Cheukting/mathqa huggingface dataset:
Question (general): the average salary of all the workers in a workshop is rs . 9000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
Options: a ) a ) 23 , b ) b ) 21 , c ) c ) 52 , d ) d ) 56 , e ) e ) 14
Rationale: "let the total number of workers be x . then , 9000 x = ( 12000 * 7 ) + 6000 ( x - 7 ) = > 3000 x = 42000 = x = 14 . answer : e"
Answer: e
Question (general): find the sum of first 30 natural numbers
Options: a ) 470 , b ) 468 , c ) 465 , d ) 463 , e ) 485
Rationale: "explanation : sum of n natural numbers = n ( n + 1 ) 2 = 30 ( 30 + 1 ) 2 = 30 ( 31 ) 2 = 465 answer : option c"
Answer: c
Question (other): a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 3 : 1 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 4 : 3 , respectively . how many more acres of land were planted with tobacco under the new system ?
Options: a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450
Rationale: "we have ratio in 5 : 3 : 1 and this is shifted to 2 : 4 : 3 ( c : s : t ) if we observe the ratio of the tobacco increased by 2 times ( 3 - 1 ) t = 1 / 9 * 1350 = 150 . since tobacco increased by 2 times . . we get 150 * 2 = 300 . answer d is the answer . ."
Answer: d
Question (gain): the charge for a single room at hotel p is 70 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 100 % , b ) 120 % , c ) 150 % , d ) 200 % , e ) 300 %
Rationale: "p = 0.3 r = 0.9 g r = 0.9 g / 0.3 = 3 g thus r is 200 % greater than g . the answer is d ."
Answer: d
Question (general): average of 10 matches is 34 , how many runs one should should score to increase his average by 4 runs .
Options: a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 80 , e ) e ) 88
Rationale: explanation : average after 11 innings should be 38 so , required score = ( 11 * 38 ) - ( 10 * 34 ) = 418 - 340 = 78 answer : option c
Answer: c
Question (general): what least number should be added to 1021 , so that the sum is completely divisible by 25 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 0 , e ) 5
Rationale: "1021 ã · 25 = 40 with remainder = 21 21 + 4 = 25 . hence 4 should be added to 1021 so that the sum will be divisible by 25 answer : option a"
Answer: a
Question (gain): in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 40 0 vers to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 6.5 , c ) 6.75 , d ) 7 , e ) none
Rationale: "sol . required run rate = 282 – ( 3.2 × 10 / 40 ) = 240 / 40 = 6.25 . answer a"
Answer: a
Question (general): how many positive integers less than 50 are multiples of 6 but not multiples of 8 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "the lcm of 6 and 8 is 24 . if x < 50 and x is divisible by 6 not by 8 - - > x is not divisible by 24 . from 1 - - > 50 , we have 2 numbers which is divisible by 24 : 24 , 48 . from 1 - - > 50 , we have ( 48 - 6 ) / 6 + 1 = 8 numbers divisible by 6 . therefore , our answer is 8 - 2 = 6 numbers . b"
Answer: b
Question (gain): a reduction of 10 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) s . 42 , b ) s . 46 , c ) s . 40 , d ) s . 41 , e ) s . 16
Rationale: "800 * ( 10 / 100 ) = 80 - - - - 5 ? - - - - 1 = > rs . 16 answer : e"
Answer: e
Question (other): the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 17000 , then find the annual income of a ?
Options: a ) rs . 571200 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these
Rationale: "b ' s monthly income = 17000 * 112 / 100 = rs . 19040 b ' s monthly income = 2 parts - - - - > rs . 19040 a ' s monthly income = 5 parts = 5 / 2 * 19040 = rs . 47600 a ' s annual income = rs . 47600 * 12 = rs . 571200 answer : a"
Answer: a
Question (physics): two pipes can fill a tank in 18 minutes and 30 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 1 / 15 , b ) 1 / 16 , c ) 1 / 11 , d ) 1 / 10 , e ) 1 / 12
Rationale: part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 30 - 1 / 45 = 1 / 15 so , the tank becomes full in 15 minutes . answer : a
Answer: a
Question (general): 17 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 154 , b ) 184 , c ) 240 , d ) 272 , e ) 306
Rationale: "2 * 17 c 2 = 2 * 136 = 272 the answer is d ."
Answer: d
Question (general): if a farmer sells 5 of his chickens , his stock of feed will last for 4 more days than planned , but if he buys 20 more chickens , he will run out of feed 1 day earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
Options: a ) 15 , b ) 20 , c ) 20 / 3 , d ) 25 , e ) 10
Rationale: "let x = total feed required for the planned period n = number of chicken t = total time of the planned feed x = nt 1 ) x = ( n - 5 ) * ( t + 4 ) 2 ) x = ( n + 20 ) * ( t - 1 ) equating 1 & 2 ( n - 5 ) * ( t + 4 ) = ( n + 20 ) * ( t - 1 ) 5 n = 25 t n = 5 t x = n * n / 5 substituting this value in 1 n * n / 5 = ( n - 5 ) * ( n / 5 + 4 ) 15 n = 100 n = 20 / 3 c"
Answer: c
Question (general): what will be the reminder when ( 13 ^ 13 + 13 ) is divided by 14 ?
Options: a ) 16 , b ) 14 , c ) 12 , d ) 18 , e ) 21
Rationale: ( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 13 ^ 13 + 1 ) will be divisible by ( 13 + 1 ) ; ( 13 ^ 13 + 1 ) + 12 when divided by 14 will give 12 as remainder . correct option : c
Answer: c
Question (other): two whole numbers whose sum is 40 can not be in the ratio
Options: a ) 4 : 10 , b ) 2 : 3 , c ) 1 : 3 , d ) 2 : 4 , e ) 3 : 5
Rationale: d ) 2 : 4
Answer: d
Question (general): the remainder when positive integer nn ( n > 1 n > 1 ) is divided by 25 is 1 and the remainder when nn is divided by 7 is also 1 . what is the least value of nn ?
Options: a ) 76 , b ) 101 , c ) 126 , d ) 151 , e ) 176
Rationale: we ' re asked to find the least number that gives us a remainder of 1 when divided by 25 and gives us a remainder of 1 when divided by 7 . you might notice , rather quickly , that all of the answers gives us a remainder when divided by 25 . . . 76 = 75 + 1 101 = 100 + 1 126 = 125 + 1 151 = 150 + 1 176 = 175 + 1 so the real question is ` ` which of these 5 is the least number that has a remainder of 1 when divided by 7 ? ' ' from here , you can just do the ` ` brute force ' ' math : a : 76 / 7 = 10 r 6 not a match b : 101 / 7 = 14 r 3 not a match c : 126 / 7 = 18 r 0 not a match d : 151 / 7 = 21 r 4 not a match none of these numbers ` ` fits ' ' the description , so the answer must be e . e : 176 / 7 = 25 r 1 ; answer : e
Answer: e
Question (general): a tank is filled in sixteen hours by 3 pipes a , b and c . pipe a is twice as fast as pipe b , and b is twice as fast as c . how much time will pipe b alone take to fill the tank ?
Options: a ) 56 hours , b ) 28 hours , c ) 55 hours , d ) 66 hours , e ) 47 hours
Rationale: 1 / a + 1 / b + 1 / c = 1 / 16 ( given ) also given that a = 2 b and b = 2 c = > 1 / 2 b + 1 / b + 2 / b = 1 / 16 = > ( 1 + 2 + 4 ) / 2 b = 1 / 16 = > 2 b / 7 = 16 = > b = 56 hours . answer : a
Answer: a
Question (physics): two numbers n and 16 have lcm = 48 and gcf = 18 . find n .
Options: a ) 24 , b ) 34 , c ) 44 , d ) 54 , e ) 64
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 16 × n = 48 × 18 n = 48 × 18 / 16 = 54 correct answer d"
Answer: d
Question (general): when n is divided by 20 , the remainder is 5 . what is the remainder when n + 16 is divided by 5 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "assume n = 15 remainder ( n / 20 ) = 5 n + 16 = 31 remainder ( 31 / 5 ) = 1 option a"
Answer: a
Question (general): if a = { 10 , 15 , 18 , 22 , 36 , 44 } , what is the product of mean and median of the numbers in a ?
Options: a ) 105 , b ) 245 , c ) 360 , d ) 480 , e ) 542
Rationale: "mean = ( 10 + 15 + 18 + 22 + 36 + 43 ) / 6 = 24 median = ( 18 + 22 ) / 2 = 20 product = 24 * 20 = 480 option d"
Answer: d
Question (general): of the 3,600 employees of company x , 1 / 6 are clerical . if the clerical staff were to be reduced by 1 / 3 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 25 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.7 %
Rationale: "welcome , just post the question and the choices let ' s see , the way i did it was 1 / 6 are clerical out of 3600 so 600 are clerical 600 reduced by 1 / 3 is 600 * 1 / 3 so it reduced 200 people , so there is 400 clerical people left but since 200 people left , it also reduced from the total of 3600 so there are 3400 people total since 400 clerical left / 3400 people total you get ( a ) 11.7 % answer : e"
Answer: e
Question (physics): two trains leave a station traveling in the same direction . train a leaves traveling at a constant speed of 50 mph , while train b leaves traveling at a constant speed of 80 mph . if train b left the station 30 minutes after train a left , in how many minutes will train b overtake train a ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: we can use a form of the equation d = rt [ distance = rate * time ] train a will have traveled for 30 minutes longer when train b overtakes it so time of train a : t + 30 minutes = t + 1 / 2 hours ( switch to hours since the rates are in hours ) time of train b : t rate of train a : 50 mph rate of train b : 80 mph the distance traveled by each will be the same when b overtakes a so set the right side of d = rt equal to each other for the two trains 50 * ( t + 1 / 2 ) = 80 * t 50 t + 25 = 80 t 25 = 30 t 25 / 30 = t 5 / 6 hours = t which is 5 / 6 * 60 = 50 minutes c
Answer: c
Question (general): if 4 : 6 : : x : 36 , then find the value of x
Options: a ) 24 , b ) 22 , c ) 28 , d ) 30 , e ) 18
Rationale: explanation : treat 4 : 6 as 4 / 6 and x : 36 as x / 36 , treat : : as = so we get 4 / 6 = x / 36 = > 6 x = 144 = > x = 24 option a
Answer: a
Question (general): what is the value of 4 ^ 6 + 4 ^ 8 ?
Options: a ) 4 ^ 12 , b ) 4 ^ 35 , c ) 17 ( 4 ^ 6 ) , d ) 8 ^ 12 , e ) 7 ( 4 ^ 5 )
Rationale: "4 ^ 6 + 4 ^ 8 = 4 ^ 6 ( 1 + 4 ^ 2 ) = 4 ^ 6 * 17 answer c"
Answer: c
Question (general): let the least number of 6 digits , which when divided by 4 , 610 and 15 leaves in each case the same remainder of 2 , be n . the sum of the digits in n is :
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: solution least number of 6 digital is 100000 . l . c . m . of 4 , 610 and 15 = 60 . on dividing 100000 by 60 , the remainder obtained is 40 . so , least number of 6 digits divisible by 4 , 610 and 15 = 100000 + ( 60 - 40 ) = 100020 . so , n = ( 100020 + 2 ) = 100022 . sum of digits in n = ( 1 + 2 + 2 ) = 5 . answer c
Answer: c
Question (general): if a = 105 and a ^ 3 = 21 * 25 * 35 * b , what is the value of b ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 63
Rationale: "first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 25 = 5 * 5 35 = 7 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 5 * 5 * 7 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 * 5 ^ 3 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 * 5 ^ 3 * 7 ^ 2 b = 3 ^ 2 * 7 = 9 * 7 = 63 correct answer e ."
Answer: e
Question (physics): what is the maximum number of pieces of birthday cake of size 2 ” by 2 ” that can be cut from a cake 20 ” by 20 ” ?
Options: a ) 5 , b ) 100 , c ) 16 , d ) 20 , e ) 25
Rationale: the prompt is essentially asking for the maximum number of 2 x 2 squares that can be cut from a larger 20 by 20 square . since each ' row ' and each ' column ' of the larger square can be sub - divided into 10 ' pieces ' each , we have ( 10 ) ( 10 ) = 100 total smaller squares ( at maximum ) . b
Answer: b
Question (general): how many positive integers less than 50 are multiples of 2 but not multiples of 5 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 20
Rationale: "imo the answer is c ( 8 numbers ) the lcm of 2 and 5 is 10 . if x < 50 and x is divisible by 2 not by 5 - - > x is not divisible by 10 . from 1 - - > 50 , we have 5 numbers which is divisible by 10 : 10 , 20 , 30 , 40 , 50 . from 1 - - > 50 , we have ( 50 - 2 ) / 2 + 1 = 25 numbers divisible by 2 . therefore , our answer is 25 - 5 = 20 numbers . e"
Answer: e
Question (general): if | 4 x + 14 | = 46 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 7 , c ) 4 , d ) - 5 , e ) 6
Rationale: "there will be two cases 4 x + 14 = 46 or 4 x + 14 = - 46 = > x = 8 or x = - 15 sum of both the values will be - 15 + 8 = - 7 answer is b"
Answer: b
Question (general): what is the least number . which should be added to 0.0282 to make it a perfect square ?
Options: a ) 0.0007 , b ) 0.0042 , c ) 0.0002 , d ) 0.0003 , e ) 0.0004
Rationale: "0.0282 + 0.0007 = 0.0289 ( 0.17 ) ^ 2 answer : a"
Answer: a
Question (other): at the faculty of aerospace engineering , 302 students study random - processing methods , 232 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?
Options: a ) 444 , b ) 432 , c ) 346 , d ) 422 , e ) 448
Rationale: "302 + 232 - 112 ( since 112 is counted twice ) = 422 d is the answer"
Answer: d
Question (other): in a group of 100 people , 55 have visited iceland and 43 have visited norway . if 61 people have visited both iceland and norway , how many people have visited neither country ?
Options: a ) 60 , b ) 61 , c ) 62 , d ) 63 , e ) 64
Rationale: "this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 100 = 55 + 43 - 61 + ( # in neither group ) = 63 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d"
Answer: d
Question (general): a car was driving at 60 km / h for 20 minutes , and then at 90 km / h for another 40 minutes . what was its average speed ?
Options: a ) 80 . , b ) 75 , c ) 70 , d ) 65 . , e ) 54 .
Rationale: "driving at 60 km / h for 20 minutes , distance covered = 60 * 1 / 3 = 20 km driving at 90 km / h for 40 minutes , distance covered = 90 * 2 / 3 = 60 km average speed = total distance / total time = 80 / 1 = 80 km / h answer : a"
Answer: a
Question (general): if ( a + b ) = 5 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 1 .
Rationale: given a + b = 5 b + c = 9 c + d = 3 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 5 - 9 + 3 = - 1 . option e . . .
Answer: e
Question (gain): in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 13 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 104 %
Rationale: x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,13 = 13 / 100 x = 80 * 13 / 100 x = 10.4 10.4 / 10 = 1,04 = 104 % , answer e
Answer: e
Question (general): 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration c of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: "do not need any computation 30 % - - - - - - - - - - - 21 % - - - - - - - - - 12 % if volume of both sol . were equal the concentration c would be 21 % = 1 / 5 , but 12 % is more than 3 times only possibility is 1 / 6 d"
Answer: d
Question (gain): a , b and c invests rs . 2000 , rs . 3000 and rs . 4000 in a business . after one year a removed his money ; b and c continued the business for one more year . if the net profit after 2 years be rs . 3200 , then a ' s share in the profit is ?
Options: a ) 299 , b ) 267 , c ) 269 , d ) 400 , e ) 276
Rationale: "2 * 12 : 3 * 12 : 4 * 24 1 : 3 : 4 1 / 8 * 3200 = 400 answer : d"
Answer: d
Question (physics): a train is moving at a speed of 100 km / hour . the length of the train is 100 metre . in how much time will it cross a pole ?
Options: a ) 1 second , b ) 2.5 second , c ) 4 second , d ) 3.6 second , e ) 4.5 second
Rationale: in order to cross the pole , the train will need to cover its own length of 100 meter . to cover 100 x 1000 meter , train takes 60 minutes or 60 x 60 = 3600 second . so , to cover 100 meter , train would take 3600 x 100 / 100 x 1000 = 3.6 second . answer : d .
Answer: d
Question (gain): a ladder 14 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 9 feet from the base of the wall . if the top of the ladder slips down 1 feet , how many feet will the bottom of the ladder slip ?
Options: a ) 4 , b ) 10 , c ) 18 , d ) 19 , e ) 25
Rationale: "14 ^ 2 - 9 ^ 2 = 115 it means that the height is equal to 10.72 . since the top of the ladder slips down 1 feet , then the height of the wall = 10.72 - 1 = 9.72 the bottom = sqrt ( 14 ^ 2 - 9.72 ^ 2 ) = sqrt ( 196 - 94.47 ) = 10.07 ~ = 10 ans is b"
Answer: b
Question (gain): a trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 30 per metre of cloth . how much profit will the trder earn on 40 metres of cloth ?
Options: a ) rs . 950 , b ) rs . 1500 , c ) rs . 1000 , d ) rs . 1200 , e ) none of these
Rationale: "explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 30 = rs . 175 cp on 40 metres = 175 x 40 = rs . 7000 profit earned on 40 metres cloth = rs . 8200 – rs . 7000 = rs . 1200 . answer : option d"
Answer: d
Question (physics): a train 330 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 18 , e ) 9
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 330 * 3 / 55 = 18 sec . answer : option d"
Answer: d
Question (physics): a completes 80 % of a work in 20 days . then b also joins and a and b together finish the remaining work in 3 days . how long does it need for b if he alone completes the work ?
Options: a ) 37 1 / 2 days , b ) 22 days , c ) 31 days , d ) 22 days , e ) 25 1 / 2 days
Rationale: work done by a in 20 days = 80 / 100 = 8 / 10 = 4 / 5 work done by a in 1 day = ( 4 / 5 ) / 20 = 4 / 100 = 1 / 25 - - - ( 1 ) work done by a and b in 3 days = 20 / 100 = 1 / 5 ( because remaining 20 % is done in 3 days by a and b ) work done by a and b in 1 day = 1 / 15 - - - ( 2 ) work done by b in 1 day = 1 / 15 – 1 / 25 = 2 / 75 = > b can complete the work in 75 / 2 days = 37 ½ days option a
Answer: a
Question (general): if - 3 / ( a - 3 ) = 3 / ( a + 2 ) , then a = ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: multiply all terms of the given equation by ( a - 3 ) ( a + 2 ) , simplify and solve ( a - 3 ) ( a + 2 ) [ - 3 / ( a - 3 ) ] = ( a - 3 ) ( a + 2 ) [ 3 / ( a + 2 ) ] - 3 ( a + 2 ) = 3 ( a - 3 ) a = 1 / 2 correct answer a
Answer: a
Question (gain): company p had 15 percent more employees in december than it had in january . if company p had 460 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 400 , c ) 410 , d ) 423 , e ) 445
Rationale: given : january * 1.15 = december - - > january * 1.15 = 460 - - > january = 460 / 1.15 = 400 . answer : b .
Answer: b
Question (general): if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 1 / 3 : 3 / 4 , then the second part is ?
Options: a ) a ) 426 , b ) b ) 526 , c ) c ) 207 , d ) d ) 165 , e ) e ) 297
Rationale: given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 4 : 9 1 st part = 782 * 4 / 19 = rs . 165 answer : d
Answer: d
Question (general): a number is doubled and 5 is added . if the resultant is trebled , it becomes 117 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 27 , d ) 17 , e ) 99
Rationale: "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 117 6 x + 15 = 117 6 x = 102 x = 17 answer : d"
Answer: d
Question (general): find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 years .
Options: a ) 306.05 , b ) 306.00 , c ) 306.04 , d ) 306.05 , e ) 306.01
Rationale: "a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : a"
Answer: a
Question (physics): what is the greatest of 3 consecutive integers whose sum is 24 ?
Options: a ) 3 , b ) 76 , c ) 8 , d ) 9 , e ) 10
Rationale: explanation : the sum of three consecutive integers can be written as n + ( n + 1 ) + ( n + 2 ) = 3 n + 3 if the sum is 24 , we need to solve the equation 3 n + 3 = 24 ; = > 3 n = 21 ; = > n = 7 the greatest of the three numbers is therefore 7 + 2 = 9 answer : d ) 9
Answer: d
Question (gain): i sold a book at a profit of 10 % . had i sold it for $ 120 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 2000 , b ) $ 2500 , c ) $ 2400 , d ) $ 3120 , e ) $ 1540
Rationale: "115 % of cost - 110 % of cost = $ 120 5 % of cost = $ 120 cost = 120 * 100 / 5 = $ 2400 answer is c"
Answer: c
Question (general): how much is 25 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 10 , b ) 776 , c ) 66 , d ) 12 , e ) 99
Rationale: "( 25 / 100 ) * 40 – ( 4 / 5 ) * 25 10 - 20 = 10 answer : a"
Answer: a
Question (general): in a division , divident is 760 , divisior is 36 and quotient is 21 . find the remainder .
Options: a ) a ) 4 , b ) b ) 3 , c ) c ) 2 , d ) d ) 5 , e ) e ) 6
Rationale: "explanation : 760 = 36 x 21 + r 760 = 756 + r r = 760 - 756 = 4 answer : option a"
Answer: a
Question (physics): a certain car uses 12 gallons of gasoline in traveling 360 miles . in order for the car to travel the same distance using 10 gallons of gasoline , by how many miles per gallon must the car ’ s gas mileage be increased ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "360 / 10 = 36 . the difference is 36 - 30 = 6 . answer c"
Answer: c
Question (gain): in an election between two candidates - lange and sobel - 70 % of the voters voted for sobel . of the election ` s voters , 60 % were male . if 35 % of the female voters voted for lange , what percentage of the male voters voted for sobel ?
Options: a ) 14 , b ) 16 , c ) 26 , d ) 44 , e ) 65
Rationale: m f total l 16 14 30 s 44 70 tot 60 40 100 35 % of 40 = 14 - - - - - - female voters that means 16 male voted for l so 60 - 16 = 44 d is correct
Answer: d
Question (general): a 100 - litre mixture of milk and water contains 49 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 25 % . what is the value of x ?
Options: a ) 27.5 litres , b ) 26.67 litres , c ) 27.67 litres , d ) 28.57 litres , e ) 26 litres
Rationale: "working formula . . . initial concentration * initial volume = final concentration * final volume . let x is the part removed from 100 lts . 49 % ( 1 - x / 100 ) ^ 2 = 25 % * 100 % ( 1 - x / 100 ) ^ 2 = 25 / 49 - - - - - - > ( 1 - x / 100 ) ^ 2 = ( 5 / 7 ) ^ 2 100 - x = 500 / 7 x = 28.57 . . . ans d"
Answer: d
Question (general): the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 46 . what is a possible value for the mean of the distribution ?
Options: a ) 46 , b ) 52 , c ) 48 , d ) 49 , e ) 50
Rationale: "the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 46 : { mean } - 3 * { sd } > 46 ; { mean } - 6 > 46 ; { mean } > 52 . answer : b ."
Answer: b