regisss/math_qa huggingface dataset:
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 49 hours and 25 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 9 , b ) 5 : 7 , c ) 4 : 5 , d ) 4 : 1 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 25 : √ 49 = 5 : 7 answer : b"
Answer: b
Problem: the area of a square is equal to 2 times the area of a rectangle of dimensions 8 cm * 64 cm . what is the perimeter of the square ?
Options: a ) 482 , b ) 268 , c ) 800 , d ) 128 , e ) 632
Rationale: "area of the square = s * s = 2 ( 8 * 64 ) = > s = 4 * 8 = 32 cm perimeter of the square = 4 * 32 = 128 cm . answer : d"
Answer: d
Problem: total dinning bill for 6 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 40.44 , c ) 34.66 , d ) 32.29 , e ) 33.16
Rationale: "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 6 = 40.44 answer : b"
Answer: b
Problem: there are 7 baskets numbered from 1 to 7 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 90 , b ) 120 , c ) 250 , d ) 720 , e ) 910
Rationale: "each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 = 7 * 8 / 2 = 28 apples . the total number of apples taken by 10 children is 10 * 28 = 280 the number of apples left in the end is 1000 - 280 = 720 apples . the answer is d ."
Answer: d
Problem: there are 400 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) none of these
Rationale: as per question stem 2 / 5 m ( portion of men employees who are managers ) + 400 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 400 = 2 / 5 t , or 2 / 5 ( t - m ) = 400 , from here we get that t - m = 1000 , that would be total number of female employees and the answer ( c )
Answer: c
Problem: a and b together can do a work in 6 days . if a alone can do it in 42 days . in how many days can b alone do it ?
Options: a ) 11 , b ) 7 , c ) 8 , d ) 20 , e ) 25
Rationale: "b 7 1 / 6 â € “ 1 / 42 = 1 / 7 = > 7"
Answer: b
Problem: a bucket full of nuts was discovered by the crow living in the basement . the crow eats a fifth of the total number of nuts in 8 hours . how many hours in total will it take the crow to finish a quarter of the nuts ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: in one hour , the crow eats 1 / 40 of the nuts . ( 1 / 4 ) / ( 1 / 40 ) = 10 hours the answer is b .
Answer: b
Problem: if all the numbers between 11 and 100 are written on a piece of paper . how many times will the number 4 be used ?
Options: a ) 87 , b ) 267 , c ) 68 , d ) 26 , e ) 21
Rationale: we have to consider the number of 4 ' s in two digit numbers . _ _ if we fix 4 in the 10 th place , unit place be filled with 10 ways . if we fix 4 in units place , 10 th place be filled with 9 ways ( 0 is not allowed ) so total 19 ways . alternatively : answer : a
Answer: a
Problem: the length and breadth of a square are increased by 40 % and 30 % respectively . the area of the rectangle so formed exceeds the area of the square by ?
Options: a ) 82 %
b ) 78 %
c ) 80 %
d ) 90 %
e ) none of these
Rationale: since side 1 x side 2 = area therefore , net % change in area = ( x + y + xy / 100 ) % = [ 40 + 30 + ( 40 x 30 ) / 100 ] % or 82 % . therefore , area is increased by 82 % . answer : a
Answer: a
Problem: when asked what the time is , a person answered that the amount of time left is 2 / 6 of the time already completed . what is the time .
Options: a ) 2 pm , b ) 9 pm , c ) 3 pm , d ) 6 pm , e ) 7 pm
Rationale: a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 2 / 6 x ⇒ x = 18 time is 6 pm answer : d
Answer: d
Problem: a walks at 10 kmph and 7 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?
Options: a ) 100 km , b ) 140 km , c ) 50 km , d ) 120 km , e ) 200 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 7 hours . x / 10 - x / 20 = 7 x = 140 km answer is b"
Answer: b
Problem: the length of a rectangualr hll is 5 m more than its breadth . the area of the hall is 750 m . the length of the hall is
Options: a ) 15 m
b ) 22.5 m
c ) 25 m
d ) 30 m
e ) none
Rationale: solution let the length = xmetres . then length = ( x + 5 ) metres . then , x ( x + 5 ) = 750 = x ² + 5 x - 750 = 0 ( x + 30 ) ( x - 25 ) = 0 x = 25 . answer c
Answer: c
Problem: how many distinct integer values of n satisfy the inequality | | n - 3 | + 2 | ≤ 12 ?
Options: a ) 15 , b ) 16 , c ) 12 , d ) 18 , e ) 19
Rationale: "so i can write this as in - 3 i + 2 < = 12 or in - 3 i < = 10 so n can have - 7 to 13 = 12 true values . . . . c"
Answer: c
Problem: if a = 105 and a ^ 3 = 21 * 35 * 45 * b , what is the value of b ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 35 = 7 * 5 45 = 3 * 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 7 * 5 * 3 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 2 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 ^ 2 * 7 ^ 2 b = 5 * 7 = 35 correct answer a ."
Answer: a
Problem: a thief is spotted by a policeman from a distance of 175 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
Options: a ) 350 m , b ) 200 m , c ) 400 m , d ) 700 m , e ) none of them
Rationale: relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 175 m / 1000 ) x 1 / 2 hr = 7 / 80 hr . in 7 / 80 hrs , the thief covers a distance of 8 x 7 / 80 km = 7 / 10 km = 700 m answer is d .
Answer: d
Problem: in an election between two candidates , one got 60 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 2000 , the number of valid votes that the other candidate got , was :
Options: a ) 1200 , b ) 750 , c ) 800 , d ) 600 , e ) 900
Rationale: "number of valid votes = 80 % of 2000 = 1600 . valid votes polled by other candidate = 40 % of 2000 = ( 40 / 100 ) x 2000 = 800 answer = c"
Answer: c
Problem: a semicircle has a radius of 20 . what is the approximate perimeter of the semicircle ?
Options: a ) 50 , b ) 25 , c ) 86 , d ) 75 , e ) 102
Rationale: "circumference of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 20 + 2 * 20 = 102.8 approximately 102 answer e"
Answer: e
Problem: amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.5 km ?
Options: a ) 375 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m
Rationale: "a 375 m distance covered by amar = 18 / 4.8 ( 1.5 km ) = 3 / 8 ( 1500 ) = 375 m"
Answer: a
Problem: a prize of $ 400 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?
Options: a ) $ 100 , b ) $ 220 , c ) $ 280 , d ) $ 300 , e ) $ 360
Rationale: "total value of the prize = $ 400 number of people = 20 2 / 5 of 400 ( = $ 160 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 400 - 160 = $ 240 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 240 - 140 = $ 100 , hence a is the correct answer ."
Answer: a
Problem: the average height of 35 boys in a class was calculated as 181 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?
Options: a ) 178.27 cm , b ) 179.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm
Rationale: "calculated average height of 35 boys = 181 cm . wrong total height of 35 boys = 181 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - 60 / 35 cm = 181 cm - 1.71 cm = 179.29 cm . answer : b"
Answer: b
Problem: if 10 typists can type 20 letters in 20 minutes , then how many letters will 40 typists working at the same rate complete in 1 hour ?
Options: a ) 220 , b ) 210 , c ) 200 , d ) 240 , e ) 260
Rationale: "no . of letters typing by 10 typists in 20 minutes = 20 no . of letters typing by 10 typists in 60 minutes = 20 * 3 = 60 no . of letters typing by 40 typists in 60 minutes = 60 / 10 * 40 = 240 answer : d"
Answer: d
Problem: john and steve are speed walkers in a race . john is 16 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
Options: a ) 13 seconds , b ) 17 seconds , c ) 36 seconds , d ) 34 seconds , e ) 51 seconds
Rationale: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 16 + 2 - - - > 0.5 t = 18 - - - > t = 36 seconds . c is the correct answer ."
Answer: c
Problem: a lady builds 9 cm length , 12 cm width , and 3 cm height box using 3 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 107 , b ) 108 , c ) 109 , d ) 110 , e ) 111
Rationale: "number of cubes required = volume of box / volume of cube = 9 * 12 * 3 / 3 = 108 cubes answer : b"
Answer: b
Problem: dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 58 of gas ?
Options: a ) 242 , b ) 353 , c ) 464 , d ) 575 , e ) 686
Rationale: "58 / 4 = 14.5 gallons 14.5 * 32 = 464 miles the answer is c ."
Answer: c
Problem: of the two - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 24 , b ) 9 , c ) 72 , d ) 144 , e ) 216
Rationale: of the two - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for x - 9 ways ; # of permutations of 3 digits in xx - 2 ! / 2 ! total : 9 * 2 ! / 2 ! = 9 . answer : b .
Answer: b
Problem: . 3 + 33 + 333 + 33.3 = ?
Options: a ) 362.33 , b ) 399.6 , c ) 702.33 , d ) 702 , e ) none of them
Rationale: ". 3 33 333 33.3 - - - - - - - - - - 399.6 - - - - - - - - - - answer is b"
Answer: b
Problem: if a certain number x is divided by 82 , the reminder is 5 . what is the reminder when x + 17 is divided by 41 ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 22 , e ) 18
Rationale: "x can be written as 82 k + 5 or x = 5 , 87,169 , etc . x + 17 = 82 k + 5 + 17 = 82 k + 22 or x + 17 = 22,104 , 186 etc . when divided by 41 , we will get the remainder 22 . d"
Answer: d
Problem: at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 15 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 15 pieces of fruit is 48 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 45 cents ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 8 , e ) 9
Rationale: let number of apples = a number of oranges = b a + b = 15 - - - 1 . 48 = ( . 4 a + . 6 b ) / 15 = > 48 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 9 b = 6 let the number of oranges put back = c 45 * ( 15 - c ) = 40 * 9 + 60 ( 6 - c ) = > c = 3 answer c
Answer: c
Problem: on the richter scale , which measures the total amount of energy released during an earthquake , a reading of x - 1 indicates one - tenth the released energy as is indicated by a reading of x . on that scale , the frequency corresponding to a reading of 5 is how many times as great as the frequency corresponding to a reading of 3 ?
Options: a ) 100 , b ) 200 , c ) 10 ^ 4 , d ) 10 ^ 5 , e ) 10 ^ 6
Rationale: if richter scale reading goes from x - 1 to x it will be 10 if richter scale reading goes from 3 to 4 it will be 10 if richter scale reading goes from 4 to 5 it will be 10 so it will from 3 to 5 i . e 4,5 = 10 * 10 = 10 ^ 2 answer is a
Answer: a
Problem: the balance of a trader weighs 8 % less than it should . still the trader marks up his goods to get an overall profit of 30 % . what is the mark up on the cost price ?
Options: a ) 40 % , b ) 19 % , c ) 25 % , d ) 16.66 % , e ) 9 %
Rationale: "the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 92 gms because it weighs 8 % less . say , the cost price is $ 92 ( $ 1 / gm ) . since he gets a profit of 30 % , the selling price must be 92 + ( 30 / 100 ) * 90 = $ 119 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 119 , the mark up is simply 19 % ans : b ."
Answer: b
Problem: 115 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 12 liters , b ) 32 liters , c ) 46 liters , d ) 50 liters , e ) 34 liters
Rationale: "milk = 3 / 5 * 115 = 69 liters water = 46 liters 69 : ( 46 + p ) = 3 : 4 138 + 3 p = 276 = > p = 46 46 liters of water are to be added for the ratio become 3 : 4 . answer : c"
Answer: c
Problem: a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1406 ?
Options: a ) s . 109 , b ) s . 108 , c ) s . 100 , d ) s . 95 , e ) s . 102
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1406 74 x = 1406 = > x = 19 5 x = 95 rs . answer : d"
Answer: d
Problem: efrida and frazer who live 10 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is four miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "it ' s a simple geometry problem . look at the diagram below : answer : a ."
Answer: a
Problem: 2 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.05555 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: "approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 2 / 36 = . 05 something answer ( b )"
Answer: b
Problem: if p ( a ) = 4 / 7 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .
Options: a ) 7 / 25 , b ) 3 / 25 , c ) 8 / 35 , d ) 2 / 13 , e ) 3 / 17
Rationale: p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 4 / 7 . 2 / 5 p ( a n b ) = 8 / 35 . c
Answer: c
Problem: bottle r contains 250 capsules and costs $ 6.25 . bottle t contains 100 capsules and costs $ 3.0 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?
Options: a ) $ 0.25 , b ) $ 0.12 , c ) $ 0.05 , d ) $ 0.003 , e ) $ 0.005
Rationale: "cost per capsule in r is 6.25 / 250 = 0.625 / 25 = 0.025 cost per capsule in t is 3.00 / 100 = 0.03 the difference is 0.005 the answer is e"
Answer: e
Problem: for what value of “ k ” will the equation ( 2 kx 2 + 5 kx + 2 ) = 0 have equal roots ?
Options: a ) 2 / 7 , b ) 9 / 4 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2
Rationale: for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 5 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 16 / 25 answer : c
Answer: c
Problem: the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams w ?
Options: a ) w = 16 , b ) w = 32 , c ) 64 , d ) 128 , e ) 512
Rationale: "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"
Answer: b
Problem: it takes 30 days to fill a laboratory dish with bacteria . if the size of the bacteria doubles each day , how long did it take for the bacteria to fill one sixteenth of the dish ?
Options: a ) 16 days , b ) 26 days , c ) 27 days , d ) 28 days , e ) 29 days
Rationale: the bacteria doubles each day , so after 29 days , the dish was half full . after 28 days , the dish was one quarter full . after 27 days , the dish was one eighth full . after 26 days , the dish was one sixteenth full . the answer is b .
Answer: b
Problem: some persons can do a piece of work in 8 days . two times the number of these people will do half of that work in ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "8 / ( 2 * 2 ) = 2 days answer : a"
Answer: a
Problem: rectangular tile each of size 35 cm by 30 cm must be laid horizontally on a rectangular floor of size 1000 cm by 210 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 600
b ) 400
c ) 200
d ) 500
e ) 100
Rationale: area of tile = 35 * 30 = 1050 area of floor = 1000 * 210 = 210000 no of tiles = 210000 / 1050 = 200 so , the no of tile = 200 answer : c
Answer: c
Problem: ( 1000 ) 7 ÷ ( 10 ) 18 = ?
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
Rationale: "explanation : = ( 103 ) 7 / ( 10 ) 18 = ( 10 ) 21 / ( 10 ) 18 = 10 ( 3 ) = 1000 option c"
Answer: c
Problem: the length of a rectangular garden is 2 feet longer than 3 times its width . if the perimeter of the garden is 100 feet , find the width and the length of the garden .
Options: a ) 80 , b ) 90 , c ) 100 , d ) 70 , e ) 110
Rationale: "let l and w be the length and width of the garden . the statement ` ` the length of a rectangular garden is 2 feet longer than 3 times its width ' ' may be formulated by l = 2 + 3 w the formula for the perimeter is given by p = 2 l + 2 w substitute p and l in the above equation by 100 and 2 + 3 w respectively to obtain 100 = 2 ( 2 + 3 w ) + 2 w solve for w and l w = 12 and l = 2 + 3 w = 38 . check that the perimeter of the rectangular garden is 100 p = 2 l + 2 w = 76 + 24 = 100 answer c"
Answer: c
Problem: if a certain toy store ' s revenue in november was 3 / 5 of its revenue in december and its revenue in january was 1 / 6 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 ) 3 / 2 , b ) 5 / 4 , c ) 10 / 3 , d ) 20 / 7 , e ) 25 / 9
Rationale: n = 3 d / 5 j = n / 6 = d / 10 the average of november and january is ( n + j ) / 2 = 7 d / 10 / 2 = 7 d / 20 d is 20 / 7 times the average of november and january . the answer is d .
Answer: d
Problem: mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 462 ?
Options: a ) 25.6 % , b ) 21 % , c ) 20 % , d ) 19 % , e ) none of these
Rationale: "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 462 , discount = 621 - 462 = 159 discount % = 159 / 621 * 100 = 25.6 % answer : a"
Answer: a
Problem: the cost price of an book is 64 % of the marked price . calculate the gain percent after allowing a discount of 16 % ?
Options: a ) 31.25 % , b ) 35.5 % , c ) 37.5 % , d ) 39.5 % , e ) 30.5 %
Rationale: "let marked price = $ 100 . then , c . p . = $ 64 , s . p . = $ 84 gain % = 20 / 64 * 100 = 31.25 % . a"
Answer: a
Problem: what is the value of 3 x ^ 2 − 1.8 x + 0.8 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0.8 , c ) 0.3 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 1.8 x + 0.8 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.8 = 0 + 0.8 = 0.8 answer : b"
Answer: b
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 64.50 , his capital is ?
Options: a ) 24,602 , b ) 28,888 , c ) 25,800 , d ) 24,628 , e ) 24,6012
Rationale: "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 64.50 32 x - 31 x = 6450 * 4 x = 25,800 . answer : c"
Answer: c
Problem: what is the sum of all digits for the number 10 ^ 27 - 48 ?
Options: a ) 212 , b ) 222 , c ) 232 , d ) 242 , e ) 252
Rationale: "10 ^ 27 is a 28 - digit number : 1 followed by 27 zeros . 10 ^ 27 - 48 is a 27 - digit number : 25 9 ' s and 52 at the end . the sum of the digits is 25 * 9 + 5 + 2 = 232 . the answer is c ."
Answer: c
Problem: what is the units digit of ( 493 ) ( 913 ) ( 381 ) ( 756 ) ( 29 )
Options: a ) 0 , b ) 1 , c ) 4 , d ) 3 , e ) 6
Rationale: "just multiply the digits in the units place for each term and you will get the answer . it should be 0 . you got a 5 as a unit digit and an even number term . so the multiplication of this will definitely yield a 0 . answer has to be 0 . i also tried it using the calculator and the answer is 3 . imo d ."
Answer: d
Problem: the greatest number which on dividing 1557 and 2037 leaves remainders 7 and 5 respectively , is :
Options: a ) 123 , b ) 127 , c ) 2 , d ) 305 , e ) 505
Rationale: "explanation : required number = h . c . f . of ( 1557 - 7 ) and ( 2037 - 5 ) = h . c . f . of 1550 and 2032 = 2 . answer : c"
Answer: c
Problem: there is a right angle triangle inside a circle of diameter 18 cm . inside this triangle , there is another circle of diameter 6 cm . find the perimeter of the triangle .
Options: a ) 24 cm
b ) 36 * 2 ^ 1 / 2 cm
c ) 36 cm
d ) 54 cm
e ) 42 cm
Rationale: 1 ) the radius of the incircle of a right triangle with legs a and b and hypotenuse c is r = ( a + b - c ) / 2 2 ) the radius of the circumcircle is half the length of the hypotenuse r = c / 2 3 ) thus the sum of the circumradius and the inradius is half the sum of the legs r + r = ( a + b ) / 2 from 2 nd rule c = 18 cm from 3 rd rule a + b = 2 * ( 9 + 3 ) = 24 cm hence perimeter a + b + c = 24 + 18 = 42 cm answer : e
Answer: e
Problem: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 14 % ?
Options: a ) 20 % , b ) 29 % , c ) 13 1 / 30 % , d ) 12 % , e ) 13 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 86 2 / 3 sp 1 = 86 sp 1 = 129 100 - - - 29 = > 29 % answer : b"
Answer: b
Problem: p and q can complete a work in 10 days and 6 days respectively . p alone started the work and q joined him after 2 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 26 days
Rationale: "explanation : work done by p in 1 day = 1 / 10 work done by q in 1 day = 1 / 6 work done by p in 2 days = 2 ã — ( 1 / 10 ) = 1 / 5 remaining work = 1 â € “ 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 10 + 1 / 6 = 4 / 15 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 4 / 15 ) = 3 total days = 2 + 3 = 5 answer : option a"
Answer: a
Problem: david is 18 years older than his daughter rosy . in 6 years david will be twice as old as rosy . what is rosy current age .
Options: a ) 12 , b ) 14 , c ) 18 , d ) 24 , e ) 23
Rationale: now : rosy = x , david = x + 18 in 6 years rosy = x + 6 , david = x + 18 + 6 or 2 ( x + 6 ) x + 24 = 2 x + 12 x = 12 rosy is 12 years old answer : a
Answer: a
Problem: you collect pens . suppose you start out with 20 . mike gives you another 22 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 65 , d ) 42 , e ) 43
Rationale: solution start with 20 pens . mike gives you 22 pens : 20 + 22 = 42 pens . cindy doubles the number of pens you have : 42 ã — 2 = 84 pens . sharon takes 19 pens from you : 84 - 19 = 65 pens . so you have 65 at the end . correct answer : c
Answer: c
Problem: a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 210 - mile journey ? assume that the train makes no intermediate stops .
Options: a ) 6 , b ) 6.5 , c ) 7 , d ) 7.5 , e ) 5
Rationale: "a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 210 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 it takes a total of nine hours to cover the 210 mile distance . answer : a 6"
Answer: a
Problem: sarah is driving to the airport . after driving at 40 miles per hour for one hour , she realizes that if she continues at that same average rate she will be an hour late for her flight . she then travels 50 miles per hour for the rest of the trip , and arrives 30 minutes before her flight departs . how many miles did she drive in all ?
Options: a ) 140 , b ) 340 , c ) 210 , d ) 245 , e ) 280
Rationale: "after driving at 40 miles per hourfor one hour , this distance left to cover is d - 40 . say this distance is x miles . now , we know that the difference in time between covering this distance at 40 miles per hour and 50 miles per hour is 1 + 1 / 2 = 3 / 2 hours . so , we have that x / 40 - x / 50 = 3 / 2 - - > 5 x / 200 - 4 x / 200 = 3 / 2 - - > x / 200 = 3 / 2 - - > x = 300 . total distance = x + 40 = 340 miles . answer : b"
Answer: b
Problem: the sum of the 1 st and 3 rd of 3 consecutive odd integers is 131 less than 3 times the second integer . find the 3 integers ?
Options: a ) 121 , b ) 133 , c ) 145 , d ) 150 , e ) 165
Rationale: let x , x + 2 and x + 4 be three integers . the sum of the first x and third x + 4 is given by x + ( x + 4 ) 131 less than three times the second 3 ( x + 2 ) is given by 3 ( x + 2 ) - 131 ` ` the sum of the first and third is 131 less than three times the second ' ' gives x + ( x + 4 ) = 3 ( x + 2 ) - 131 solve for x and find all three numbers x = 129 , x + 2 = 131 , x + 4 = 133 as an exercise , check that the sum of the first and third is 131 less than three times b
Answer: b
Problem: a local business made a $ 125000 profit on its first $ 1 million in sales and a $ 80000 profit on its next $ 2 million in sales . by approximately what percent did the ratio of profit to sales decrease from the first $ 1 million in sales to the next $ 2 million in sales ?
Options: a ) 100 % , b ) 150 % , c ) 200 % , d ) 250 % , e ) 300 %
Rationale: solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of profits to sales . the first ratio will be for the first 1 million in sales , and the second ratio will be for the next 2 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 1 million profit / sales = 125 / 1000 = 1 / 8 next 2 million profit / sales = 8 / 200 = 2 / 50 we can simplify each ratio by multiplying each by the lcm of the two denominators , which is 400 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 1 million royalties / sales = ( 1 / 8 ) x 400 = 50 next 2 million royalties / sales = ( 2 / 50 ) x 400 = 16 we can plug 5 and 6 into our percent change formula : ( new – old ) / old x 100 [ ( 16 – 50 ) / 16 ] x 100 = - 34 / 16 x 100 so approximately a 200 % decrease . answer c .
Answer: c
Problem: in town x , 64 percent of the population are employed , and 44 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 55 % , c ) 29 % , d ) 40 % , e ) 52 %
Rationale: "answer b male - employed - 64 % female - employed - 20 % total employed 64 % means total unemployed = 36 % therefore d and e are not correct because female unemployed has to be less than 36 % female - unemployed = 32 % male unemployed = 4 % 48 % + 4 % = 52 % 16 % + 32 % = 48 % plug in a and b in place of 32 % and the sum is not 100 % 20 / 64 = 29 c"
Answer: c
Problem: for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score t for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: "a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean t = 74 . answer : a ."
Answer: a
Problem: √ 5 percent of 5 √ 5 =
Options: a ) 0.05 , b ) 0.25 , c ) 0.5 , d ) 2.5 , e ) 25
Rationale: "√ / 1005 / 100 * 55 √ 5 = ( 5 * 5 ∗ 5 − − √ 5 ∗ 5 ) / 100 = ( 5 * 5 ) / 100 = 25 / 100 = . 25 answer : b"
Answer: b
Problem: how many numbers from 10 to 31 are exactly divisible by 3 ?
Options: a ) 13 , b ) 15 , c ) 16 , d ) 7 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 . 7 numbers . 10 / 3 = 3 and 31 / 3 = 10 = = > 10 - 3 = 7 . therefore 7 digits d )"
Answer: d
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 4 more than the average of 10 , 70 , and what number ?
Options: a ) 28 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 4 = 36 sum of second list = 36 * 3 = 108 therefore the number = 108 - 80 = 28 answer : a"
Answer: a
Problem: what is the least number . which should be added to 221 to make it a perfect square ?
Options: a ) 5 , b ) 8 , c ) 4 , d ) 6 , e ) 7
Rationale: "221 + 4 = 225 15 ^ 2 answer : c"
Answer: c
Problem: when positive integer n is divided by positive integer j , the remainder is 42 . if n / j = 204.07 , what is value of j ?
Options: a ) 200 , b ) 400 , c ) 800 , d ) 600 , e ) 1200
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.07 here 204 is the quotient . given that remainder = 42 so , 204.07 = 204 + 42 / j so , j = 600 answer : d"
Answer: d
Problem: 8796 x 223 + 8796 x 77 = ?
Options: a ) 2736900 , b ) 2738800 , c ) 2658560 , d ) 2716740 , e ) none of them
Rationale: "= 8796 x ( 223 + 77 ) ( by distributive law ) = 8796 x 300 = 2638800 answer is b"
Answer: b
Problem: an agent , gets a commission of 5 % on the sales of cloth . if on a certain day , he gets rs . 12.50 as commission , the cloth sold through him on that day is worth
Options: a ) 333 , b ) 500 , c ) 887 , d ) 250 , e ) 132
Rationale: "explanation : let the total sale be rs . x . then , 5 % . of x = 12.50 < = > ( 5 / 100 * x ) = 125 / 10 < = > x = 250 . answer : d"
Answer: d
Problem: 121 x 5 ^ 4 = ?
Options: a ) 75625 , b ) 68225 , c ) 72325 , d ) 71225 , e ) 72225
Rationale: explanation : 121 × 5 ^ 4 = 121 × ( 10 / 2 ) ^ 4 = ( 121 × 10000 ) / 16 = 7.5625 × 10000 = 75625 answer is a
Answer: a
Problem: the number n is h , 284 , where h represents the 10 ' s digit . if n is divisible by 6 , what is the value of h ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8
Rationale: if the number is divisible by 6 , then the sum of the digits must also be divisible by both 3 and 2 . only 1 yields such a number . answer : a
Answer: a
Problem: a 360 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 220 meter , b ) 225 meter , c ) 140 meter , d ) 235 meter , e ) none of these
Rationale: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 360 / 9 = 500 / 9 = > x + 360 = 500 = > x = 140 so the length of the train is 140 meters option c"
Answer: c
Problem: how long does a train 100 m long traveling at 54 kmph takes to cross a station of 250 m in length ?
Options: a ) 22 sec , b ) 20 sec , c ) 15 sec , d ) 23 sec , e ) 16 sec
Rationale: "d = 100 + 245 = 345 m s = 54 * 5 / 18 = 15 t = 345 * 1 / 15 = 23 sec answer : d"
Answer: d
Problem: a certain store sells all maps at one price and all books at another price . on monday the store sold 9 maps and 6 books for a total of $ 20.00 , and on tuesday the store sold 9 maps and 8 books for a total of $ 30.00 . at this store , how much less does a map sell for than a book ?
Options: a ) $ 0.25 , b ) $ 0.50 , c ) $ 0.75 , d ) $ 3.9 , e ) $ l . 25
Rationale: "9 x + 6 y = 20 9 x + 8 y = 30 subtracting 1 from 2 - 2 y = - 10 y = 5 therefore x = 1.1 difference in price = 3.9 d"
Answer: d
Problem: the ratio of efficiency of a is to c is 5 : 3 . the ratio of no . of days taken by b is to c is 2 : 3 . a takes 6 days less than c , when a and c completes the work individually . b and c left the work after 2 days . the no of days taken by a to finish the remaining work ?
Options: a ) 4.5 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: a : b : c efficiency 10 : 9 : 6 no of days 9 x : 10 x : 15 x given = > 15 x - 9 x = 6 hence , x = 1 number of days taken by a = 9 and daily work done = 10 number of days taken by b = 10 and daily work done = 9 ( total work = 90 ) number of days taken by c = 15 and daily work done = 6 work done by b and c in initial 2 days = 30 rest work = 60 number of days required by a to finish = 60 / 10 = 6 days answer : c
Answer: c
Problem: a train covers a distance of 16 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) m , b ) m , c ) m , d ) m , e ) m
Rationale: "speed = ( 16 / 10 * 60 ) km / hr = ( 96 * 5 / 18 ) m / sec = 80 / 3 m / sec . length of the train = 80 / 3 * 6 = 160 m . answer : c"
Answer: c
Problem: a man sitting in a train which is traveling at 70 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 50 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 42 kmph
Rationale: "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 70 ) kmph = 42 kmph . answer : e"
Answer: e
Problem: if s = { 8 , 16 , 24 , 32 , 40 , 48 } , what is the product of mean and median of the numbers in s ?
Options: a ) 652 , b ) 589 , c ) 456 , d ) 620 , e ) 784
Rationale: mean = ( 8 + 16 + 24 + 32 + 40 + 48 ) / 6 = 28 median = ( 24 + 32 ) / 2 = 28 product = 28 * 28 = 784 option e
Answer: e
Problem: after an ice began to melt out from the freezer , in the first hour lost 3 / 4 , in the second hour lost 3 / 4 of its remaining . if after two hours , the volume is 0.2 cubic inches , what is the original volume of the cubic ice , in cubic inches ?
Options: a ) 2.5 , b ) 3.2 , c ) 4.0 , d ) 6.5 , e ) 8.0
Rationale: "let initial volume of ice be = x ice remaining after 1 hour = x - 0.75 x = 0.25 x ice remaining after 2 hour = ( 1 / 4 ) x - ( 3 / 4 * 1 / 4 * x ) = ( 1 / 16 ) x ( 1 / 16 ) x = 0.2 x = 3.2 alternate solution : try to backsolve . initial volume = 3.2 after one hour - - > ( 1 / 4 ) 3.2 = 0.8 after two hours - - > ( 1 / 4 ) 0.8 = 0.2 answer : b"
Answer: b
Problem: one fourth of a solution that was 22 % sugar by weight was replaced by a second solution resulting in a solution that was 35 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 74 % , b ) 24 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.22 + 1 / 4 * x = 1 * 0.35 - - > x = 0.74 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.22 + 25 * x = 100 * 0.35 - - > x = 0.74 . answer : a ."
Answer: a
Problem: if 2994 ã · 14.5 = 171 , then 29.94 ã · 1.45 = ?
Options: a ) 17.1 , b ) 17.3 , c ) 17.5 , d ) 17.7 , e ) 17.2
Rationale: "29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 171 in the place of 2994 / 14.5 ] = 171 / 10 = 17.1 answer is a ."
Answer: a
Problem: when positive integer n is divided by positive integer j , the remainder is 27 . if n / j = 204.09 , what is value of j ?
Options: a ) 300 , b ) 320 , c ) 360 , d ) 410 , e ) 420
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.09 here 204 is the quotient . given that remainder = 27 so , 204.09 = 204 + 27 / j so , j = 300 answer : a"
Answer: a
Problem: there are 840 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 140 , b ) 100 , c ) 125 , d ) 175 , e ) 225
Rationale: "female = x male = 840 - x x / 2 + 840 - x / 4 = 1 / 3 * ( 840 ) = 280 x = 280 x / 2 = 140 is supposed to be the answer m is missing something correct option a"
Answer: a
Problem: p alone can complete a job in 7 days . the work done by q alone in one day is equal to one - sixth of the work done by p alone in one day . in how many days can the work be completed if p and q work together ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "p ' s rate is 1 / 7 q ' s rate is 1 / 42 the combined rate is 1 / 7 + 1 / 42 = 1 / 6 if they work together , the job will take 6 days . the answer is e ."
Answer: e
Problem: there are 4 members in a family . their average income is rs . 10000 per month . 3 members get rs . 8000 , rs . 15000 , rs . 6000 respectively . therefore what is the income of the fourth member of the family ?
Options: a ) rs . 10000 , b ) rs . 11000 , c ) rs . 12000 , d ) rs . 9000 , e ) rs . 8500
Rationale: explanation total income of 3 members = rs . ( 8000 + 15000 + 6000 ) = rs . 29000 . required income = rs . [ ( 10000 x 4 ) – 29000 ] = rs . ( 40000 – 29000 ) = rs . 11000 . answer b
Answer: b
Problem: if ( 3 / 2 ) x - 3 = 15 what is the value of x ?
Options: a ) - 12 , b ) 12 , c ) - 1 / 12 , d ) 1 / 12 , e ) 3
Rationale: ( 3 / 2 ) x - 3 = 15 = > 3 x - 6 = 30 = > 3 x = 36 = > x = 12 answer : b
Answer: b
Problem: a man can row 8 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 3.58 , b ) 3.68 , c ) 3.78 , d ) 3.88 , e ) 3.98
Rationale: "m = 8 s = 1.2 ds = 8 + 1.2 = 9.2 us = 8 - 1.2 = 6.8 x / 9.2 + x / 6.8 = 1 x = 3.68 . answer : b"
Answer: b
Problem: a and b invests rs . 3000 and rs . 8000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 6 , b ) 9 : 8 , c ) 9 : 16 , d ) 9 : 9 , e ) 9 : 5
Rationale: "( 3 * 6 + 6 * 6 ) : ( 8 * 12 ) 54 : 96 = > 9 : 16 . answer : c"
Answer: c
Problem: a rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 34 , b ) 77 , c ) 36 , d ) 56 , e ) 91
Rationale: "explanation : perimeter of the plot = 2 ( 90 + 50 ) = 280 m no of poles = 280 / 5 = 56 m answer : d"
Answer: d
Problem: the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 9.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 4.50 , b ) $ 5.10 , c ) $ 9.30 , d ) $ 5.50 , e ) $ 5.60
Rationale: "i tried using time / rate approach : - initial price difference = 9.80 - 3.20 = 6.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 6.6 = t ( 5.4 x ) - > t = ( 6.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 6.6 / 5.4 = 9.3 answer c ."
Answer: c
Problem: how many two - element subsets of { 1,2 , 3,4 } are there that do not contain the pair of elements 2 and 4 ?
Options: a ) one , b ) two , c ) four , d ) five , e ) six
Rationale: "{ 1,2 } , { 1,3 } , { 1,4 } , { 2,3 } , { 3,4 } . or : c 24 − 1 = 5 answer : d ."
Answer: d
Problem: at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 19 employees are trained to work in the family buffet , 16 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 4 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 39 = 19 + 16 + 12 - 4 - 2 x 2 x = 19 + 16 + 12 - 4 - 39 = 43 - 39 = 4 x = 2 a
Answer: a
Problem: there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is seven - third that of the smaller circle . find the circumference of the smaller circle ?
Options: a ) 6
b ) 5
c ) 8
d ) 6
e ) 3
Rationale: let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 ∏ s = 12 ∏ cm . answer : c
Answer: c
Problem: for any number z , z * is defined as the greatest positive even integer less than or equal to z . what is the value of 5.2 – 5.2 * ?
Options: a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0
Rationale: "since z * is defined as the greatest positive even integer less than or equal to z , then 5.2 * = 4 ( the greatest positive even integer less than or equal to 5.2 is 4 ) . hence , 5.2 – 5.2 * = 5.2 - 4 = 1.2 answer : b ."
Answer: b
Problem: if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 17,000 is invested at the same interest rate , what is the interest from the investment ?
Options: a ) $ 700 , b ) $ 750 , c ) $ 800 , d ) $ 850 , e ) $ 900
Rationale: "5000 * r * t / 100 = 250 rt = 5 17000 * 5 / 100 = 850 answer is d"
Answer: d
Problem: 30 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 87 , b ) 18 , c ) 17 , d ) 36 , e ) 10
Rationale: binders books days 30 1400 21 x 1600 20 x / 30 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 36 answer : d
Answer: d
Problem: if the radius of a circle is decreased 30 % , what happens to the area ?
Options: a ) 51 % decrease , b ) 20 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 50 % decrease
Rationale: "area of square = pi * radius ^ 2 new radius = 0.7 * old radius so new area = ( 0.7 ) ^ 2 old area = > 0.49 of old area = > 49 % old area ans : a"
Answer: a
Problem: find the amount on rs . 5000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ?
Options: a ) 3377 , b ) 2678 , c ) 5460 , d ) 1976 , e ) 1671
Rationale: "5000 * 104 / 100 * 105 / 100 = > 5460 answer : c"
Answer: c
Problem: the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 410 per month . the salary of the new supervisor is :
Options: a ) 233 , b ) 690 , c ) 287 , d ) 771 , e ) 191
Rationale: "explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 410 = 3690 salary of the new supervisor = 3690 â ˆ ’ 3000 = 690 answer : b"
Answer: b
Problem: if there are 4 peanuts in a box and mary puts 6 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: 6 + 4 = 10 correct answer is c ) 10
Answer: c
Problem: how many 3 digit positive integers exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: "explanatory answer step 1 : find the first and last term of the series the smallest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 103 . the largest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 999 . the series of numbers that satisfy the condition that the number should leave a remainder of 5 when divided by 7 is an a . p ( arithmetic progression ) with the first term being 103 and the last term being 999 . the common difference of the sequence is 7 . step 2 : compute the number of terms in an a . p , the last term l = a + ( n - 1 ) * d , where ' a ' is the first term , ' n ' is the number of terms of the series and ' d ' is the common difference . therefore , 999 = 103 + ( n - 1 ) * 7 or 999 - 103 = ( n - 1 ) * 7 or 896 = ( n - 1 ) * 7 so , n - 1 = 128 or n = 129 choice e is the correct answer ."
Answer: e
Problem: if ( 10 ^ 4 * 3.456789 ) ^ 9 is written as a single term , how many digits would be to the right of the decimal place ?
Options: a ) 6 , b ) 12 , c ) 18 , d ) 32 , e ) 48
Rationale: "3.456789 ^ 9 has 6 * 9 = 54 decimal places . 10 ^ 36 moves the decimal place to the right 36 places . ( 10 ^ 4 * 3.456789 ) ^ 9 has 54 - 36 = 18 digits after the decimal point . the answer is c ."
Answer: c
Problem: if c is 30 % of a and 25 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 15 % , c ) 120 % , d ) 35 % , e ) 250 %
Rationale: "answer = c 30 a / 100 = 25 b / 100 b = 30 a / 25 = 120 a / 100 = 120 %"
Answer: c
Problem: find the principal which yields a simple interest of rs . 20 and compound interest of rs . 24 in two years , at the same percent rate per annum ?
Options: a ) s . 50 , b ) s . 48 , c ) s . 42 , d ) s . 20 , e ) s . 60
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 24 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 24 – 20 ) / 20 ] * 100 = 20 % p . a . let the principal be rs . x time = t = 2 years % rate = 20 % p . a . si = ( prt / 100 ) 20 = ( x * 20 * 2 ) / 100 x = rs . 50 answer : a"
Answer: a