regisss/math_qa huggingface dataset:
Problem: reema took a loan of rs 1200 with simple interest for as many years as the rate of interest . if she paid rs . 432 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "explanation : let rate = r % then time = r years . = > 1200 ∗ r ∗ r / 100 = 432 = > r 2 = 36 = > r = 6 % option b"
Answer: b
Problem: each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 26 have long fur , 22 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?
Options: a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 6
Rationale: "no of dogs = 45 long fur = 26 brown = 22 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 26 + 22 - both both = 11 answer c"
Answer: c
Problem: evaluate : 6202.5 + 620.25 + 62.025 + 6.2025 + 0.62025
Options: a ) 6819.59775 , b ) 6981.59775 , c ) 6918.59775 , d ) 6198.59775 , e ) 6891.59775
Rationale: "6202.5 620.25 62.025 6.2025 + 0.62025 - - - - - - - - - - - - - - - 6891.59775 answer is e ."
Answer: e
Problem: a van takes 5 hours to cover a distance of 465 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?
Options: a ) 56 , b ) 58 , c ) 60 , d ) 62 , e ) 64
Rationale: "( 3 / 2 ) * 5 = 7.5 hours 465 / 7.5 = 62 kph the answer is d ."
Answer: d
Problem: the product of two numbers is 120 and the sum of their squares is 289 . the sum is :
Options: a ) 23 , b ) 21 , c ) 43 , d ) 56 , e ) 30
Rationale: "xy = 120 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 120 ) = 529 x + y = 529 = 23 . answer a"
Answer: a
Problem: in what time will a railway train 60 m long moving at the rate of 54 kmph pass a telegraph post on its way ?
Options: a ) 4 sec , b ) 7 sec , c ) 2 sec , d ) 6 sec , e ) 9 sec
Rationale: "t = 60 / 54 * 18 / 5 = 4 sec answer : a"
Answer: a
Problem: a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 4 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 0.25 , b ) 0.5 , c ) 0.75 , d ) 1 , e ) 1.25
Rationale: "time = 2 / 4 + 2 / 8 = 6 / 8 = 0.75 hours the answer is c ."
Answer: c
Problem: mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 60 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least 4 hours , how long after he passed the gas station did paul catch up with mary ?
Options: a ) 2 , b ) 1.5 , c ) 1.6 , d ) 1.7 , e ) 1.25
Rationale: "d = rt m : r = 50 mph , t = t + 1 / 4 hr d = 50 ( t + 1 / 4 ) p : r = 60 , t = t d = 60 t since they went the same distance : 50 t + 50 / 4 = 60 t 10 t = 50 / 4 t = 1.25 or 1 hr , 15 min e"
Answer: e
Problem: the sum of three consecutive even numbers is 36 . find the middle number of the three ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 24 , e ) 36
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 36 6 p = 36 = > p = 6 . the middle number is : 6 p = 36 . answer : e"
Answer: e
Problem: the average of runs of a cricket player of 10 innings was 32 . 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 ) 17
Rationale: "average after 11 innings = 36 required number of runs = ( 36 * 11 ) - ( 32 * 10 ) = 396 - 320 = 76 . answer : d"
Answer: d
Problem: the guests at a football banquet consumed a total of 323 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: "to minimize one quantity maximize other . 161 * 2 ( max possible amount of food a guest could consume ) = 322 pounds , so there must be more than 161 guests , next integer is 162 . answer : c ."
Answer: c
Problem: a person can swim in still water at 10 km / h . if the speed of water 4 km / h , how many hours will the man take to swim back against the current for 12 km ?
Options: a ) 2 , b ) 7 , c ) 5 , d ) 9 , e ) 6
Rationale: "m = 10 s = 4 us = 10 - 4 = 6 d = 12 t = 12 / 6 = 2 answer : a"
Answer: a
Problem: in plutarch enterprises , 70 % of the employees are marketers , 20 % are engineers , and the rest are managers . marketers make an average salary of $ 70,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
Options: a ) $ 80,000 , b ) $ 150,000 , c ) $ 240,000 , d ) $ 290,000 , e ) $ 320,000
Rationale: "for sake of ease , let ' s say there are 10 employees : 7 marketers , 2 engineers , and 1 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 7 * $ 70,000 ) and the engineers ( 2 * $ 80,000 ) > > > $ 800,000 - $ 490,000 - $ 160,000 = $ 150,000 . the correct answer is b ."
Answer: b
Problem: 2525 * 9
Options: a ) 22725 , b ) 25675 , c ) 22655 , d ) 27575 , e ) none of these
Rationale: "explanation : 2525 * ( 10 - 1 ) = 25250 - 2525 = 22725 option a"
Answer: a
Problem: the diagonals of a rhombus are 15 cm and 21 cm . find its area ?
Options: a ) 277 , b ) 266 , c ) 150 , d ) 288 , e ) 157.5
Rationale: "1 / 2 * 15 * 21 = 157.5 answer : e"
Answer: e
Problem: rs . 500 amounts to rs . 620 in 2 years at simple interest . if the interest is increased by 2 % , it would amount to how much ?
Options: a ) 120 , b ) 25 , c ) 614 , d ) 530 , e ) 210
Rationale: "( 500 * 3 * 2 ) / 100 = 30 500 + 30 = 530 answer : d"
Answer: d
Problem: if the sales tax be reduced from 3 ( 1 / 5 ) % to 2 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 6400 ?
Options: a ) rs . 150.40 , b ) rs . 44.80 , c ) rs . 140.40 , d ) rs . 50.48 , e ) none of these
Rationale: "explanation : required difference = ( 3 ( 1 / 5 ) of rs . 6400 ) - ( 2 ( 1 / 2 ) of rs . 6400 ) = ( 16 / 5 – 5 / 2 ) % of rs . 6400 = ( 7 / 10 ) x ( 1 / 100 ) x 6400 = rs . 44.80 answer b"
Answer: b
Problem: circles x and y are concentric . if the radius of circle x is 6 times that of circle y , what is the probability that a point selected inside circle x at random will be outside circle y ?
Options: a ) 13 , b ) pi / 3 , c ) pi / 2 , d ) 35 / 36 , e ) 8 / 9
Rationale: small circle radius = a , so area = pi a ^ 2 large circle radius = 6 a , so area = 9 . pi a ^ 2 area of shaded region = 36 pi a ^ 2 - pi a ^ 2 = 35 pi a ^ 2 so , probability = ( 35 pi a ^ 2 ) / ( 36 pi a ^ 2 ) = 35 / 36 = answer = d
Answer: d
Problem: if x + y = 8 and y − 3 x = 7 , then what is the value of y - x ?
Options: a ) 1 / 7 , b ) 3 , c ) 15 , d ) 15 / 2 , e ) 60 / 7
Rationale: x + y = 8 . . . equation 1 - 3 x + y = 7 . . . equation 2 adding both the equations - 2 x + 2 y = 15 = > y - x = 15 / 2 correct answer option d
Answer: d
Problem: if 6 / w + 6 / x = 6 / y and wx = y , then the average ( arithmetic mean ) of w and x is
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: "given : 6 / w + 6 / x = 6 / ywx = y find : ( w + x ) / 2 = ? 6 ( 1 / w + 1 / x ) = 6 ( 1 / y ) - divide both sides by 6 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a"
Answer: a
Problem: a cycle is bought for rs . 900 and sold for rs . 1350 , find the gain percent ?
Options: a ) 39 % , b ) 20 % , c ) 23 % , d ) 50 % , e ) 83 %
Rationale: "900 - - - - 450 100 - - - - ? = > 50 % answer : d"
Answer: d
Problem: some persons can do a piece of work in 24 days . two times the number of these people will do half of that work in ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "24 / ( 2 * 2 ) = 6 days answer : d"
Answer: d
Problem: if 1 / 12 of the passengers on a ship are from north america , 1 / 4 are europeans , 2 / 9 are from africa , 1 / 6 are from asia and the remaining 50 people are citizens of other continents , then how many passengers are on board the ship ?
Options: a ) 120 , b ) 140 , c ) 150 , d ) 160 , e ) 180
Rationale: "1 / 12 + 1 / 4 + 2 / 9 + 1 / 6 = ( 3 + 9 + 8 + 6 ) / 36 = 13 / 18 let x be the number of passengers on the ship . 50 = ( 5 / 18 ) x x = 180 the answer is e ."
Answer: e
Problem: what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 3 ?
Options: a ) 897 , b ) 164,850 , c ) 164,749 , d ) 149,700 , e ) 156,720
Rationale: "explanatory answer step 1 : identify the series the smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101 . the next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107 . the largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998 . it is evident that any number in the sequence will be a 3 digit positive integer of the form ( 3 n + 2 ) . so , the given numbers are in an arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3 . step 2 : compute the sum sum of an arithmetic progression ( ap ) = [ first term + last term / 2 ] n we know the first term : 101 we know the last term : 998 . the only unknown is the number of terms , n . in an a . p . , the nth term an = a 1 + ( n - 1 ) * d in this case , therefore , 998 = 101 + ( n - 1 ) * 3 or 897 = ( n - 1 ) * 3 ( n - 1 ) = 299 or n = 300 . sum of the ap will therefore , be [ 101 + 998 / 2 ] ∗ 300 = 164,850 choice b is the correct answer ."
Answer: b
Problem: if it takes 4 movers 40 minutes to unpack their van , how long would 5 movers take ?
Options: a ) 38 minutes , b ) 35 minutes , c ) 32 minutes , d ) 29 minutes , e ) 26 minutes
Rationale: 4 * 40 = 5 * x x = 32 answer : c
Answer: c
Problem: a person can row at 9 kmph and still water . he takes 5 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 32 , b ) 28 , c ) 29 , d ) 24 , e ) 20
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 5.5 = > x / 10 + x / 8 = 11 / 2 = > ( 4 x + 5 x ) / 40 = 11 / 2 = > x = 24 km . answer : d"
Answer: d
Problem: a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6300 ?
Options: a ) rs . 5870 , b ) rs . 5991 , c ) rs . 6020 , d ) rs . 7670 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6300 * 6 ) – 30,130 ] = rs . ( 37800 – 30,130 ) = rs . 7670 answer d"
Answer: d
Problem: a train moves with a speed of 189 kmph . its speed in metres per second is
Options: a ) 60.8 , b ) 18 , c ) 30 , d ) 52.5 , e ) none
Rationale: "solution speed = 189 kmph = ( 189 x 5 / 18 ) m / sec = 52.5 m / sec . answer d"
Answer: d
Problem: a man has some hens and cows . if the number of heads be 100 and the number of feet equals 180 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 80 , d ) 90 , e ) 28
Rationale: "explanation : let the number of hens be x and the number of cows be y . then , x + y = 100 . . . . ( i ) and 2 x + 4 y = 220 x + 2 y = 110 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 90 , y = 10 . the required answer = 90 . answer : d"
Answer: d
Problem: if 5 x = 6 y and xy ≠ 0 , what is the ratio of 1 / 3 * x to 1 / 5 * y ?
Options: a ) 25 / 6 , b ) 36 / 25 , c ) 2 , d ) 5 / 6 , e ) 25 / 36
Rationale: 5 x = 6 y = > x / y = 6 / 5 1 / 3 * x to 1 / 5 * y = x / y * 5 / 3 = ( 6 / 5 ) * ( 5 / 3 ) = 2 ans : c
Answer: c
Problem: john and jacob set out together on bicycle traveling at 12 and 9 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john one hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 12 miles per hour ? ( consider john ' s deceleration / acceleration before / after the flat to be negligible )
Options: a ) 3 , b ) 2 1 / 3 , c ) 3 1 / 2 , d ) 4 , e ) 4 1 / 2
Rationale: "john ' s speed - 12 miles / hr jacob ' s speed - 9 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 12 x 2 / 3 = 8 miles . jacob continues to ride for a total of 1 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 1 hour 40 min ( i . e 5 / 3 hr ) = 9 x 5 / 3 = 15 miles . now , when john starts riding back , the distance between them is 7 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 12 - 9 = 3 miles / hr . thus , to cover 7 miles at 3 miles / hr , john will take 7 / 3 = 2 1 / 3 hours answer b"
Answer: b
Problem: the proportion of water to alcohol in solution a is 5 : 1 and the proportion of water to alcohol in solution b is 2 : 3 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?
Options: a ) 36.7 % , b ) 37.6 % , c ) 38.3 % , d ) 39.8 % , e ) 40.5 %
Rationale: "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 6 ) ( v / 2 ) + ( 3 / 5 ) ( v / 2 ) = v / 12 + 3 v / 10 = 23 v / 60 . the concentration of alcohol is 23 / 60 = 38.3 % the answer is c ."
Answer: c
Problem: 51 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 14 , d ) 15 , e ) 17
Rationale: "according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 51 x 12 x 5 = 30 x 6 x x x = 17 hence , the number of days = 17 . answer : e"
Answer: e
Problem: a palindrome is a word or a number that reads the same forward and backward . for example , 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits 1 , 2 , 3 , 4 , 5 , and 6 , how many palindromes are possible ?
Options: a ) 36 , b ) 96 , c ) 132 , d ) 216 , e ) 256
Rationale: "there are 6 choices for each of the first three digits . the number of possible palindromes is 6 ^ 3 = 216 . the answer is d ."
Answer: d
Problem: a sells a bicycle to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays rs . 225 for it , the cost price of the bicycle for a is ?
Options: a ) 277 , b ) 268 , c ) 270 , d ) 150 , e ) 282
Rationale: "125 % of 120 % of a = 225 125 / 100 * 120 / 100 * a = 225 a = 225 * 2 / 3 = 150 . answer : d"
Answer: d
Problem: the average marks of a class of 30 students is 50 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 56.25 , b ) 52.9 , c ) 52.1 , d ) 52.3 , e ) 42.5
Rationale: "sum of the marks for the class of 30 students = 30 * 50 = 1500 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 1500 + 3000 = 4500 average marks of all the students = 4500 / 80 = 56.25 answer : a"
Answer: a
Problem: if equation | x / 2 | + | y / 2 | = 1 encloses a certain region on the coordinate plane , what is the area of this region ?
Options: a ) 8 , b ) 50 , c ) 100 , d ) 200 , e ) 400
Rationale: the equation can be reduced to intercept form as | x / 2 | + | y / 2 | = 1 , so these are lines in four quadrants with x and y intercept as 2 , so it is a rhombus with diagonals of 4 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 4 * 4 = 8 . answer a .
Answer: a
Problem: andrea wants to fill in two sections of her backyard with sod that must be purchased in 2 - x - 2 - foot squares . if the two sections measure 30 x 40 feet and 60 x 80 feet , how many squares of sod does she need to buy ?
Options: a ) 1000 , b ) 1250 , c ) 1500 , d ) 1600 , e ) 2000
Rationale: to begin , find the area of each of the two sections by multiplying the lengths of the sides : 30 feet × 40 feet = 1200 square feet 60 feet × 80 feet = 4800 square feet the total area that needs sod has an area of 1200 + 4800 = 6000 square feet . each individual square is 2 feet by 2 feet , so each has an area of 4 square feet . because all the numbers are even , there will be no waste when the squares of sod are placed . therefore , you just have to find the number of squares needed by dividing : 6000 ÷ 4 = 1500 correct answer c ) 1500
Answer: c
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 4 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 25 , b ) 23 , c ) 32 , d ) 30 , e ) 18
Rationale: "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 4 w = 120 = > w = 30 answer d"
Answer: d
Problem: this year , mbb consulting fired 7 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ?
Options: a ) 98.5 % , b ) 100.0 % , c ) 102.3 % , d ) 104.5 % , e ) 105.0 %
Rationale: "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 7 % reduction in employees lead to 93 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 93 employees is 93 * 1100 = 102300 now the new salary is more than previous salary by x % . x = ( 102300 / 100000 ) * 100 = 102.3 % so the answer is c"
Answer: c
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 6 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 6 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: "salary grade of 6 is p ( 6 ) = 9.50 + 0.25 ( 6 – 1 ) = 9.50 + 0.25 * 5 ; salary grade of 1 is p ( 1 ) = 9.50 + 0.25 ( 1 – 1 ) = 9.50 ; p ( 6 ) - p ( 1 ) = 9.50 + 0.25 * 5 - 9.50 = 1.25 . answer : c ."
Answer: c
Problem: the sale price sarees listed for rs . 400 after successive discount is 12 % and 5 % is ?
Options: a ) 338 , b ) 277 , c ) 342 , d ) 334.4 , e ) 212
Rationale: "400 * ( 88 / 100 ) * ( 95 / 100 ) = 334.4 answer : d"
Answer: d
Problem: if 4 b ^ 4 − 41 b ^ 2 + 100 = 0 , then what is the sum of the two greatest possible values of b ?
Options: a ) 4 , b ) 9 / 2 , c ) 7 , d ) 41 / 4 , e ) 25
Rationale: just forget about the value of b ^ 4 for the moment and let b ^ 2 = x . ( its better to work with power of 2 than 4 ) now we have equation as 4 x ^ 2 - 41 x + 100 = 0 , factoring them gives us 4 x ^ 2 - 16 x - 25 x + 100 = 0 . which can be solved as ( 4 x - 25 ) ( x - 4 ) , so x = 4 and 25 / 4 . so b ^ 2 = 4 and 25 / 4 so b = + 2 and minus 2 and + 5 / 2 and minus 5 / 2 the two greatest values are + 2 and + 5 / 2 . so their sum 2 + 5 / 2 = 9 / 2 = b
Answer: b
Problem: having scored 99 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24
Rationale: explanation : let the average score of the first 18 innings be n 18 n + 99 = 19 ( n + 4 ) = > n = 23 so , average score after 19 th innings = x + 4 = 27 . answer : b
Answer: b
Problem: a company decreased the price of its main product by 10 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?
Options: a ) 4.3 , b ) 5.6 , c ) 6.2 , d ) 10.0 , e ) 12.0
Rationale: "for the total revenue to remain the same when the price is 1 / 10 , the number of products sold must 1 / 10 times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 10 % = 10.0 answer : d"
Answer: d
Problem: of all the homes on gotham street , 1 / 3 are termite - ridden , and 7 / 10 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?
Options: a ) 1 / 4 , b ) 1 / 6 , c ) 1 / 8 , d ) 1 / 9 , e ) 1 / 10
Rationale: "the fraction of homes which are termite - infested but not collapsing is 3 / 10 * 1 / 3 = 1 / 10 the answer is e ."
Answer: e
Problem: a train 150 meters long completely crosses a 320 meters long bridge in 40 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 42 , c ) 54 , d ) 66 , e ) 09
Rationale: "s = ( 150 + 320 ) / 40 = 470 / 40 * 18 / 5 = 42 answer : b"
Answer: b
Problem: jar x is 1 / 2 full of water . jar y , which has half the capacity of jar x , is 1 / 4 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ?
Options: a ) 3 / 4 , b ) 5 / 8 , c ) 7 / 8 , d ) 5 / 12 , e ) 7 / 12
Rationale: "let p be the capacity of jar x . the amount of water in jar y is 1 / 4 * p / 2 = p / 8 then the total amount in jar x is p / 2 + p / 8 = 5 p / 8 the answer is b ."
Answer: b
Problem: how much is 80 % of 40 is greater than 4 / 5 of 15 ?
Options: a ) 12 , b ) 20 , c ) 18 , d ) 12 , e ) 81
Rationale: "( 80 / 100 ) * 40 â € “ ( 4 / 5 ) * 15 32 - 12 = 20 answer : b"
Answer: b
Problem: a rainstorm increased the amount of water stored in state j reservoirs from 160 billion gallons to 200 billion gallons . if the storm increased the amount of water in the reservoirs to 50 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 240 , b ) 250 , c ) 260 , d ) 270 , e ) 300
Rationale: "let total capacity be x we know 200 = 0.50 x x = 200 / 0.50 = 400 prior to storm , we had 160 bn gallons 400 - 160 = 240 answer : a"
Answer: a
Problem: if 6 spiders make 6 webs in 6 days , then 1 spider will make 1 web in how many days ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 6 webs 6 : 1 1 x 6 x x = 6 x 1 x 6 = > x = 6 answer is b"
Answer: b
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 250 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?
Options: a ) 250 / 3 , b ) 750 , c ) 400 , d ) 480 , e ) 600
Rationale: "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 250 then y = 750 answer : b"
Answer: b
Problem: a man is walking at a speed of 10 km per hour . after every kilometre , he takes rest for 10 minutes . how much time will be take to cover a distance of 10 kilometres ?
Options: a ) 148 min . , b ) 150 min . , c ) 145 min . , d ) 155 min . , e ) none of these
Rationale: "rest time = number of rest ã — time for each rest = 9 ã — 10 = 90 minutes total time to cover 10 km = ( 10 â  „ 10 ã — 60 ) minutes + 90 minutes = 150 minutes answer b"
Answer: b
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 3 hours to complete the journey . if the distance between city a and city b is 600 kms and city a and city c is 300 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 2 / 1 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 5 / 3
Rationale: "distance traveled by eddy = 600 km time taken by eddy = 3 hours average speed of eddy = 600 / 3 = 200 km / hour distance traveled by freddy = 300 km time taken by freddy = 3 hours average speed of freddy = 300 / 3 = 100 km / hour ratio of average speed of eddy to freddy = 200 / 100 = 2 / 1 answer a"
Answer: a
Problem: a motorcyclist goes from nagpur to pune , a distance of 500 kms at an average of 100 kmph speed . another man starts from nagpur by car 3 â ½ hours after the first , and reaches pune â ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 1 : 7 , c ) 3 : 5 , d ) 1 : 5 , e ) 1 : 1
Rationale: t = 500 / 100 = 10 h t = 10 - 4 = 6 time ratio = 10 : 6 = 5 : 3 speed ratio = 3 : 5 answer : c
Answer: c
Problem: if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 287 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 178 , b ) 182 , c ) 186 , d ) 190 , e ) 194
Rationale: "j + k = 287 and so k = 287 - j j - 8 = 2 k j - 8 = 2 ( 287 - j ) 3 j = 582 j = 194 the answer is e ."
Answer: e
Problem: what is the greatest positive integer q such that 3 ^ q is a factor of 9 ^ 10 ?
Options: a ) q = 5 , b ) q = 9 , c ) q = 10 , d ) q = 20 , e ) 30
Rationale: "what is the greatest positive integer q such that 3 ^ q is a factor of 9 ^ 10 ? 9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 d . 20"
Answer: d
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum s of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: "i would solve it in a different way . first of all , total number of even integers between 99 and 301 are , ( 301 - 99 ) / 2 = 202 / 2 = 101 average = ( 301 + 99 ) / 2 = 400 / 2 = 200 sum s = average * total count = 200 * 101 = 20,200 answer is b"
Answer: b
Problem: a can do a piece of work in 4 days . b can do it in 15 days . with the assistance of c they completed the work in 24 days . find in how many days can c alone do it ?
Options: a ) 0.391 days , b ) 0.491 days , c ) 0.331 days , d ) 1.391 days , e ) 0.301 days
Rationale: "c = 1 / 2 - 1 / 24 - 1 / 15 = 0.391 days answer : a"
Answer: a
Problem: find 10 / 11 = 110 / ?
Options: a ) 111 , b ) 1100 , c ) 121 , d ) 100 , e ) none of these
Rationale: "answer let 10 / 11 = 110 / n , then , 10 n = 11 x 110 ∴ n = ( 11 x 110 ) / 10 = 121 . option : c"
Answer: c
Problem: in a dairy farm , 46 cows eat 46 bags of husk in 46 days . in how many days one cow will eat one bag of husk ?
Options: a ) 1 , b ) 46 , c ) 20 , d ) 26 , e ) 30
Rationale: "explanation : one bag of husk = 46 cows per day ⇒ 46 × 1 × 46 = 1 × 46 × x for one cow = 46 days answer : b"
Answer: b
Problem: [ ( 3.242 x 14 ) / 100 ] = ?
Options: a ) 0.045388 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) none of these
Rationale: "answer multiplying 3.242 x 14 = 4.5388 now divide 4.5388 by 100 so , 4.5388 ÷ 100 = 0.045388 ∴ shift the decimal two places to the left as 100 correct option : a"
Answer: a
Problem: i chose a number and divide it by 5 . then i subtracted 154 from the result and got 6 . what was the number i chose ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) none
Rationale: "solution : let xx be the number i chose , then x / 5 − 154 = 6 x / 5 = 160 x = 800 answer c"
Answer: c
Problem: a man rows his boat 80 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 8 , c ) 5 , d ) 7 , e ) 9
Rationale: "speed downstream = d / t = 80 / ( 2 1 / 2 ) = 32 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 32 - 18 ) / 2 = 7 kmph answer : d"
Answer: d
Problem: find out the c . i on rs . 6000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 367.25 , b ) 306.07 , c ) 306.04 , d ) 306.03 , e ) 306.01
Rationale: a = 6000 ( 51 / 50 ) 3 = 6367.248 6000 - - - - - - - - - - - 367.25 answer : a
Answer: a
Problem: a card is drawn from a pack of 52 cards . the probability of getting a queen club or a king of heart ?
Options: a ) 3 / 26 , b ) 1 / 26 , c ) 4 / 26 , d ) 6 / 26 , e ) 10 / 26
Rationale: "n ( s ) = 52 let e = event of getting a queen of club or a king of heart . n ( e ) = 2 p ( e ) = n ( e ) / n ( s ) = 2 / 52 = 1 / 26 option : b"
Answer: b
Problem: a , b and c run around a circular track starting from the same point simultaneously and in the same direction at speeds of 4 kmph , 6 kmph and 8 kmph respectively . if the length of the track is 400 meters , when will a , b and c meet at the starting point for the first time after they started the race ?
Options: a ) 1 minute , b ) 5 minutes , c ) 12 minutes , d ) 20 minutes , e ) 24 minutes
Rationale: 4 kmph , 6 kmph and 8 kmph is equal to 4000 / 60 mtrs / min , 6000 / 60 mtrs / min and 8000 / 60 mtrs / min or 200 / 3 , 100 , 400 / 3 mtrs / min respectively . seeing this we can infer that the answer should be at least divisible by 3 . ( minutes in options are integers . so if the answer is not divisible by 3 , we will have 200 / 3 * answer = distance traveled by a in fractions whereas 100 * answer = distance traveled by a as integer ) so , a , b and d are out . at 12 min a , b and c will travel 800 , 1200 and 1600 mtrs respectively . length of the circle is given as 400 mtrs . as 800 , 1200 and 1600 are divisible by 400 , we can say that a , b and c will be at starting point after 12 min . hence , c will be the answer .
Answer: c
Problem: if 15 workers can build a wall in 48 hours , how many workers will be required to do the same work in 30 hours ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 25 , e ) 23
Rationale: let the number of workers employed to build the wall in 30 hours be y 48 * 15 = 30 * y ( 48 * 15 ) / 30 = y y = 24 answer : b
Answer: b
Problem: the least number of 4 digits which is divisible by 15 , 25 , 40 and 75 is :
Options: a ) 9000 , b ) 9400 , c ) 9600 , d ) 9800 , e ) 9700
Rationale: greatest number of 4 digits is 9999 . l . c . m of 15 , 25 , 40 and 75 is 600 . on dividing 9999 by 600 , the remainder is 399 . required number = 9999 - 399 = 9600 answer : c
Answer: c
Problem: find the probability that a leap year chosen at random will have 53 sundays
Options: a ) 2 / 7 , b ) 2 / 6 , c ) 2 / 5 , d ) 2 / 3 , e ) 2 / 4
Rationale: "a leap year has 366 day which is 52 full weeks + 2 odd days . now these two odd days may be ( sun + mon ) , ( mon + tue ) , . . . . ( sat + sun ) . now there are total 7 ways . of which sunday appeared two times . so answer 2 / 7 answer : a"
Answer: a
Problem: three pipes a , b and c can fill a tank from empty to full in 20 minutes , 20 minutes and 30 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution r in the liquid in the tank after 3 minutes ?
Options: a ) 1 / 2 , b ) 1 / 5 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 6
Rationale: part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 20 + 1 / 20 + 1 / 30 ) = 6 / 15 part filled by c in 3 minutes = 3 / 30 required ratio = 3 / 30 * 15 / 6 = 1 / 4 answer : d
Answer: d
Problem: a man ' s speed with the current is 25 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is ?
Options: a ) 10 , b ) 80 , c ) 50 , d ) 30 , e ) 20
Rationale: "man ' s speed with the current = 25 km / hr = > speed of the man + speed of the current = 25 km / hr speed of the current is 2.5 km / hr hence , speed of the man = 25 - 2.5 = 22.5 km / hr man ' s speed against the current = speed of the man - speed of the current = 22.5 - 2.5 = 20 km / hr answer is e ."
Answer: e
Problem: in a fraction , if numerator is added by 2 and denominator by 1 it results 1 , and if numerator added again by 4 and denominator by 2 it results 1 / 2 . find the fraction ?
Options: a ) 3 / 4 , b ) 5 / 4 , c ) 7 / 4 , d ) 9 / 4 , e ) 11 / 4
Rationale: x + 2 / y + 1 = 1 i . e , x - y + 1 = 0 ; - - - - - - - - ( 1 ) x + 4 / y + 2 = 1 / 2 i . e . , 2 x - y + 6 = 0 ; - - - - - - - - - ( 2 ) solving 1 and 2 . . . we get x = - 5 and y = - 4 answer is 5 / 4 . . . answer : b
Answer: b
Problem: a rectangular room has the rectangular shaped rug shown as above figure such that the rug ’ s area is 180 square feet and its length is 8 feet longer than its width . if the uniform width between the rug and room is 8 feet , what is the area of the region uncovered by the rug ( shaded region ) , in square feet ?
Options: a ) 32
b ) 36
c ) 704
d ) 46
e ) 104
Rationale: rug ' s area = 180 which is ( x ) x ( 8 + x ) = 180 so x = 10 rug maintains a uniform distance of 8 feet so room has dimension 10 + 16 and 18 + 16 i . e . 26 and 34 area of room 26 x 34 = 884 area covered is 180 so uncovered area is 884 - 180 = 704 ( answer c )
Answer: c
Problem: 7 people average age is 30 . youngest person age is 4 . find average of the people when youngest was born .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 32 = 182 so average age would be 182 / 7 = 26 answer : d"
Answer: d
Problem: in a group of cows and chickens , the number of legs was 10 more than twice the number of heads . the number of cows was :
Options: a ) 5 , b ) 7 , c ) 10 , d ) 12 , e ) 14
Rationale: "let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 10 more than twice the number of heads . therefore , 2 × ( x + y ) + 10 = 4 x + 2 y . or , 2 x + 2 y + 10 = 4 x + 2 y . or , 2 x + 10 = 4 x [ subtracting 2 y from both sides ] . or , 10 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 10 = 2 x . or , x = 5 [ dividing by 2 on both sides ] . therefore , the number of cows = 5 . correct answer : a ) 5"
Answer: a
Problem: the cash difference between the selling prices of an article at a profit of 4 % and 6 % is rs . 3 . the ratio of the two selling prices is :
Options: a ) 51 : 52 , b ) 52 : 53 , c ) 51 : 53 , d ) 52 : 55 , e ) 52 : 56
Rationale: "let c . p . of the article be rs . x . then , required ratio = 104 % of x / 106 % of x = 104 / 106 = 52 / 53 = 52 : 53 answer : b"
Answer: b
Problem: the area of a circle is increased by 300 % . by what percent has the radius of the circle increased ?
Options: a ) 400 % , b ) 200 % , c ) 100 % , d ) 600 % , e ) 800 %
Rationale: "the area of the circle is increased by 300 % , thus the area is increased 4 times . the area of a circle it proportional to the square of the radius ( area = π r ^ 2 ) , therefore the radius must increase 2 times ( diameter increase 2 times = area increase 4 times ) , which is increase by 100 % . answer : c"
Answer: c
Problem: the total number of digits used in numbering the pages of a book having 356 pages is
Options: a ) 732 , b ) 990 , c ) 1098 , d ) 960 , e ) 1405
Rationale: "total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 257 ) = ( 9 + 180 + 771 ) = 960 . answer : d"
Answer: d
Problem: working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 2 days at a time . if a starts they finish the task in exact 8 days . if b starts , they take a day more . how long does it take to complete the task if they both work together ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 2
Rationale: "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 4 no . of days when b works = 4 → 4 x + 4 y = 1 when b starts : no . of days when a works = 5 no . of days when b works = 3 → 5 x + 3 y = 1 solving the above two equations for xy x = 1 / 8 y = 1 / 8 → total work done by ab in a day = 1 / 8 + 1 / 8 = 1 / 4 → no . of days to complete the work when both work together = 4 answer : 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 45 kmph when will the owner over take the thief from the start ?
Options: a ) a ) 2 , b ) b ) 5 , c ) c ) 7 , d ) d ) 4 , e ) e ) 8
Rationale: "explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 45 40 d = 20 rs = 45 – 40 = 5 t = 20 / 5 = 4 hours answer : option d"
Answer: d
Problem: the area of a right triangle pcm is 18 . length of smallest side cm is 3 units . find the length of the other two sides .
Options: a ) 12 , 9
b ) 18 , 3
c ) 15.16 , 6
d ) 12 , 12.37
e ) 12 , 15.16
Rationale: cm = 3 area = pm * cm / 2 , thus pm = 12 by pythagorean theorem , we can now find the value of pc . d is the correct option .
Answer: d
Problem: each machine of type a has 2 steel parts and 2 chrome parts . each machine of type b has 6 steel parts and 5 chrome parts . if a certain group of type a and type b machines has a total of 20 steel parts and 22 chrome parts , how many machines are in the group
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: "look at the below representation of the problem : steel chrome total a 2 2 20 > > no . of type a machines = 20 / 4 = 5 b 6 5 22 > > no . of type b machines = 22 / 11 = 2 so the answer is 7 i . e e . hope its clear ."
Answer: e
Problem: there is a square with sides of 9 . what is the area of the biggest circle that can be cut out of this square ?
Options: a ) 72.83 , b ) 63.62 , c ) 81 , d ) 254.47 , e ) 100
Rationale: "area of a circle = area = ï € r ^ 2 square is 9 wide , so circle ' s diameter would be 9 , and radius would be 4.5 area = ï € 4.5 ^ 2 which is approximately 63.62 answer is b"
Answer: b
Problem: a boat can travel with aspeed of 30 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 70 km downstream .
Options: a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs
Rationale: "speed downstream = ( 30 + 5 ) km / hr = 35 km / hr . time taken to travel 68 km downstream = 70 / 35 hrs = 2 hrs . b"
Answer: b
Problem: the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 46 years , was replaced by a new person . find the age of the new person ?
Options: a ) 18 , b ) 56 , c ) 16 , d ) 17 , e ) 14
Rationale: "initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 46 + q = > q = 16 answer : c"
Answer: c
Problem: a number whose fifth part increased by 4 is equal to its fourth part diminished by 10 , is :
Options: a ) 240 , b ) 260 , c ) 270 , d ) 280 , e ) 290
Rationale: let the number be x . then , ( ( 1 / 5 ) x + 4 ) = ( ( 1 / 4 ) x − 10 ) < = > x / 20 < = > x = 14 * 20 = 280 . answer : d
Answer: d
Problem: if 0.60 : x : : 6 : 2 , then x is equal to
Options: a ) 0.2 , b ) 0.5 , c ) 2.5 , d ) 1.8 , e ) none
Rationale: "sol . ( x × 6 ) = ( 0.60 × 2 ) ⇒ x = 0.60 / 6 = 0.2 . answer a"
Answer: a
Problem: a and b together can do a piece of work in 6 days and a alone can do it in 12 days . in how many days can b alone can do it ?
Options: a ) 11 days , b ) 15 days , c ) 12 days , d ) 21 days , e ) 22 days
Rationale: "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 12 work in 1 day b alone can do ( 1 / 6 - 1 / 12 ) = 1 / 12 work in 1 day = > complete work can be done in 12 days by b answer : option c"
Answer: c
Problem: in a certain town , the ratio of ny yankees fans to ny mets fans is 2 : 1 , and the ratio of ny mets fans to boston red sox fans is 3 : 7 . if there are 352 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?
Options: a ) 58 , b ) 66 , c ) 74 , d ) 82 , e ) 90
Rationale: "the ratio of yankees : mets : red sox = 6 : 3 : 7 the mets fans are 3 / 16 of the population . ( 3 / 16 ) * 352 = 66 the answer is b ."
Answer: b
Problem: in a certain neighborhood , 60 percent of the student are going to school ( a ) , and the rest are going to school ( b ) . a new school ( c ) is opened , if 30 percent of student of school ( a ) and 40 percent of student of school ( b ) are expected to go to the new school ( c ) , what percent of student are expected to go to the new school ( c ) ?
Options: a ) 30 % , b ) 34 % , c ) 38 % , d ) 42 % , e ) 46 %
Rationale: say there are total of 100 students in the neighborhood , 60 students are going to school ( a ) and 40 student are going to school ( b ) 60 * 0.3 = 18 student of school ( a ) are expected to go to the new school ( c ) 40 * 0.4 = 16 student of school ( b ) are expected to go to the new school ( c ) thus total of 18 + 16 = 34 student are expected to go to the new school ( c ) , which is 34 % of students . answer : b .
Answer: b
Problem: two trains of equal length , running with the speeds of 60 and 100 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 , b ) 6.25 , c ) 7.35 , d ) 2.62 , e ) 2.28
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 100 = 160 * 5 / 18 t = 2500 / 9 * 18 / 800 = 6.25 sec . answer : b"
Answer: b
Problem: find the number of elements in the power set of { 1,2 }
Options: a ) 4 , b ) 0 , c ) 2 , d ) 3 , e ) 5
Rationale: "power set is the set of subsets of { 1,2 } that is { { 1,2 } , { 1 } , { 2 } , f } answer : a"
Answer: a
Problem: 64 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 22 , b ) 77 , c ) 29 , d ) 65 , e ) 21
Rationale: 64 + 5 * 12 / ( 180 / 3 ) = 64 + 5 * 12 / ( 60 ) = 64 + ( 5 * 12 ) / 60 = 64 + 1 = 65 . answer : d
Answer: d
Problem: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1021 . find the cost of each ice - cream cup ?
Options: a ) 35 , b ) 66 , c ) 77 , d ) 99 , e ) 91
Rationale: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1021 96 + 225 + 490 + 6 x = 1021 6 x = 210 = > x = 35 . answer : a"
Answer: a
Problem: the length of a train and that of a platform are equal . if with a speed of 54 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 227 , b ) 299 , c ) 450 , d ) 750 , e ) 211
Rationale: "speed = [ 54 * 5 / 18 ] m / sec = 15 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 15 è x = 15 * 60 / 2 = 450 answer : c"
Answer: c
Problem: jack went on a diet 6 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 180 pounds ?
Options: a ) 3 , b ) 35 , c ) 4 , d ) 45 , e ) 5
Rationale: joe lost his weigh 24 pounds during 6 months . that means that he lost 4 pounds per month . he should lose more 18 pounds to be 180 pounds . so it would take 18 / 4 = 4.5 months . correct answer is d
Answer: d
Problem: if 2 x = 3 y = 10 , then 3 xy = ?
Options: a ) 100 , b ) 200 , c ) 120 , d ) 50 , e ) 20
Rationale: "2 x = 10 ; x = 5 3 y = 10 ; y = 10 / 3 multiply : 3 xy = 3 * 5 * 10 / 3 = 50 answer : d ."
Answer: d
Problem: b completes a work in 7 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 3.75 days , b ) 4.11 days , c ) 5.11 days , d ) 6.75 days , e ) 7.33 days
Rationale: "1 / 7 + 1 / 10 = 17 / 70 70 / 17 = 4.11 days answer : b"
Answer: b
Problem: excluding the stoppages , the speed of a bus is 48 km / hr and including the stoppages the speed of the bus is 24 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 30 min , b ) 10 min , c ) 12 min , d ) 20 min , e ) 18 min
Rationale: "speed of the bus without stoppage = 48 km / hr speed of the bus with stoppage = 24 km / hr difference in speed = 24 km / hr so , the time taken in the stoppages = time taken to cover 24 km = ( 24 / 48 ) hr = 1 / 2 hr = 30 min answer : a"
Answer: a
Problem: what is the % change in the area of a rectangle when its length increases by 20 % and its width decreases by 20 % ?
Options: a ) 0 % , b ) 20 % increase , c ) 20 % decrease , d ) 4 % decrease , e ) insufficient data
Rationale: "( 12 / 10 ) * ( 8 / 10 ) = 96 / 100 of original area 96 / 100 is a 4 % decrease from 100 / 100 - > d"
Answer: d
Problem: 5 pieces of wood have an average length of 128 cm and a median length of 140 cm . what is the maximum possible length , in cm , of the shortest piece of wood ?
Options: a ) a ) 90 , b ) b ) 100 , c ) c ) 110 , d ) d ) 130 , e ) e ) 140
Rationale: c . 110 sum of all lengths of all 5 pieces of wood = 128 * 5 = 640 3 rd piece ( sorted in increasing length ) length = 140 ( median ) for sum of first 2 wood length to become max , last two should be least . let 4 th , 5 th wood also have length 140 each . total of last 3 = 140 * 3 = 420 sum of first 2 = 640 - 420 = 220 each of these 2 will have length 220 / 2 = 110 answer c
Answer: c
Problem: if a certain toy store ' s revenue in november was 4 / 5 of its revenue in december and its revenue in january was 3 / 4 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 2 / 3 , d ) 2 , e ) 4
Rationale: "let dec rev = 100 then nov rev is 4 / 5 ( 100 ) = > 80 therefore jan rev = 3 / 4 ( nov rev ) = 3 / 4 ( 80 ) = > 60 hence dec rev = x * ( nov rev + jan rev ) / 2 100 = x * ( 80 + 60 ) / 2 x = 100 / 70 = > 1.42 = 2 ans ) d"
Answer: d
Problem: a car started running at a speed of 34 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
Options: a ) 43 km , b ) 76 km , c ) 25 km , d ) 15 km , e ) 30 km
Rationale: "a 43 km the total distance covered by the car in the first 10 hours = 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 = sum of 10 terms in ap whose first term is 34 and last term is 52 = 10 / 2 [ 34 + 52 ] = 430 km ."
Answer: a
Problem: two boys starts from the same place walking at the rate of 4 kmph and 5.5 kmph respectively in the same direction . what time will they take to be 10.5 km apart ?
Options: a ) 8 , b ) 5 , c ) 7 , d ) 9 , e ) 6
Rationale: "explanation : relative speed = 5.5 - 4 = 1.5 kmph ( because they walk in the same direction ) distance = 10.5 km time = distance / speed = 10.5 / 1.5 = 7 hr answer : c"
Answer: c
Problem: mr . kramer , the losing candidate in a two - candidate election , received 942568 votes , which was exactly 30 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 29 % , e ) 20 %
Rationale: let me try a simpler one . lets assume that candidate got 30 % votes and total votes is 100 . candidate won = 30 remaining = 70 to get 50 % , candidate requires 20 votes from 100 which is 20 % and 20 votes from 70 . 20 / 70 = 2 / 7 = . 285 = 28.5 % which is approx 29 % . hence the answer is d .
Answer: d
Problem: how many pieces of 0.40 meteres can be cut from a rod 47.5 meteres long
Options: a ) 100 , b ) 118 , c ) 120 , d ) 125 , e ) 70
Rationale: "explanation : we need so simple divide 47.5 / 0.40 , = ( 4750 / 40 ) = 118 option b"
Answer: b