a ) 2 , b ) 3 , c ) 12 , d ) 43 , e ) 57
Rationale: 57 % unsatisfied . so ~ 43 % satisfied but 100 % should be an integer only and since the above percentages are approximations 100 % should be as close as possible to an integer . now substitute value [ 1 ] if 43 % is 2 what is 100 % - > 200 / 43 is not giving a number which is closest to an integer . [ 2 ] if 43 % is 3 what is 100 % - > 300 / 43 [ 43 * 7 = 301 ] . . . therefore closest possible to an integer . [ it also satisfies the least possible and hence we need not check for other choices which are greater than 3 ] therefore ans is b .
Answer: b
Problem: a bag consists of 30 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?
Options: a ) 5 / 6 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "bag consists of 20 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 30 - 5 - 9 = 16 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 30 + 16 / 30 = 25 / 30 = 5 / 6 hence , answer will be a ."
Answer: a
Problem: the sides of a cube are in the ratio of 1 : 2 the ratio of their volumes is ?
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 1 : 8 , d ) 2 : 1 , e ) 2 : 4
Rationale: 1 : 8 answer : c
Answer: c
Problem: what is the least value of x , so that 23 x 57 is divisible by 3
Options: a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4
Rationale: "explanation : 23257 is not divisible by 3 23057 is not divisible by 3 23157 is divisible by 3 23357 is not divisible by 3 2 + 3 + 1 + 5 + 7 = 18 18 / 3 = 6 . x = 1 answer : option c"
Answer: c
Problem: a present value of a machine is $ 1000 . its value depletiation rate is 10 % per annum then find the machine value after 2 years ?
Options: a ) $ 900 , b ) $ 810 , c ) $ 915 , d ) $ 715 , e ) $ 795
Rationale: "p = $ 1000 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 1000 * 9 / 10 * 9 / 10 = $ 810 answer is b"
Answer: b
Problem: in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 48 . what is the total number of students in the school ?
Options: a ) 72 , b ) 80 , c ) 120 , d ) 100 , e ) 150
Rationale: "let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 48 + 2 / 3 of 48 ( 80 / 100 ) x = 80 x = 100 . answer d"
Answer: d
Problem: to produce an annual income of rs . 1200 from a 15 % stock at 90 , the amount of stock needed is :
Options: a ) s . 10,000 , b ) s . 10,800 , c ) s . 14,400 , d ) s . 16,000 , e ) s . 46,000
Rationale: "solution for an income of rs . 15 , stock needed = rs . 100 . for an income of rs . 1500 , stock needed = rs . 10 / 12 x 15000 = 10,000 answer a"
Answer: a
Problem: a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 756 find the share of a .
Options: a ) 240 , b ) 388 , c ) 288 , d ) 277 , e ) 122
Rationale: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 756 = 288 answer : c"
Answer: c
Problem: what is 2 2 / 3 - 1 1 / 4 divided by 1 / 2 - 1 / 3 ?
Options: a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 6 , d ) 17 / 2 , e ) 51 / 4
Rationale: "2 2 / 3 - 1 1 / 4 = 8 / 3 - 5 / 4 = ( 32 - 15 ) / 12 = 17 / 12 1 / 3 - 1 / 6 = ( 2 - 1 ) / 6 = 1 / 6 so 17 / 12 / 1 / 6 = 17 / 12 * 6 = 17 / 2 answer - d"
Answer: d
Problem: 100 people are attending a newspaper conference . 35 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?
Options: a ) 21 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 35 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 35 + { editors } - x + 2 x - - > x = 65 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 65 - 39 = 26 . answer : b ."
Answer: b
Problem: there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 78 . how tall is the fourth person ?
Options: a ) 82 , b ) 84 , c ) 86 , d ) 88 , e ) 90
Rationale: "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 78 ) = 312 x = 74 and the fourth person has a height of 74 + 10 = 84 inches the answer is b ."
Answer: b
Problem: if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability w that this product will be a multiple of 45 ?
Options: a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14
Rationale: "there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability w = 1 / 24 . answer c ."
Answer: c
Problem: during a pizza buffet where a eats more times 1.8 than b , and b eats 8 times less than c . find the leat number of times all the 3 has to eat
Options: a ) 350 , b ) 260 , c ) 360 , d ) 380 , e ) 285
Rationale: a eats more than b if b eats 1 times than the ratio of a and b is a : b is 1.8 : 1 or 9 : 5 and as b eat 8 times less the c the the ratio of b : c is 5 : 40 the the least number of times all three has eat is the lcm of a , b , c that is 360 . . answer : c
Answer: c
Problem: ashok secured average of 72 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 ) 62 , b ) 74 , c ) 78 , d ) 80 , e ) none of these
Rationale: explanation : number of subjects = 6 average of marks in 6 subjects = 72 therefore total marks in 6 subjects = 72 * 6 = 432 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 432 – 370 = 62 answer a
Answer: a
Problem: at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 85 . if the restaurant serves 120 customers today , raising the average to 90 customers per day , what is the value of x ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 15 , e ) 30
Rationale: "withoutusing the formula , we can see that today the restaurant served 30 customers above the average . the total amount above the average must equal total amount below the average . this additional 30 customers must offset the “ deficit ” below the average of 90 created on the x days the restaurant served only 85 customers per day . 30 / 5 = 6 days . choice ( a ) . withthe formula , we can set up the following : 90 = ( 85 x + 120 ) / ( x + 1 ) 90 x + 90 = 85 x + 120 5 x = 30 x = 6 answer choice ( c )"
Answer: c
Problem: two boys starts from the same place walking at the rate of 5.5 kmph and 7.5 kmph respectively in the same direction . what time will they take to be 20 km apart ?
Options: a ) 10 , b ) 11 , c ) 14 , d ) 15 , e ) 20
Rationale: "explanation : relative speed = 7.5 - 5.5 = 2 kmph ( because they walk in the same direction ) distance = 20 km time = distance / speed = 20 / 2 = 10 hr answer : a"
Answer: a