regisss/math_qa huggingface dataset:
Problem: a clock shows the time as 12 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 45 minutes , b ) 55 minutes , c ) 35 minutes , d ) 30 minutes , e ) 40 minutes
Rationale: "there are 6 hours in between 12 a . m . to 6 p . m . 6 * 5 = 30 minutes . answer : d"
Answer: d
Problem: what will be the cost of building a fence around a square plot with area equal to 36 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 3944 , b ) 2882 , c ) 2999 , d ) 2667 , e ) 1392
Rationale: "let the side of the square plot be a ft . a 2 = 36 = > a = 6 length of the fence = perimeter of the plot = 4 a = 24 ft . cost of building the fence = 24 * 58 = rs . 1392 . answer : e"
Answer: e
Problem: a person want to give his money of $ 4500 to his 4 children a , b , c , d in the ratio 2 : 4 : 5 : 4 . what is the a + b share ?
Options: a ) $ 1000 , b ) $ 2000 , c ) $ 1800 , d ) $ 1500 , e ) $ 1600
Rationale: "a ' s share = 4500 * 2 / 15 = $ 600 b ' s share = 4500 * 4 / 15 = $ 1200 a + b = $ 1800 answer is c"
Answer: c
Problem: if the price of a certain computer increased 30 percent from y dollars to 351 dollars , then 2 y =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = y after 30 % price increase price = y + ( 30 / 100 ) * y = 1.3 y = 351 ( given ) i . e . y = 351 / 1.3 = $ 270 i . e . 2 y = 2 * 270 = 540 answer : option a"
Answer: a
Problem: if price of t . v set is reduced by 22 % , then its sale increases by 86 % , find net effect on sale value
Options: a ) 44 , b ) 45 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 22 + 86 + ( - 22 * 86 ) / 100 = - 22 + 86 - 19 = 45 answer : b"
Answer: b
Problem: there are 76 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "editing my solution : number of switches = 76 number of switches turned on by a : 3 , 6 , . . . 75 = 25 number of switches turned on by b : 5 , 10 , . . . . 75 = 15 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 25 - 6 ) + ( 15 - 6 ) = 28 answer : a"
Answer: a
Problem: each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 99 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
Options: a ) $ 2400 , b ) $ 3300 , c ) $ 6000 , d ) $ 6400 , e ) $ 9600
Rationale: "let x be the monthly salary 15 % of 1 / 5 * x = 99 x = 3300 answer b"
Answer: b
Problem: a goat is tied to one corner of a square plot of side 12 m by a rope 7 m long . find the area it can graze ?
Options: a ) 32
b ) 36.5
c ) 38.5
d ) 39
e ) 39.5
Rationale: area covered by goat = pi * r ^ 2 / 4 ( here we divide by 4 because rope is tied at the corner of the plot and only 1 / 4 part , the goat can graze ) where r = 7 m = length of rope so area = ( 22 / 7 ) * 7 * 7 / 4 = 38.5 sq m answer : c
Answer: c
Problem: a retailer bought a hat at wholesale and marked it up 60 % to its initial price of $ 24 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x be the wholesale price . then 1.6 x = 24 and x = 24 / 1.6 = 15 . to achieve a 100 % markup , the price needs to be $ 30 . the retailer needs to increase the price by $ 6 more . the answer is d ."
Answer: d
Problem: the cube root of . 000343 is
Options: a ) 0.7 , b ) 0.07 , c ) 0.007 , d ) 7 , e ) none of these
Rationale: "explanation : ( . 000343 ) 1 / 3 = ( 343 / 106 ) 1 / 3 = ( 7 * 7 * 7 / 102 * 102 * 102 ) 1 / 3 = 7 / 102 = 7 / 100 = 0.07 answer b"
Answer: b
Problem: a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 200 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 6
Rationale: "the distance between the nest and the ditch is 200 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 200 = 6000 . d = st 6000 / 1.5 = t , i think we can take 6000 meters as 6 km , then only we get t = 4 . ( 1000 meters = 1 km ) d )"
Answer: d
Problem: 3 seventh of a number is 12 more than 40 % of that number . what will be the 30 % of that number ?
Options: a ) a ) 148 , b ) b ) 210 , c ) c ) 63 , d ) d ) 248 , e ) e ) 258
Rationale: 3 / 7 x – 40 / 100 x = 12 x = 35 * 12 35 * 12 * 30 / 100 = 126 / 2 = 63 answer : c
Answer: c
Problem: find last digits of ( 1023 ^ 3923 ) + ( 3081 ^ 3921 )
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: we have ( 1023 ^ 3923 ) + ( 3081 ^ 3921 ) ( 3923 / 4 ) = 4 n + 3 ( 3921 / 4 ) = 4 n + 1 where n can be any integer now through cyclicity we can obtain or you can learn the chart from arun sharma number ending in 4 n + 1 4 n + 2 4 n + 3 4 n 1 1 1 1 1 2 2 4 8 6 3 3 9 7 1 in this way 7 + 1 = 8 is the unit ' s place digit answer : a
Answer: a
Problem: the sum of 4 consecutive even numbers is 36 . find the sum of the squares of these numbers ?
Options: a ) 296 , b ) 252 , c ) 344 , d ) 388 , e ) none of these
Rationale: let the four numbers be x , x + 2 , x + 4 and x + 6 . = > x + x + 2 + x + 4 + x + 6 = 36 = > 4 x + 12 = 36 = > x = 6 the numbers are 6 , 8 , 10 and 12 . sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344 . answer : c
Answer: c
Problem: two trains , each 150 m long , moving in opposite directions , cross other in 8 sec . if one is moving twice as fast the other , then the speed of the faster train is ?
Options: a ) 90 , b ) 98 , c ) 60 , d ) 88 , e ) 12
Rationale: "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 150 + 150 ) / 8 = 3 x = > x = 25 / 2 . so , speed of the faster train = 50 / 2 = 25 * 18 / 5 = 90 km / hr . answer : a"
Answer: a
Problem: with an average speed of 40 km / hr a car reaches its destination on time . if it goes with an average speed of 35 km / h , it is late by 15 minutes . the total journey is ?
Options: a ) 30 km , b ) 40 km , c ) 70 km , d ) 80 km , e ) 90 km
Rationale: let the total journey be x km . x / 35 - x / 40 = 15 / 60 solving for x , we get x = 70 therefore , total journey = 70 km . answer : c
Answer: c
Problem: find the remainder q when 12 ^ 190 is divided by 1729 ?
Options: a ) 12 , b ) 1 , c ) 1728 , d ) 1717 , e ) 4
Rationale: 12 ^ ( 190 ) can be written as . ( ( 12 ^ 3 ) ^ 63 ) * 12 . 12 ^ 3 when divided by 1729 gives a remainder q - 1 . so in the numerator we have - 12 . now acccording to remainder theorm the answer will be 1729 - 12 = 1717 . d
Answer: d
Problem: how much 70 % of 100 is greater than 60 % of 80 ?
Options: a ) 18 , b ) 99 , c ) 22 , d ) 26 , e ) 71
Rationale: "( 70 / 100 ) * 100 – ( 60 / 100 ) * 80 70 - 48 = 22 answer : c"
Answer: c
Problem: the main line train starts at 5.00 am and the harbor line train starts at 5.02 am . each train has the frequency of 10 minutes . if a guy goes in the morning at a random time what is the probability of he getting main line train ?
Options: a ) . 5 , b ) 0.6 , c ) 0.4 , d ) 0.7 , e ) 0.8
Rationale: out of 10 minutes there is only 2 minutes chance of getting harbour line train and there is 8 minutes chance for getting main line train . so , probability = 8 / 10 = 0.8 answer : e
Answer: e
Problem: an uneducated retailer marks all his goods at 60 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ?
Options: a ) 20 % , b ) 13.50 % , c ) 14 % , d ) 14.50 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 160 . s . p . = 75 % of rs . 160 = rs . 120 . ∴ gain % = 20 % . answer a"
Answer: a
Problem: a plane flies 420 miles with the wind and 350 miles against the wind in the same length of time . if the speed of the wind is 23 mph , what is the speed of the plain in still air ?
Options: a ) 253 mph . , b ) 275 mph . , c ) 296 mph . , d ) 278 mph . , e ) 235 mph .
Rationale: the speed of the plane in still air = x miles / hour the speed of the wind is 23 mph speed with the wind = ( x + 23 ) mph speed against the wind = ( x – 23 ) mph time = distance / speed according to the problem , 420 / ( x + 23 ) = 350 / ( x – 23 ) 420 ( x – 23 ) = 350 ( x + 23 ) 420 x – 9660 = 350 x + 805 420 x – 350 x = 8050 + 9660 70 x = 17710 x = 17710 / 70 x = 253 therefore , the speed of the plane in still air = 253 mph . correct answer a
Answer: a
Problem: rs 80000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 9000 find money given by 10 % ?
Options: a ) 30000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000
Rationale: "let first parrt is x and second part is y then x + y = 80000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 9000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 90000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 90000 = 80000 + y so y = 10000 then x = 80000 - 10000 = 70000 first part = 70000 answer : e"
Answer: e
Problem: at the end of year x , automobile installment credit accounted for 43 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 50 billion of credit , or 1 / 4 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
Options: a ) 450 , b ) 465.12 , c ) 475 , d ) 500.15 , e ) 200
Rationale: system of equations a = ( 43 / 100 ) c ( 1 / 4 ) a = 50 - - > a = 200 substitution 200 = ( 43 / 100 ) c c = ( 100 / 43 ) 200 calculate 200 / 43 * 100 - the the correct answer is 465.12 . the correct answer is b .
Answer: b
Problem: what is the lowest positive integer that is divisible by 1 through 3 , inclusive ?
Options: a ) 12 , b ) 6 , c ) 8 , d ) 18 , e ) 33
Rationale: "the integer should be divisible by : 1 , 2 , and 3 . the least common multiple of these integers is lcm = 1 * 2 * 3 = 6 answer : b"
Answer: b
Problem: a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 1.85 ?
Options: a ) 1680 , b ) 1420 , c ) 1120 , d ) 970 , e ) 740
Rationale: "the charge is 65 cents for the first 250 grams . this leaves a charge of $ 1.85 - $ 0.65 = $ 1.20 the charge for the next 1100 grams is $ 1.10 which leaves a charge of $ 0.10 the weight is somewhere between 1350 and 1450 . the answer is b ."
Answer: b
Problem: during a certain two - week period , 60 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 4 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 14 , b ) 12 , c ) 10 , d ) 8 , e ) 7.5
Rationale: "total movies = 100 . comedies = 60 . action + drama = 40 . since there were 5 times as many dramas as action movies , then action + 4 * action = 40 - - > action = a = 8 . comedies = 60 = 7.5 a . answer : e"
Answer: e
Problem: a fruit seller sells mangoes at the rate of rs . 9 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 8.81 , b ) rs 9.81 , c ) rs 10.81 , d ) rs 11.81 , e ) none of these
Rationale: "explanation : 85 : 9 = 105 : x x = ( 9 × 105 / 85 ) = rs 11.81 option d"
Answer: d
Problem: if 21 / 22 = 0 . 95.45 , what is the 57 th digit to the right of the decimal point of the fraction ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 7 , e ) 9
Rationale: we are not concerned what 21 / 22 means . . we have to look at the decimal . . 0.9544 means 0.95454545 . . . . so leaving first digit to the right of decimal , all odd numbered digits are 4 and all even numbered are 5 . . here 57 is odd , so ans is 4 answer is b
Answer: b
Problem: an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 20000 people who applied for the army and 196 were finally selected , what was the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "step ( 1 ) 8000 accepted . step ( 2 ) another 40 % of 8000 = 3200 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 3200 = 1600 step ( 4 ) 50 % of 1600 = 800 step ( 5 ) 50 % of 800 = 400 step ( 6 ) 50 % of 400 = 200 70 % of 400 = 280 and last step of accepting 70 % of 280 = 196 ( our target ) total 8 steps required . ans d"
Answer: d
Problem: how many multiples of 5 are there between 50 and 500 ?
Options: a ) 128 , b ) 91 , c ) 89 , d ) 61 , e ) 60
Rationale: "it should be mentioned whether 50 and 500 are inclusive . if 50 and 500 are inclusive , then the answer is ( 500 - 50 ) / 5 + 1 = 91 . if 50 and 500 are not inclusive , then the answer is ( 495 - 55 ) / 5 + 1 = 89 . since oa is c , then we have not inclusive case ."
Answer: c
Problem: two stations a and b are 110 km apart on a straight line . one train starts from a at 4 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 15 a . m , b ) 10 a . m , c ) 7 a . m , d ) 02 a . m , e ) 05 a . m
Rationale: "suppose they meet x hours after 4 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 7 a . m . answer : c"
Answer: c
Problem: the height of the wall is 6 times its width and lenght of the wall is 7 times its height . if the volume of the wall be 16128 cu . m . its width is
Options: a ) 4 m
b ) 5 m
c ) 6 m
d ) 7 m
e ) 8 m
Rationale: explanation : let width = x then , height = 6 x and length = 42 x 42 x × 6 x × x = 16128 x = 4 answer : a
Answer: a
Problem: find the sum of all odd numbers upto 100 .
Options: a ) 200 , b ) 1000 , c ) 2500 , d ) 3140 , e ) 3200
Rationale: "sol . the given numbers are 1 , 3 , 5 , 7 , . . . , 99 . this is an a . p . with a = 1 and d = 2 . let it contain n terms . then , 1 + ( n - 1 ) x 2 = 99 or n = 50 .  required sum = ( n / 2 ) ( first term + last term ) = 50 ( 1 + 99 ) / 2 = 2500 . answer c 2500"
Answer: c
Problem: two stations p and q are 110 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ?
Options: a ) 10.30 , b ) 10 , c ) 8.45 , d ) 9.3 , e ) 11
Rationale: "explanation : assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 110 = > 20 x + 25 ( x - 1 ) = 110 = > 45 x = 135 = > x = 3 means , they meet after 3 hours after 7 am , ie , they meet at 10 am . answer : b"
Answer: b
Problem: a milk man has 10 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :
Options: a ) 20 % , b ) 15 % , c ) 33.33 % , d ) 18 % , e ) none of these
Rationale: "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 10 liters of milk . therefore , profit percentage = 15 % . answer : b"
Answer: b
Problem: if * stands for / , / stands for - , + stands for * and - stands for + , then 9 / 8 * 7 + 5 - 10 = ?
Options: a ) 13.3 , b ) 10.8 , c ) 10.7 , d ) 11.4 , e ) 12.5
Rationale: 9 / 8 * 7 + 5 - 10 this expression becomes 9 - 8 / 7 * 5 + 10 after exchanging the symbols then the values for it would be 9 - 1.142 * 5 + 10 = 13.290 ( app ) = 13.3 answer : a
Answer: a
Problem: hcf and lcm two numbers are 12 and 396 respectively . if one of the numbers is 36 , then the other number is ?
Options: a ) 36 , b ) 66 , c ) 132 , d ) 264 , e ) 152
Rationale: "12 * 396 = 36 * x x = 132 answer : c"
Answer: c
Problem: what is the tens digit of 36 ^ 30 ?
Options: a ) 1 , b ) 7 , c ) 5 , d ) 3 , e ) 9
Rationale: "36 ^ 10 = 6 ^ 20 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 30 ( dont actually calculate full values ) and answer is b : 7"
Answer: b
Problem: a 4 digit number is such that the product of all of its digits is 126 . the sum of all the digits is equal to the 2 digit number formed by using thousands digit and tens digit ( 1000 digit in tens place & 10 digit in units place ) which in turn is equal to 19 . then difference of units and 1000 place of the number is , given that this difference is positive .
Options: a ) 1692 , b ) 1792 , c ) 1795 , d ) 1892 , e ) 1992
Rationale: the number is 1792 . let the number be represented as 1000 x + 100 y + 10 z + t acc to ques , xyzt = 126 x + y + z + t = 10 x + z = 19 so , number in thousands and tens place are 1 and 9 respectively . the remaining factor is 14 which is 7 * 2 so the number is 1792 . answer : b
Answer: b
Problem: p and q started a business investing rs . 54,000 and rs . 18,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 3 : 1 , b ) 4 : 3 , c ) 5 : 4 , d ) 6 : 5 , e ) 17 : 4
Rationale: "p : q = 54000 : 18000 = 3 : 1 . answer : a"
Answer: a
Problem: a man loses 1 / 3 rd of his money , then wins rs . 10 loses 1 / 3 rd of what he has and wins rs . 20 and finds that he has exactly what be had at the beginning . what was the amount he originally bad ?
Options: a ) 25 , b ) 36 , c ) 10 , d ) 48 , e ) 45
Rationale: let x be that amount so accordind to question , eqn will be like : ( ( ( x - x / 3 ) + 10 ) - ( ( ( x - x / 3 ) + 10 ) / 3 ) ) + 20 = x = > ( ( 2 x / 3 + 10 ) - ( ( 2 x / 3 + 10 ) / 3 ) ) + 20 = x = > 3 x - 4 x / 3 = 80 = > x = 48 answer : d
Answer: d
Problem: what is the probability of getting sum of 10 on rolling three dices ?
Options: a ) 28 / 216 , b ) 27 / 216 , c ) 29 / 216 , d ) 26 / 216 , e ) 25 / 216
Rationale: "the no of ways to roll three dies is 6 ^ 3 = 216 the possibles of getting sum as 10 is 631 = 3 ! = 6 622 = 3 ! / 2 ! = 3 541 = 3 ! = 6 523 = 3 ! = 6 442 = 3 ! / 2 ! = 3 433 = 3 ! / 2 ! = 3 total possibles for getting sum as 10 is 27 the probabilty is 27 / 216 answer : b"
Answer: b
Problem: for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "given that n * denotes the product of all the integers from 1 to n , inclusive so , 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 . now , notice that we can factor out 2 our of 6 ! + 2 so it can not be a prime number , we can factor out 3 our of 6 ! + 3 so it can not be a prime number , we can factor out 4 our of 6 ! + 4 so it can not be a prime number , . . . the same way for all numbers between 6 * + 2 = 6 ! + 2 and 6 * + 6 = 6 ! + 6 , inclusive . which means that there are no primes in this range . answer : a ."
Answer: a
Problem: a carpenter worked alone for 1 day on a job that would take him 6 more days to finish . he and another carpenter completed the job in 7 more days . how many days would it have taken the second carpenter to do the complete job working alone ?
Options: a ) 4.5 , b ) 7.5 , c ) 9.5 , d ) 14.5 , e ) 24.5
Rationale: "a carpenter worked only 1 day on something that takes him 6 more days . means ; carpenter finishes his work in 7 days . let his buddy finish the same task in x days . respective rates per day : 1 / 7 and 1 / x to complete 1 work : first guy worked for 5 days @ rate = 1 / 7 per day . second one worked for 7 days @ rate = 1 / x per day expression : days * rate = work 5 * 1 / 7 + 7 * 1 / x = 1 5 x + 49 = 7 x 2 x = 49 x = 24.5 days . ans : e"
Answer: e
Problem: if 4 is the remainder when m is divided by 10 , what is the remainder when 4 m is divided by 10 ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "we can put m = 10 * k + 4 . so 4 * m = 40 * k + 16 - - - > 40 * k + 16 = 10 * ( 4 * m + 1 ) + 6 - - - > the remainder is 6 . the answer is , therefore , ( c ) ."
Answer: c
Problem: for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 25 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 12 % , b ) 26 % , c ) 29 % , d ) 30 % , e ) 60 %
Rationale: in the first plot 25 % of 300 seeds germinated , so 0.25 x 300 = 75 seeds germinated . in the second plot , 35 % of 200 seeds germinated , so 0.35 x 200 = 70 seeds germinated . since 75 + 70 = 145 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 145 / 500 ) x 100 % , or 29 % . answer : c .
Answer: c
Problem: on the first day of her vacation , louisa traveled 240 miles . on the second day , traveling at the same average speed , she traveled 420 miles . if the 240 - mile trip took 3 hours less than the 420 - mile trip , what was the average speed , in miles per hour ?
Options: a ) 65 , b ) 50 , c ) 55 , d ) 60 , e ) 58
Rationale: "( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 240 / t = 420 / ( t + 3 ) - - > 4 / t = 7 / ( t + 3 ) - - > 4 t + 12 = 7 t - - - - > 3 t = 12 . t = 4 - - - - > ( rate ) = 240 / 4 = 60 answer : d"
Answer: d
Problem: the number of positive integers n in the range 12 ≤ n ≤ 40 such that the product ( n − 1 ) ( n − 2 ) . . . 3 . 2.1 is not divisible by n is
Options: a ) 5 , b ) 7 , c ) 13 , d ) 14 , e ) 16
Rationale: explanation : ( n - 1 ) ! is always divisible by n unless and untill n is a prime number e . g . ( 5 - 1 ) ! = 4 ! which is not divisible by 5 bcuz 5 is a prime number therefore , find all prime numbers in the range of 12 to 40 i . e 13 , 17 , 19 , 23 , 29 , 31 and 37 hence , the number of positive integers n is 7 . answer : b
Answer: b
Problem: 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,073 bacteria each . how many bacteria are there approximately ?
Options: a ) 10 ^ 7 , b ) 10 ^ 9 , c ) 10 ^ 8 , d ) 10 ^ 10 , e ) 10 ^ 11
Rationale: 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,073 bacteria each . how many bacteria are there approximately ? a . 10 ^ 7 b . 10 ^ 8 c . 10 ^ 9 d . 10 ^ 10 e . 10 ^ 11 - > due to approximately , 79 = 80 , 48 = 50 , 25,073 = 25,000 are derived , which makes ( 79 ) ( 48 ) ( 25,075 ) = ( 80 ) ( 50 ) ( 25,000 ) = 10 ^ 8 . the answer is c .
Answer: c
Problem: a set consists of 15 numbers , all are even or multiple of 5 . if 8 numbers are even and 10 numbers are multiple of 5 , how many numbers is multiple of 10 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "{ total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 15 = 8 + 10 - { both } + 0 ; { both } = 3 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : d ."
Answer: d
Problem: the greatest number that divides 2928 and 3240 leaving remainders 5 and 1 respectively is :
Options: a ) 74 , b ) 78 , c ) 79 , d ) 81 , e ) 85
Rationale: "explanation : 2928 - 5 = 2923 , 3240 - 1 = 3239 highest number that can divide 2923 and 3239 is hcf of numbers . hcf of 2923 and 3239 = 79 answer : c"
Answer: c
Problem: find large number from below question the difference of 2 no ' s is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1236 , b ) 1356 , c ) 1470 , d ) 1556 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"
Answer: e
Problem: a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 72 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480
Options: a ) 2000 , b ) 2100 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: 1 percent for 3 years = 72 1 percent for 1 year = 24 = > 100 percent = 2400 answer : e
Answer: e
Problem: a and b together can do a work in 3 days . if a alone can do it in 6 days . in how many days can b alone do it ?
Options: a ) 10 , b ) 99 , c ) 77 , d ) 55 , e ) 6
Rationale: "1 / 3 – 1 / 6 = 1 / 6 = > 6 answer : e"
Answer: e
Problem: a man is 26 years older than his studen . in two years , his age will be twice the age of his student . the present age of his student is :
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: let the student ' s present age be x years . then , man ' s present age = ( x + 26 ) years . ( x + 26 ) + 2 = 2 ( x + 2 ) x + 28 = 2 x + 4 x = 24 . answer : e
Answer: e
Problem: a = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set a and one integer from set b . what is the probability t that the sum of the two integers will equal 9 ?
Options: a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33
Rationale: rearrange the first set : a = { 54 , 32 } b = { 45 , 67 , 8 } as you can see numbers in each column ( the numbers of the same color ) give the sum of 9 . so there are 4 such pares possible , total # of pairs is 4 * 5 = 20 . t = favorable / total = 4 / 20 = 0.2 . answer : b . or : we can select any number from set a ( 4 / 4 = 1 ) but in this case we must select its matching pair from set b ( the number of the same color ) and since there are only one matching pair of this particular number in b then the probability of this is 1 / 5 . so , overall : t = 1 * 1 / 5 . answer : b .
Answer: b
Problem: the population of a bacteria culture doubles every 4 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
Options: a ) 10 , b ) 12 , c ) 14 , d ) 36 , e ) 18
Rationale: "this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 4 minutes so answer is 9 * 4 = 36 minutes answer ( d )"
Answer: d
Problem: how many pieces can a square pizza be cut into by making 4 linear cuts ?
Options: a ) 10
b ) 11
c ) 12
d ) 13
e ) 14
Rationale: 1 cut makes two pieces a second cut can make 4 pieces by cutting through 2 of the pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces b
Answer: b
Problem: two trains of length 220 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 28 , b ) 266 , c ) 990 , d ) 25 , e ) 11
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 220 + 280 = 500 m . the time required = d / s = 500 / 20 = 25 sec . answer : d"
Answer: d
Problem: we bought orange juice and apple juice at the store . a bottle of orange juice costs 70 cents and a bottle of apple juice costs 60 cents . we bought a total of 70 bottles for $ 46.20 . how many bottles of orange juice did we buy ?
Options: a ) 32 , b ) 36 , c ) 38 , d ) 42 , e ) 48
Rationale: let oj be the bottles of orange juice and let aj be the bottles of apple juice . ( oj ) + aj = 70 . aj = 70 - ( oj ) . 70 ( oj ) + 60 aj = 4620 . 70 ( oj ) + 60 ( 70 - oj ) = 4620 . 10 ( oj ) + 4200 = 4620 . oj = 42 . the answer is d .
Answer: d
Problem: if x is to be chosen at random from the integers between 1 to 7 , inclusive , and y is to be chosen at random from the integers between 7 and 11 , inclusive , what is the probability that x + y will be even ?
Options: a ) 3 / 5 , b ) 4 / 7 , c ) 5 / 7 , d ) 18 / 35 , e ) 23 / 35
Rationale: "x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 3 / 7 * 2 / 5 = 6 / 35 p ( x and y are both odd ) = 4 / 7 * 3 / 5 = 12 / 35 p ( x + y is even ) = 6 / 35 + 12 / 35 = 18 / 35 the answer is d ."
Answer: d
Problem: a glucose molecule contains 6 carbon , 12 hydrogen and 6 oxygen atoms . during photosynthesis , green plants create glucose daily . if , over a period of 12 days , an eucalyptus plant ( a green plant ) creates 12000 molecules of glucose then approximately how many more atoms of hydrogen than carbon are created on average per day ?
Options: a ) 60,000 , b ) 6,000 , c ) 2,500 , d ) 250 , e ) 0
Rationale: solution : we know that 12,000 glucose molecules are created over a period of 12 days . therefore 12,000 / 12 = 1,000 glucose molecules are created on average per day . each glucose molecule contains 6 carbon atoms and 12 hydrogen atoms . so 1,000 glucose molecules contain 6 × 1,000 = 6,000 carbon atoms and 12 × 1,000 = 12,000 hydrogen atoms . the difference is 12,000 – 6,000 = 6,000 . the correct answer is b .
Answer: b
Problem: a basketball player practices 2 hours a day monday through friday . how many hours must he practice saturday and sunday combined if he wants to practice an average ( arithmetic mean ) of 3 hours a day for the 7 day week ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: total number of hours practiced mon through fri : 5 * 2 = 10 total number of hours that will be practiced in a 7 day week considering 3 hours a day average : 7 * 3 = 21 thus 21 - 10 = 11 hours still need to be practiced ( on sat and sun combined ) d
Answer: d
Problem: when the positive integer k is divided by the positive integer n , the remainder is 11 . if k / n = 83.2 , what is the value of n ?
Options: a ) 9 , b ) 20 , c ) 55 , d ) 70 , e ) 81
Rationale: here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : e
Answer: e
Problem: what sum of money will produce rs . 90 as simple interest in 4 years at 4 1 / 2 percent ?
Options: a ) rs . 550 , b ) rs . 650 , c ) rs . 600 , d ) rs . 500 , e ) rs . 700
Rationale: "explanation : 90 = ( p * 4 * 9 / 2 ) / 100 90 = 36 p / 100 p = 500 answer : option d"
Answer: d
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 7 seconds . find the length of the faster train ?
Options: a ) 70 , b ) 20 , c ) 30 , d ) 75 , e ) 15
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 7 * 10 = 70 m . the length of the faster train = 70 m . answer : a"
Answer: a
Problem: if the average ( arithmetic mean ) of a and b is 80 , and the average of b and c is 180 , what is the value of a − c ?
Options: a ) − 220 , b ) − 200 , c ) 100 , d ) 135 , e ) it can not be determined from the information given
Rationale: "a + b = 160 b + c = 360 a - c = - 200 . imo option b ."
Answer: b
Problem: exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 8 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 24 , b ) 35 , c ) 39 , d ) 60 , e ) 65
Rationale: "the total number of the people in the room must be a multiple of both 7 and 8 ( in order 3 / 7 and 5 / 8 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 8 , which is 56 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 56 people in the room . therefore there are 3 / 7 * 56 = 24 people in the room under the age of 21 . answer : a ."
Answer: a
Problem: alice picked a number of pears , each of which she sold , canned , or poached . she canned 20 percent more than she poached , and she poached 50 percent less than she sold . if there were a total of 42 pears , then how many pears did she sell ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: let x be the amount of pears that she sold . then she poached 0.5 x . then she canned 1.2 * 0.5 x = 0.6 x . the total amount of pears is x + 0.5 x + 0.6 x = 2.1 x the fraction of pears that she sold is 1 / 2.1 = 10 / 21 . the number of pears she sold is ( 10 / 21 ) * 42 = 20 . the answer is a .
Answer: a
Problem: the value of x + x ( x ^ x ) when x = 10 is
Options: a ) 100000000010 , b ) 10000000010 , c ) 10000000000 , d ) 1200000000 , e ) 12000000010
Rationale: solution : x + x ( x ^ x ) put the value of x = 10 in the above expression we get , 10 + 10 ( 10 ^ 10 ) = 10 + 10 ( 10 ã — 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 ) = 10 + 10 ( 10000000000 ) = 10 + 100000000000 = 100000000010 answer : ( a )
Answer: a
Problem: if k is a non - negative integer and 30 ^ k is a divisor of 929260 then 3 ^ k - k ^ 3 =
Options: a ) 0 , b ) 1 , c ) 45 , d ) 130 , e ) 520
Rationale: 9 + 2 + 9 + 2 + 6 + 0 = 28 , so this number is not divisible by 3 and thus not divisible by 30 . therefore , k = 0 3 ^ k - k ^ 3 = 1 - 0 = 1 the answer is b .
Answer: b
Problem: a sum was put at simple interest at a certain rate for 4 years had it been put at 2 % higher rate , it would have fetched 56 more . find the sum .
Options: a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) none of these
Rationale: "difference in s . i . = p × t / 100 ( r 1 − r 2 ) ⇒ 56 = p × 4 × 2 / 100 ( ∵ r 1 - r 2 = 2 ) ⇒ p = 56 × 100 / 4 × 2 = 700 answer c"
Answer: c
Problem: a vending machine randomly dispenses 4 different types of fruit candy . there are twice as many apple candies as orange candies , twice as many strawberry candies as grape candies , and twice as many apple candies as strawberry candies . if each candy cost $ 0.1 , and there are exactly 90 candies , what is the minimum amount of money required to guarantee that you would buy at least 3 of each type of candy ?
Options: a ) $ 8.30 , b ) $ 20.75 , c ) $ 22.50 , d ) $ 42.75 , e ) $ 45.00
Rationale: let number of apple , orange , strawberry and grape candies be a , o , s and g respectively . a = 2 o s = 2 g a = 2 s a = 4 g a + o + s + g = 90 = > a + a / 2 + a / 2 + a / 4 = 90 = > 9 a / 4 = 90 = > a = 40 o = 20 s = 20 g = 10 cost of each candy = . 1 $ mininum amount of money required to guarantee that you would buy at least three of each type of candy we can buy 40 apple candies , 20 orange candies , 20 strawberry candies and 3 grape candies to ensure atleast 3 of each type of candies . total = 83 candies amount required = 83 * . 1 = 8.30 $ answer a
Answer: a
Problem: a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 4 days . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 0.1 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) 0.5
Rationale: "b work 1 / 8 * 4 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 take reciprocal 4 * remaining work = 2 * 1 / 4 = 0.5 answer : e"
Answer: e
Problem: the tax on a commodity is diminished by 20 % and its consumption increased by 25 % . the effect on revenue is ?
Options: a ) 2 % decrease , b ) 8 % decrease , c ) 9 % decrease , d ) 0 % no change , e ) 2 % decrease
Rationale: "100 * 100 = 10000 80 * 125 = 10000 - - - - - - - - - - - 10000 - - - - - - - - - - - 0 100 - - - - - - - - - - - ? = > 0 % no change answer : d"
Answer: d
Problem: if n is a prime number greater than 4 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 2 , c ) 1 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question including the one under the spoiler . but the easiest way is as follows : since we can not have two correct answersjust pick a prime greater than 4 , square it and see what would be the remainder upon division of it by 12 . n = 7 - - > n ^ 2 = 49 - - > remainder upon division 49 by 12 is 1 . answer : c ."
Answer: c
Problem: a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 3680 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) s . 380 , b ) s . 600 , c ) s . 460 , d ) s . 400 , e ) s . 480
Rationale: "explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 3680 × ( 1 / 8 ) = 460 answer : option c"
Answer: c
Problem: in what time will a train 100 meters long cross an electric pole , if its speed is 36 km / hr
Options: a ) 8.5 seconds , b ) 10 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds
Rationale: "first convert speed into m / sec speed = 36 * ( 5 / 18 ) = 10 m / sec time = distance / speed = 100 / 10 = 10 seconds answer : b"
Answer: b
Problem: if x / ( 12 p ) is an odd prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 22 , b ) 33 , c ) 44 , d ) 66 , e ) 72
Rationale: "x / ( 12 p ) = odd prime number x = odd prime number * 11 p least value of x = lowest odd prime number * 11 * lowest value of p = 3 * 12 * 2 = 72 answer e"
Answer: e
Problem: given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] – 16 = f ( x – 6 ) ?
Options: a ) 1 , b ) 4 , c ) 6 , d ) 7 , e ) 13
Rationale: "2 ( 3 x - 5 ) - 16 = 3 ( x - 6 ) - 5 3 x = 3 x = 1 the answer is a ."
Answer: a
Problem: a batsman in his 12 th innings makes a score of 80 and thereby increases his average by 3 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 47
Rationale: let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 3 ) + 80 ∴ x = 47 answer e
Answer: e
Problem: each of the three people individually can complete a certain job in 4 , 5 , and 8 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?
Options: a ) 9 / 20 , b ) 11 / 20 , c ) 11 / 32 , d ) 13 / 40 , e ) 17 / 40
Rationale: "the two slowest people work at rates of 1 / 5 and 1 / 8 of the job per hour . the sum of these rates is 1 / 5 + 1 / 8 = 13 / 40 of the job per hour . the answer is d ."
Answer: d
Problem: a train travels from new york to chicago , a distance of approximately 840 miles , at an average rate of 60 miles per hour and arrives in chicago at 7 : 00 in evening , chicago time . at what hour in the morning , new york time , did the train depart for chicago ? ( note : chicago time is one hour earlier than new york time )
Options: a ) 3 : 00 , b ) 4 : 00 , c ) 5 : 00 , d ) 6 : 00 , e ) 7 : 00
Rationale: "7 : 00 in evening in chicago = 8 : 00 in evening in new york . so , the train was in chicago 8 : 00 in the evening , new york time . the trip took t = d / r = 840 / 60 = 14 hours . therefore , the train depart from new york at 8 : 00 - 14 hours = 6 : 00 in the morning , new york time . answer : d ."
Answer: d
Problem: if the ratio of a to b is 4 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
Options: a ) 4 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6
Rationale: a : b = 4 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 4 : 15 answer a
Answer: a
Problem: the h . c . f . of two numbers is 63 and the other two factors of their l . c . m . are 11 and 17 . the larger of the two numbers is :
Options: a ) 3421 , b ) 2132 , c ) 1111 , d ) 4323 , e ) 1071
Rationale: ": explanation : clearly , the numbers are ( 63 x 11 ) and ( 63 x 17 ) . { \ color { blue } \ therefore } larger number = ( 63 x 17 ) = 1071 . answer : e ) 1071"
Answer: e
Problem: a rectangular swimming pool is 10 feet by 12 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 360 square feet . what is the width of the deck ?
Options: a ) 7 , b ) 2 , c ) 3 , d ) 4 , e ) 6
Rationale: "let the width = w total area of the pool and deck = ( 2 w + 10 ) ( 2 w + 12 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 14 * 16 has unit digit 4 . . . . . . . . . . eliminate b ) 2.5 feet . . . . . . . . . 15 * 17 has unit digit 5 . . . . . . . . . . eliminate c ) 3 feet . . . . . . . . . . . . 16 * 18 has unit digit 8 . . . . . . . . . . . eliminate d ) 4 feet . . . . . . . . . . . . 18 * 20 has unit digit 0 . . . . . . . . . . . hold e ) 5 feet . . . . . . . . . . . . 20 * 22 has unit digit 0 . . . . . . . . . . . eliminate ( bigger size ) answer : d w = 4"
Answer: d
Problem: find the probability that a leap year selected at random will not have 53 sundays or mondays .
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7
Rationale: "there are 366 days in a leap year : 52 weeks and 2 more days . so , 52 sundays , 52 mondays and 2 days . these 2 days can be : { mon , tue } , { tue , wed } , { wed , thu } , { thu , fri } , { fri , sat } , { sat , sun } and { sun , mon } ( 7 cases ) . in order to have 53 sundays or 53 mondays we should have either { mon , tue } { sat , sun } or { sun , mon } case . the probability of that is 3 / 7 . so probability of not having 53 sundays or mondays , probability is 1 - 3 / 7 = 4 / 7 answer : c ."
Answer: c
Problem: a copy machine , working at a constant rate , makes 25 copies per minute . a second copy machine , working at a constant rate , makes 55 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?
Options: a ) 90 , b ) 2,400 , c ) 4,500 , d ) 5,400 , e ) 324,000
Rationale: "together the two machines make 25 + 55 = 80 copies per minute . so , in half an hour they will make 80 * 30 = 2,400 copies . answer : b ."
Answer: b
Problem: a student multiplied a number by 3 / 5 instead of 5 / 3 . what is the percentage error .
Options: a ) 64 % , b ) 65 % , c ) 66 % , d ) 67 % , e ) none of these
Rationale: "explanation : let the number be x , then , 5 / 3 − 3 / 5 = 16 / 15 x error % = ( 16 / 15 x ∗ 3 / 5 ∗ 100 ) option a"
Answer: a
Problem: solve the given equation 9 ^ y = 3 ^ 12 , what is y ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 3 ^ 2 y = 3 ^ 12 2 y = 12 , therefore y = 6 e
Answer: e
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 5 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) 2277 , b ) 2977 , c ) 2677 , d ) 4530 , e ) 1971
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 5 = rs . 4530 answer : d"
Answer: d
Problem: a , b and c started a partnership business by investing rs . 30000 , rs . 45000 , rs . 50000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ?
Options: a ) 70000 , b ) 60000 , c ) 80000 , d ) 90000 , e ) 50000
Rationale: "a : b : c = 30000 : 45000 : 50000 = 6 : 9 : 10 let total profit = p then p ã — 10 / 25 = 36000 p = ( 36000 ã — 25 ) / 10 = 90000 answer is d ."
Answer: d
Problem: if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 4 is subtracted and divided by 10 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3
Rationale: "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 4 ) / 10 = ( 54 - 4 ) / 10 = 5 answer : option d"
Answer: d
Problem: integer m has 4 different prime factors and n has 3 different prime factors . if m and n has the greatest common factor of 15 , how many different prime factors does mn have ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: as m and n has gcf of 15 , 3 * 5 should be common factor for both m and n . m = 3 * 5 * p 1 * p 2 n = 3 * 5 * p 3 mn = 3 ^ 2 * 5 ^ 2 * p 1 * p 2 * p 3 mn has prime numbers of 3,5 , p 1 , p 2 p 3 b
Answer: b
Problem: if x ^ 2 + ( 1 / x ^ 2 ) = 5 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 23 , b ) 11 , c ) 12 , d ) 14 , e ) 15
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 5 ^ 2 - 2 = 23 . thus , the answer is a ."
Answer: a
Problem: on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 609 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 2 % , b ) 3 % , c ) 4 % , d ) 5 % , e ) 6 %
Rationale: "difference in c . i . and s . i for 2 years = $ 609 - $ 600 = $ 9 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 9 rate = ( 100 * 9 ) / ( 300 ) = 3 % the answer is b ."
Answer: b
Problem: in arun ' s opinion , his weight is greater than 62 kg but leas than 72 kg . his brother does not agree with arun and he thinks that arun ' s weight is greater than 60 kg but less than 70 kg . his mother ' s view is that his weight can not be greater than 65 kg . if all of them are correct in their estimation , what is the average of diferent probable weights of arun ?
Options: a ) 86.5 kg , b ) 63.5 kg , c ) 46.5 kg , d ) 26.5 kg , e ) 16.5 kg
Rationale: "let arun ' s weight be x kg . according to arun , 62 < x < 72 . according to arun ' s brother , 60 < x < 70 . according to arun ' s mother , x < 65 . the values satisfying all the above conditions are 63 and 64 . required average = ( 63 + 64 ) / 2 = 63.5 kg answer : b"
Answer: b
Problem: x and y are two towns . ganesh covers the distance from x to y at an average speed of 60 km / hr . however , he covers the distance from y to x at an average speed of 36 km / hr . his average speed during the whole journey in km / hr . is :
Options: a ) 45 , b ) 43 , c ) 40 , d ) 38 , e ) 29
Rationale: solution : average speed = 2 xy / x + y = 2 * 60 * 36 / 60 + 36 = 45 answer : a
Answer: a