Cheukting/mathqa huggingface dataset:
Question (general): if 2 ^ ( 2 w ) = 8 ^ ( w − 6 ) , what is the value of w ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: "2 ^ ( 2 w ) = 8 ^ ( w − 6 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w − 6 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 18 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 18 w = 18 the answer is c ."
Answer: c
Question (physics): tom traveled the entire 20 miles trip . if he did the first 10 miles of at a constant rate 12 miles per hour and the remaining trip of at a constant rate 10 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 12.45 mph , b ) 11.25 mph , c ) 10.95 mph , d ) 10.91 mph , e ) 10.56 mph
Rationale: avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 10 + 10 ) / ( ( 10 / 12 ) + ( 10 / 10 ) = 120 / 11 = 10.91 mph d
Answer: d
Question (general): a , b are positive integers . the remainder of a to be divided by 8 is 3 and the remainder of b to be divided by 6 is 5 . which is possible to be the remainder of a * b to be divided by 48
Options: a ) a ) 2 , b ) b ) 6 , c ) c ) 8 , d ) d ) 15 , e ) e ) 20
Rationale: two ways to do it . . . a = 8 x + 3 . . b = 6 y + 5 . . 1 ) convenient way . . take x and y as 0 , and you will get a * b as 3 * 5 = 15 answer : d
Answer: d
Question (physics): one pipe can fill a pool 1.25 times faster than a second pipe . when both pipes are opened , they fill the pool in five hours . how long would it take to fill the pool if only the faster pipe is used ?
Options: a ) 11.25 , b ) 11.52 , c ) 1.25 , d ) 7.2 , e ) 9
Rationale: say the rate of the slower pipe is r pool / hour , then the rate of the faster pipe would be 1.25 r = 5 r / 4 . since when both pipes are opened , they fill the pool in five hours , then their combined rate is 1 / 5 pool / hour . thus we have that r + 5 r / 4 = 1 / 5 - - > r = 4 / 45 pool / hour , faster pipe fills at 1.25 r which is 5 / 4 * 4 / 45 = 1 / 9 - - > time is reciprocal of rate thus it ' s 9 / 1 = 9 hours . answer : e .
Answer: e
Question (general): the revenue from sales items in 1996 increases by x percent , compared in 1995 and the revenue in 1997 decreases by x percent , compared in 1996 . if the revenue from sales items in 1997 decreases by 4 percent , compared in 1995 , what is the value of x ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 30 , e ) 35
Rationale: 1995 - let the value be z 1996 - x % increase - z ( 1 + x / 100 ) 1997 - x % decrease - z ( 1 + x / 100 ) ( 1 - x / 100 ) from 95 to 97 decrease is 4 % hence , [ z - { z ( 1 + x / 100 ) ( 1 - x / 100 ) } ] / z = 4 / 100 solving x = 20 % c is the answer
Answer: c
Question (general): peter has $ 642986 in his savings account . what is the least amount of money ( in whole number of dollars ) that he must add to his account if he wants to split this money evenly among his 9 children ?
Options: a ) $ 642986 , b ) $ 642987 , c ) $ 642988 , d ) $ 642989 , e ) $ 642990
Rationale: to find the least amount the man should add to his saving account to split the money evenly among his 9 children , he needs to make the total divisible by 9 simply add the individual digits of the total = 6 + 4 + 2 + 9 + 8 + 6 = 35 if you add 1 , the number is divisible by 9 ( 35 + 1 ) correct option : b
Answer: b
Question (geometry): the measurement of a rectangular box with lid is 25 cmx 4 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 11.12 , b ) 10.11 , c ) 72 , d ) 10.66 , e ) 9.2
Rationale: "d = 4 , r = 2 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 2 * 2 * 2 = 10.66 π cm 3 answer : d"
Answer: d
Question (physics): a car travels at a speed of 60 miles per hour . how far will it travel in 5 hours ?
Options: a ) 425 miles , b ) 625 miles , c ) 300 miles , d ) 225 miles , e ) 625 miles
Rationale: "during each hour , the car travels 65 miles . for 5 hours it will travel 60 + 60 + 60 + 60 + 60 = 5 * 65 = 300 miles correct answer c"
Answer: c
Question (physics): find the distance covered by a man walking for 72 min at a speed of 10 km / hr ?
Options: a ) 12 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "distance = 10 * 72 / 60 = 12 km answer is a"
Answer: a
Question (other): the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is
Options: a ) 276 , b ) 299 , c ) 312 , d ) 322 , e ) none
Rationale: "solution clearly , the numbers are ( 23 x 13 ) and ( 23 x 14 ) . larger number = ( 23 x 14 ) = 322 . answer d"
Answer: d
Question (gain): what percent is 2 gm of 1 kg ?
Options: a ) 0.5 % , b ) 0.2 % , c ) 1.5 % , d ) 2 % , e ) 3 %
Rationale: "1 kg = 1000 gm 2 / 1000 × 100 = 200 / 1000 = 1 / 5 = 0.2 % b )"
Answer: b
Question (general): a car travels first 160 km at 75 km / hr and the next 160 km at 70 km / hr . what is the average speed for the first 320 km of the tour ?
Options: a ) 71.11 , b ) 71.12 , c ) 72.4 , d ) 71.17 , e ) 71.13
Rationale: "car travels first 160 km at 75 km / hr time taken to travel first 160 km = distancespeed = 160 / 75 car travels next 160 km at 70 km / hr time taken to travel next 160 km = distancespeed = 160 / 70 total distance traveled = 160 + 160 = 2 × 160 total time taken = 160 / 75 + 160 / 70 average speed = total distance traveled / total time taken = 320 / ( 160 / 75 + 160 / 70 ) = 72.4 km / hr answer : c"
Answer: c
Question (physics): a train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . what is the length of the train ?
Options: a ) 62 m , b ) 54 m , c ) 50 m , d ) 55 m , e ) 56 m
Rationale: explanation : let x is the length of the train in meter and v is its speed in kmph x / 9 = ( v - 2 ) ( 10 / 36 ) - - - ( 1 ) x / 10 = ( v - 4 ) ( 10 / 36 ) - - - ( 2 ) dividing equation 1 with equation 2 10 / 9 = ( v - 2 ) / ( v - 4 ) = > 10 v - 40 = 9 v - 18 = > v = 22 substituting in equation 1 , x / 9 = 200 / 36 = > x = 9 × 200 / 36 = 50 m answer : option c
Answer: c
Question (gain): what is 15 percent of 68 ?
Options: a ) 7.6 , b ) 8.7 , c ) 9.1 , d ) 10.2 , e ) 11.6
Rationale: "( 15 / 100 ) * 68 = 10.2 the answer is d ."
Answer: d
Question (general): if a - b = 2 and a 2 + b 2 = 25 , find the value of ab .
Options: a ) a ) 10.5 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20
Rationale: "explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 25 - 4 = 21 ab = 10.5 answer : a"
Answer: a
Question (geometry): the area of a parallelogram is 98 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "2 x * x = 98 = > x = 7 answer : c"
Answer: c
Question (physics): tom and linda stand at point a . linda begins to walk in a straight line away from tom at a constant rate of 2 miles per hour . one hour later , tom begins to jog in a straight line in the exact opposite direction at a constant rate of 8 miles per hour . if both tom and linda travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes tom to cover half of the distance that linda has covered and the amount of time it takes tom to cover twice the distance that linda has covered ?
Options: a ) 40 , b ) 72 , c ) 84 , d ) 90 , e ) 108
Rationale: "a is the answer . . . . d = ts where d = distance , t = time and s = speed to travel half distance , ( 2 + 2 t ) = 8 t = = > t = 1 / 3 = = > 20 minutes to travel double distance , 2 ( 2 + 2 t ) = 8 t = = > 1 = = > 60 minutes difference , 40 minutes a"
Answer: a
Question (gain): 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 . 840 find the share of a .
Options: a ) 240 , b ) 388 , c ) 379 , d ) 277 , e ) 320
Rationale: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 840 = 320 answer : e"
Answer: e
Question (general): set # 1 = { a , b , o , d , e } set # 2 = { k , l , m , n , u , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?
Options: a ) 1 / 6 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 / 3 , e ) 2 / 3
Rationale: at least questions are best solved by taking the opposite scenario and subtracting it from 1 . probability of choosing no vowel from set 1 is 2 / 5 and set 2 is 5 / 6 . multiply these to get 1 / 3 . therefore , probability of picking at least one vowel = 1 - 1 / 3 = 2 / 3 . answer = e
Answer: e
Question (general): the value of x + ( xx ) when x = 3 is :
Options: a ) a ) 36 , b ) b ) 12 , c ) c ) 18 , d ) d ) 64 , e ) e ) 10
Rationale: x + ( xx ) put the value of x = 2 in the above expression we get , 3 + ( 33 ) = 3 + ( 3 × 3 ) = 3 + ( 9 ) = 3 + 9 = 12 b
Answer: b
Question (general): roy is now 6 years older than julia and half of that amount older than kelly . if in 2 years , roy will be twice as old as julia , then in 2 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 84 , b ) 96 , c ) 100 , d ) 108 , e ) 120
Rationale: "r = j + 6 = k + 3 r + 2 = 2 ( j + 2 ) ( j + 6 ) + 2 = 2 j + 4 j = 4 r = 10 k = 7 in 2 years ( r + 2 ) ( k + 2 ) = 12 * 9 = 108 the answer is d ."
Answer: d
Question (general): if x is equal to the sum of the integers from 30 to 40 , inclusive , and y is the number of even integers from 30 to 40 , inclusive , what is the value of x + y ?
Options: a ) 171 , b ) 281 , c ) 391 , d ) 591 , e ) 601
Rationale: "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 30 + ( 11 - 1 ) * 1 } = 11 * 35 = 385 = x number of even number = ( 40 - 30 ) / 2 + 1 = 6 = y x + y = 385 + 6 = 391 c"
Answer: c
Question (general): a small company is planning to rent either computer a or computer b to print customer mailing lists . both computer a and computer b must be rented on an hourly basis . the rental fee is based only on the amount of time the computer is turned on . it will cost 40 percent more per hour to rent computer a than to rent computer b . computer b would , however , require 20 hours more than computer a to do the job . if either computer a , or computer b were rented the total cost to rent the computer would be $ 850.00 . what would be the approximate hourly charge to rent computer b ?
Options: a ) $ 9.40 , b ) $ 11.30 , c ) $ 12.14 , d ) $ 17.80 , e ) $ 22.10
Rationale: "pa = price of a pb = price of b ta = time for a to complete the job tb = time for b to complete the job given pa = 1.4 pb ta + 20 = tb pa * ta = pb * tb = 850 1.4 pb * ( tb - 20 ) = pb * tb 1.4 pb tb - pb tb = 1.4 pb * 20 0.4 pbtb = 28 pb tb = 28 / 0.4 = 70 pb = 850 / 70 ~ 12.14 c"
Answer: c
Question (geometry): a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 100 feet . what is its area , in square feet ?
Options: a ) 4,800 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800
Rationale: "you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 100 , you can deduce the following a = 60 b = 80 60 x 80 = 4,800 a is the answer ."
Answer: a
Question (other): 19 balls are numbered 1 to 19 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?
Options: a ) 2 / 9 , b ) 4 / 19 , c ) 6 / 29 , d ) 8 / 39 , e ) 10 / 49
Rationale: "p ( 1 st ball is even ) = 9 / 19 p ( 2 nd ball is also even ) = 8 / 18 p ( both balls are even ) = 9 / 19 * 8 / 18 = 4 / 19 the answer is b ."
Answer: b
Question (gain): in the first 12 overs of a cricket game , the run rate was only 4.5 . what should be the run rate in the remaining 38 overs to reach the target of 360 runs ?
Options: a ) 9.55 , b ) 6.25 , c ) 6.75 , d ) 8.05 , e ) 7.25
Rationale: required run rate = 360 - ( 4.5 x 12 ) / 38 = 306 / 38 = 8.05 option d
Answer: d
Question (physics): a car during its journey travels 1 hour at a speed of 40 kmph , another 30 minutes at a speed of 60 kmph , and 2 hours at a speed of 60 kmph . the average speed of the car is
Options: a ) 63.07 kmph , b ) 54.28 kmph , c ) 62.02 kmph , d ) 64.02 kmph , e ) none of these
Rationale: first car travels 1 hrs at speed of 40 kmph distance = 40 x 1 = 40 m then car travels 30 min at a speed of 60 kmph distance = 30 min at speed of 60 kmph distance = 60 x 1 / 2 = 30 m at last it travels 2 hours at speed of 60 kmph distance = 60 x 2 = 120 m total distance = 40 + 30 + 120 = 190 total time = 1 + 1 / 2 + 2 = 3.50 average speed of the car = 190 / 3.25 = 54.28 answer : b
Answer: b
Question (physics): two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 26 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 3 , b ) 9 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 3 : 4
Rationale: "let the speed of the trains be x and y respectively length of train 1 = 27 x length of train 2 = 17 y relative speed = x + y time taken to cross each other = 26 s = ( 27 x + 17 y ) / ( x + y ) = 26 = ( 27 x + 17 y ) / = 26 ( x + y ) = x = 9 y = x / y = 9 / 1 answer : b"
Answer: b
Question (general): 5358 x 56 = ?
Options: a ) 272258 , b ) 272358 , c ) 300048 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 6 ) = 5358 x 50 + 5358 x 6 = 267900 + 32148 = 300048 . c )"
Answer: c
Question (physics): excluding stoppages , the speed of a bus is 80 kmph and including stoppages , it is 60 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 12 min , b ) 20 min , c ) 25 min , d ) 30 min , e ) 15 min
Rationale: "due to stoppages , it covers 20 km less . time taken to cover 20 km = ( 20 / 80 x 60 ) min = 15 min answer : e"
Answer: e
Question (general): the average age of a , b and c is 27 years . if the average age of a and c is 29 years , what is the age of b in years ?
Options: a ) 19 , b ) 35 , c ) 20 , d ) 32 , e ) 23
Rationale: age of b = age of ( a + b + c ) â € “ age of ( a + c ) = 27 ã — 3 â € “ 29 ã — 2 = 81 â € “ 58 = 23 years e
Answer: e
Question (gain): a man buys a cycle for rs . 1400 and sells it at loss of 15 % . what is the selling price of the cycle ?
Options: a ) 1192 , b ) 1191 , c ) 1118 , d ) 1190 , e ) 1112
Rationale: "explanation : s . p = 85 % of rs . 1400 ⇒ rs . ( 8510085100 × 1400 ) = rs . 1190 . answer : d"
Answer: d
Question (general): a strain of bacteria reproduces @ 25 % every 12 min . in how much time will it triple itself ? ?
Options: a ) 96 min , b ) 72 min , c ) 60 min , d ) 48 min , e ) 40 min
Rationale: the original question is : a strain of bacteria reproduces at the rate of 25 % every 12 min . in how much time will it triple itself ? 1.25 ^ x = 3 - - > x = ~ 5 - - > five 12 minute periods = 60 minutes . answer : c .
Answer: c
Question (other): a person want to give his money of $ 1000 to his 3 children a , b , c in the ratio 6 : 4 : 5 what is the a + b share ?
Options: a ) $ 660.67 , b ) $ 646.67 , c ) $ 666.67 , d ) $ 500.56 , e ) $ 600.24
Rationale: "a ' s share = 1000 * 6 / 15 = $ 400 b ' s share = 1000 * 4 / 15 = $ 266.67 a + b = $ 666.67 answer is c"
Answer: c
Question (general): in a group of cows and hens , the number of legs are 10 more than twice the number of heads . the number of cows is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 10 , e ) 12
Rationale: "let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 10 2 x = 10 x = 5 . answer : a"
Answer: a
Question (gain): a survey was sent to 60 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 14 % , d ) 28 % , e ) 4 %
Rationale: "case 1 : ( 7 / 60 ) = x / 100 x = 12 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 12 ) % = 2 % answer is a"
Answer: a
Question (physics): 12 persons can complete the work in 18 days . after working for 6 days , 4 more persons added to complete the work fast . in how many days they will complete the work ?
Options: a ) 10 , b ) 15 , c ) 17 , d ) 5 , e ) 9
Rationale: "total work = 12 * 18 = 216 units . after 6 days , work finished = 6 * 12 = 72 units . remaining units = 216 - 72 = 144 units . remaining days = 144 / ( 2 + 4 ) = 9 days the option is e"
Answer: e
Question (general): if 2 / 3 of the air in a tank is removed with each stroke of a vacuum pump , how many strokes does it take before less than 1 % of the original amount of air in the tank remains ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "my approach is to find more or less good number and plug in . lets take 90 as the total volume of an air , and the question asks after how many stokes there will be less than 0,9 air in a tank , if each stroke takes 2 / 3 of an air . so after he 1 strokethe volume will be 30 ( 90 - 60 = 30 ) , and so on 2 stroke - 30 - 20 = 10 3 stroke - 10 - 6,7 = 3,3 4 stroke - 3,3 - 2,2 = 1,1 5 stroke - 1,1 - minus something that gets us less than 0,9 for sure . so the answer is : after 5 strokes there will be less than 1 % of air left in a tank . optiond ."
Answer: d
Question (physics): mahesh can do a piece of work in 35 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ?
Options: a ) 45 , b ) 25 , c ) 37 , d ) 41 , e ) 70
Rationale: "work done by mahesh in 35 days = 20 * 1 / 35 = 4 / 7 remaining work = 1 - 4 / 7 = 3 / 7 3 / 7 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 7 / 3 = 70 days answer is e"
Answer: e
Question (general): for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.0 ?
Options: a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4 .
Rationale: "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.0 = 6 * 0 + 2 * 7.2 + 8 - 6.0 = 0 + 14.4 + 2 16.4 answer e"
Answer: e
Question (general): a parking garage rents parking spaces for $ 10 per week or $ 42 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 14 , b ) $ 16 , c ) $ 22 , d ) $ 24 , e ) $ 26
Rationale: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 42 = 504 $ 520 - 504 = 16 ans b"
Answer: b
Question (general): what is the least number which when divided by 8 , 12 , 15 and 20 leaves in each case a remainder of 5
Options: a ) 110 , b ) 125 , c ) 75 , d ) 170 , e ) 195
Rationale: "lcm of 8 , 12 , 15 and 20 = 120 required number = 120 + 5 = 125 answer : option b"
Answer: b
Question (general): if xy = 4 , x / y = 81 , for positive numbers x and y , y = ?
Options: a ) 1 / 2 , b ) 2 , c ) 2 / 9 , d ) 3 , e ) 1 / 6
Rationale: "very easy question . 2 variables and 2 easy equations . xy = 4 - - - > x = 4 / y - ( i ) x / y = 81 - - - > replacing ( i ) here - - - > 4 / ( y ^ 2 ) = 81 - - - > y ^ 2 = 4 / 81 - - - > y = 2 / 9 or - 2 / 9 the question states that x and y are positive integers . therefore , y = 2 / 9 is the answer . answer c ."
Answer: c
Question (gain): a fellow borrowed a certain sum of money at 6 % per annum at simple interest and in 6 years the interest amounted to rs . 672 less than the sum lent . what was the sum lent ?
Options: a ) 1050 , b ) 1220 , c ) 1250 , d ) 1060 , e ) 1110
Rationale: "p - 672 = ( p * 6 * 6 ) / 100 p = 1050 answer : a"
Answer: a
Question (other): the 7 th grade french and spanish classes each have 21 students in them , and there are 6 students in the 7 th grade taking both languages . if everyone in the 7 th grade is in at least one of the two language classes , how many students are taking just one of the two classes ?
Options: a ) 24 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: french class + spanish class = 42 students . six students are in both classes so they were counted twice . the number of students taking just one class is 42 - 2 ( 6 ) = 30 . the answer is c .
Answer: c
Question (general): a company that ships boxes to a total of 14 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter )
Options: a ) 7 , b ) 8 , c ) 5 , d ) 9 , e ) 6
Rationale: "back - solving is the best way to solve this problem . you basically need 14 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - c"
Answer: c
Question (physics): a , b , c hired a car for rs . 520 and used it for 7,8 and 11 hours respectively . hire charges paid by b were :
Options: a ) 160 , b ) 180 , c ) 220 , d ) 225 , e ) none
Rationale: sol . a : b : c = 7 : 8 : 11 . hire charges paid by b = rs . [ 520 * 8 / 26 ] = rs . 160 answer a
Answer: a
Question (general): maximun number of identical pieces ( of same size ) of a cake by making only 3 cuts ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 5
Rationale: since cake is a 3 d object , it will have length , breadth , height . . . first cut across length now we will get 2 pieces then cut across breadth we will get 4 parts in total now . . . now cut across height , finally we will get 8 parts . . . answer : c
Answer: c
Question (general): how many prime numbers exist in 67 x 353 x 1110 ?
Options: a ) 30 prime number , b ) 29 prime number , c ) 27 prime number , d ) 31 prime number , e ) none of these
Rationale: "solution : = ( 2 x 3 ) 7 x ( 5 x 7 ) 3 x 1110 = 27 x 37 x 53 x 73 x 1110 thus , there are ( 7 + 7 + 3 + 3 + 10 ) = 30 prime number answer : a"
Answer: a
Question (physics): a car travels at a speed of 12 miles per hour . how far will it travel in 5 hours ?
Options: a ) 50 miles , b ) 60 miles , c ) 72 miles , d ) 22 miles , e ) 62 miles
Rationale: "during each hour , the car travels 65 miles . for 5 hours it will travel 12 + 12 + 12 + 12 + 12 = 5 * 12 = 60 miles correct answer b"
Answer: b
Question (gain): a hostel had provisions for 250 men for 36 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 30 , b ) 45 , c ) 50 , d ) 60 , e ) 65
Rationale: "a hostel had provisions for 250 men for 36 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 36 250 × 36 = 200 x 5 × 36 = 4 x x = 5 × 9 = 45 answer b"
Answer: b
Question (general): 3 , 4 , 6 , 10 , 18 , ( . . . )
Options: a ) 22 , b ) 34 , c ) 27 , d ) 32 , e ) 25
Rationale: "explanation : 3 3 × 2 - 2 = 4 4 × 2 - 2 = 6 6 × 2 - 2 = 10 10 × 2 - 2 = 18 18 × 2 - 2 = 34 answer : option b"
Answer: b
Question (general): the average of runs of a cricket player of 10 innings was 15 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 87 , b ) 16 , c ) 10 , d ) 76 , e ) 59
Rationale: average after 11 innings = 19 required number of runs = ( 19 * 11 ) - ( 15 * 10 ) = 209 - 150 = 59 . answer : e
Answer: e
Question (physics): 16 men can complete a piece of work in 25 days . in how many days can 15 men complete that piece of work ?
Options: a ) 26.7 days , b ) 77 days , c ) 20 days , d ) 88 days , e ) 44 days
Rationale: "16 * 25 = 15 * x = > x = 26.7 days answer : a"
Answer: a