regisss/math_qa huggingface dataset:
Problem: each month a retailer sells 100 identical items . on each item he makes a profit of $ 50 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?
Options: a ) 191 , b ) 213 , c ) 221 , d ) 223 , e ) 226
Rationale: "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 50 sell price = $ 500 + $ 50 thus , the sell price is $ 550 for each item . selling all 100 items gives the retailer . . . 100 ( $ 50 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 550 ) = $ 27.5 discount $ 522.5 = $ 500 + $ 22.5 now , the retailer makes a profit of just $ 22.5 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 22.5 ( x ) = $ 2,000 x = 2,000 / 22.5 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"
Answer: d
Problem: the perimeter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 23.57 , b ) 25.54 , c ) 26.5 , d ) 26.55 , e ) 26.71
Rationale: "let the side of the square be a cm . perimeter of the rectangle = 2 ( 20 + 14 ) = 68 cm perimeter of the square = 68 cm i . e . 4 a = 68 a = 17 diameter of the semicircle = 17 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 17 ) = 1 / 2 ( 22 / 7 ) ( 17 ) = 26.71 cm to two decimal places answer : e"
Answer: e
Problem: working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 16 , 12 , and 8 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 5 / 2 , b ) 7 / 4 , c ) 8 / 5 , d ) 10 / 3 , e ) 12 / 5
Rationale: the time it takes printer x is 16 hours . the combined rate of y and z is 1 / 12 + 1 / 8 = 5 / 24 the time it takes y and z is 24 / 5 the ratio of times is 16 / ( 24 / 5 ) = 5 * 16 / 24 = 10 / 3 the answer is d .
Answer: d
Problem: a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs , then the weight of the pipe is
Options: a ) 3.496 kg , b ) 3.696 kg , c ) 3.690 kg , d ) 9.696 kg , e ) 3.296 kg
Rationale: explanation : external radius = 4 cm , internal radius = 3 cm . volume of iron = = weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg answer : b ) 3.696 kg
Answer: b
Problem: in may , the grounds keeper at spring lake golf club built a circular green with an area of 49 π square feet . in august , he doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 100 pi , b ) 144 pi , c ) 196 pi , d ) 80 , e ) 90
Rationale: "area of circle 49 pi sq feet = pi r ^ 2 therefore r = 7 now green radi doubled i . e r = 14 area = 196 pi c"
Answer: c
Problem: j is 25 % less than p and 20 % less than t . t is r % less than p . what is the value of r ?
Options: a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2
Rationale: "usually we can solve every question of this type by choosing appropriate value of the variable and deriving the value of other related variables . let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( r / 100 ) ] * p i . e . 100 - r = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . r = 6.25 answer : option d"
Answer: d
Problem: if k is the greatest positive integer such that 3 ^ k is a divisor of 21 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "21 / 3 = 7 21 / 9 = 2.33 = 2 7 + 2 = 9 k = 9 answer : e"
Answer: e
Problem: a chemist mixes one liter of pure water with x liters of a 30 % salt solution , and the resulting mixture is a 20 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 2
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 30 % concentration of salt in the mixed solution = 20 % the pure solution and the salt solution is mixed in the ratio of - - > ( 30 - 20 ) / ( 20 - 0 ) = 1 / 2 1 / x = 1 / 2 x = 2 answer : e"
Answer: e
Problem: in an examination 35 % of the students passed and 546 failed . how many students appeared for the examination ?
Options: a ) a ) 540 , b ) b ) 400 , c ) c ) 700 , d ) d ) 650 , e ) e ) 840
Rationale: "let the number of students appeared be x then , 65 % of x = 546 65 x / 100 = 546 x = 546 * 100 / 65 = 840 answer is e"
Answer: e
Problem: what is the unit digit in 15 ^ 100 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: unit digit in 15 ^ 100 = unit digit in [ ( 15 ^ 4 ) ^ 25 ] but unit digit in 15 ^ 4 = 5 unit digit 15 ^ 100 = 5 answer is e
Answer: e
Problem: a person walks from one end to the other of a 90 - meter long moving walkway at a constant rate in 30 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: "let v be the speed of the person and let x be the speed of the walkway . 30 ( v + x ) = 90 then 120 ( v + x ) = 360 120 ( v - x ) = 90 when we add the two equations : 240 v = 450 v = 15 / 8 time = 90 / ( 15 / 8 ) = 48 seconds the answer is c ."
Answer: c
Problem: right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 34 years . what is molly ' s age right now ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: "now , sandy is 34 - 6 = 28 molly ' s age is ( 3 / 4 ) * 28 = 21 the answer is d ."
Answer: d
Problem: a 420 meter long train crosses a platform in 60 seconds while it crosses a signal pole in 30 seconds . what is the length of the platform ?
Options: a ) 120 , b ) 840 , c ) 350 , d ) 420 , e ) 210
Rationale: "speed = [ 420 / 30 ] m / sec = 14 m / sec . let the length of the platform be x meters . then , x + 420 / 60 = 14 x + 420 = 840 è x = 420 m . answer : d"
Answer: d
Problem: a , b and c rents a pasture for rs . 435 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should b pay ?
Options: a ) 180 , b ) 227 , c ) 268 , d ) 198 , e ) 176
Rationale: 12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 12 / 29 * 435 = 180 answer : a
Answer: a
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 15000 . a ' s share is ?
Options: a ) 2999 , b ) 2778 , c ) 6000 , d ) 5000 , e ) 6612
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 15000 = 5000 answer : d"
Answer: d
Problem: a car traveled 80 % of the way from town x to town y at an average speed of 80 mph . the car traveled at an average speed of v mph for the remaining part of the trip . the average speed for the entire trip was 50 mph . what is v in mph ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 20
Rationale: assume total distance = 100 miles time taken for 80 miles = 80 / 80 = 1 hour time taken for the rest of the 20 miles = 20 / v hours . average speed = 50 therefore the total time needed = 2 hours . 2 = 1 + 20 / v hence v = 20 mph answer : e
Answer: e
Problem: a guy was asked to specify his age in years . he said , “ take my age 8 years hence , multiply it by 8 and subtract 8 times of my age 8 years ago and get the half of the result and you will know my age . ” what was the age of that guy ?
Options: a ) 18 , b ) 55 , c ) 63 , d ) 64 , e ) 70
Rationale: current age of the guy = a years . then , 8 ( a + 8 ) – 8 ( a – 8 ) = a ( 8 a + 64 ) – ( 8 a – 64 ) = a a = 128 / 2 = 64 d
Answer: d
Problem: there are 12 students in a class . on the day the test was given , ella was absent . the other 11 students took the test and their average was 74 . the next day , ella took the test , and with this grade included , the new average was 75 . what was ella ' s grade on the test ?
Options: a ) 82 , b ) 83 , c ) 84 , d ) 85 , e ) 86
Rationale: 11 * 74 + ella ' s grade = 12 * 75 ella ' s grade is 12 * 75 - 11 * 74 = 86 . the answer is e .
Answer: e
Problem: at what price must an book costing $ 47.50 be marked in order that after deducting 20 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.5 , b ) 55.5 , c ) 64.2 , d ) 82.5 , e ) 60.5
Rationale: "c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 80 / 100 ) = 59.375 mp = 74.2"
Answer: c
Problem: three fifth of the square of a certain number is 126.15 . what is the number ?
Options: a ) 210.25
b ) 75.69
c ) 14.5
d ) 145
e ) 150
Rationale: let the number be x given , 3 / 5 x ^ 2 = 126.5 x ^ 2 = 126.15 * 5 / 3 x ^ 2 = 42.05 * 5 = 210.25 x = 14.5 answer c .
Answer: c
Problem: one woman and one man can build a wall together in one hour , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them two hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ?
Options: a ) 5 / 7 , b ) 6 / 7 , c ) 10 / 7 , d ) 12 / 7 , e ) 22 / 7
Rationale: solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 1 - - > ( 1 ) , w + 2 g = 1 / 1 - - > ( 2 ) and m + g = 1 / 2 - - > ( 3 ) . no . of hours it would take forone woman , one man , and one girl , working together , to build the wall , n = 1 / m + w + g from ( 1 ) and ( 2 ) , m = 2 g and from ( 3 ) g = 1 / 6 , m = 1 / 3 and w = 2 / 3 . so , n = 1 / ( 7 / 6 ) = 6 / 7 option , b
Answer: b
Problem: in a certain circle there are 10 points . what is the number of the triangles connecting 4 points of the 10 points ?
Options: a ) 80 , b ) 96 , c ) 108 , d ) 120 , e ) 210
Rationale: "imo : e here we have to select 4 points out of 10 points . order is not important so the answer will be 10 c 4 = 210"
Answer: e
Problem: two trains of length 400 m and 200 m are 200 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 36 kmph . after how much time will the trains meet ?
Options: a ) 8 sec , b ) 20 / 7 sec , c ) 33 / 7 sec , d ) 21 / 7 sec , e ) 32 / 7 sec
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 54 + 36 ) * 5 / 18 = 25 mps . the time required = d / s = 200 / 25 = 8 sec . answer : a"
Answer: a
Problem: the diagonals of two squares are in the ratio of 3 : 7 then find the ratio of its areas ?
Options: a ) 7 : 37 , b ) 6 : 46 , c ) 9 : 49 , d ) 8 : 68 , e ) 6 : 61
Rationale: "let the diagonals of the squares be 3 x and 7 x ratio of their areas = 1 / 2 ( 3 x ) ^ 2 : 1 / 2 ( 7 x ) ^ 2 = 9 x ^ 2 : 49 x ^ 2 = 9 : 49 answer is c"
Answer: c
Problem: the average marks of a class of 30 students is 40 and that of another class of 50 students is 90 . find the average marks of all the students ?
Options: a ) 71.25 , b ) 52.9 , c ) 52.1 , d ) 52.3 , e ) 42.5
Rationale: "sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 90 = 4500 sum of the marks for the class of 80 students = 1200 + 4500 = 5700 average marks of all the students = 5700 / 80 = 71.25 answer : a"
Answer: a
Problem: in the storage room of a certain bakery , the ratio of sugar to flour is 3 to 8 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 600 , b ) 900 , c ) 1500 , d ) 1600 , e ) 1750
Rationale: "sugar : flour = 3 : 8 = 15 : 40 ; flour : soda = 10 : 1 = 40 : 4 ; thus we have that sugar : flour : soda = 15 x : 40 x : 4 x . also given that 40 x / ( 4 x + 60 ) = 8 / 1 - - > x = 60 - - > sugar = 15 x = 900 . answer : b ."
Answer: b
Problem: jacob is 18 years old . he is 2 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 36 , b ) 38 , c ) 33 , d ) 32 , e ) 38
Rationale: j = 18 ; j = 2 b ; b = 18 / 2 = 9 ; twice as old so b = 9 ( now ) + ( 9 ) = 18 ; jacob is 18 + 18 = 36 answer : a
Answer: a
Problem: 3897 x 999 = ?
Options: a ) 3883203 , b ) 3893103 , c ) 3639403 , d ) 3791203 , e ) none of them
Rationale: "= 3897 x 999 = 3897 x ( 1000 - 1 ) = 3897 x 1000 - 3897 x 1 = 3897000 - 3897 = 3893103 answer is b"
Answer: b
Problem: the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 600 . what is the manager ' s monthly salary ?
Options: a ) rs . 16003 , b ) rs . 16029 , c ) rs . 11288 , d ) rs . 14100 , e ) rs . 16011
Rationale: "explanation : manager ' s monthly salary rs . ( 2100 * 21 - 1500 * 20 ) = rs . 14100 . answer : d"
Answer: d
Problem: noelle walks from point a to point b at an average speed of 5 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 8 kilometers per hour ?
Options: a ) 6.75 , b ) 7 , c ) 7.25 , d ) 7.5 , e ) 20
Rationale: "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 8 = 2 * 5 * x / 5 + x x = 20 e is the answer"
Answer: e
Problem: a man buy a book in rs 50 & sale it rs 90 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 80 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: cp = 50 sp = 90 profit = 90 - 50 = 40 % = 40 / 50 * 100 = 80 % answer : b
Answer: b
Problem: in what time will a train 250 metres long cross an electric pole , if its speed be 162 km / hr ?
Options: a ) 4 sec , b ) 5 sec , c ) 5.55 sec , d ) 6.55 sec , e ) 4.55 sec
Rationale: "solution speed = ( 162 x 5 / 18 ) m / sec = 45 m / sec time taken = ( 250 / 45 ) sec = 5.55 sec . answer c"
Answer: c
Problem: an ant is climbing 30 meters tall pole . it climbs 3 meter during the day and slips down 2 meters down during night in sleep , how many days it takes to reach the top of the pole ?
Options: a ) a - 30 , b ) b - 29 , c ) c - 28 , d ) d - 27 , e ) e - 26
Rationale: ants overall distance covered is 3 - 2 = 1 meter per day . in 27 days it will climb 27 meters . on 28 th day it will reach the top of the pole . answer : c
Answer: c
Problem: if 50 apprentices can finish a job in 4 hours , and 30 journeymen can finish the same job in 5 hours , how much of the job should be completed by 10 apprentices and 15 journeymen in one hour ?
Options: a ) 1 / 9 , b ) 29 / 180 , c ) 26 / 143 , d ) 3 / 20 , e ) 39 / 121
Rationale: "50 apprentices can finish the job in 4 hours , thus : 10 apprentices can finish the job in 4 * 5 = 20 hours ; in 1 hour 10 apprentices can finish 1 / 20 of the job . 30 journeymen can finish the same job in 4,5 hours , thus : 15 journeymen can finish the job in 5 * 2 = 10 hours ; in 1 hour 15 journeymen can finish 1 / 10 of the job . therefore , in 1 hour 10 apprentices and 15 journeymen can finish 1 / 20 + 1 / 10 = 3 / 20 of the job . answer : d ."
Answer: d
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 3 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?
Options: a ) 7 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 3 ) = ( 7 / 16 ) * v 1 ( v 1 - 3 ) / v 1 = 3 / 4 3 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 3 = 12 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 12 = 7 litres . answer : a"
Answer: a
Problem: rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 1500 . then his monthly salary is
Options: a ) rs . 6000 , b ) rs . 7500 , c ) rs . 8000 , d ) rs . 10,000 , e ) none
Rationale: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 1500 ⇔ 20 / 100 x = 1500 ⇔ x = 1500 × 5 = 7500 . answer b"
Answer: b
Problem: what percentage of numbers from 1 to 95 have squares that end in the digit 0 ?
Options: a ) 1 , b ) 14 , c ) 9.47 , d ) 21 , e ) 22
Rationale: clearly , the numbers which have 1 or 9 in the unit ' s digit , have squares that end in the digit 1 . such numbers from 1 to 95 are 10 , 20,30 , 40,50 , 60,70 , 80,90 . number of such numbers = 14 . required percentage = ( 9 / 95 * 100 ) = 9.47 % answer : c
Answer: c
Problem: what is the square root of 400 , divided by 2 ?
Options: a ) 9 , b ) 36 , c ) 122 , d ) 6 , e ) 10
Rationale: "square root is a number times itself square root of 400 = 20 , 20 / 2 = 10 ( e ) 1"
Answer: e
Problem: for a recipe for triple berry pie calls for cups of strawberries , raspberries , and blueberries in a ratio of 1 : 2 : 3 . how many total cups of fruit will you need to make the pie ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: the ratio 1 : 2 : 3 represents 1 cup strawberries : 2 cups raspberries : 3 cups blueberries . 1 + 2 + 3 = 6 6 cups will be used for the pie . the answer is e
Answer: e
Problem: in how many ways can 21 books on english and 19 books on hindi be placed in a row on a shelf so that two books on hindi may not be together ?
Options: a ) 1540 , b ) 2314 , c ) 5420 , d ) 1240 , e ) 4512
Rationale: "we must place all these books as under : xexex … . xex there are 21 books on english , 19 books on hindi 19 places out of 22 can be chosen 22 c 19 = 22 c 3 = 1540 ways ans : a"
Answer: a
Problem: two trains 121 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.19 , b ) 7.18 , c ) 7.16 , d ) 7.15 , e ) 7.12
Rationale: "t = ( 121 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.15 answer : d"
Answer: d
Problem: the number which exceeds 16 % of it by 63 is :
Options: a ) 75 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "solution solution let the number be x . x - 16 % of x = 63 x - 16 / 100 x = 63 x - 4 / 25 x = 63 21 / 25 x = 63 x = ( 63 x 25 / 21 ) = 75 answer a"
Answer: a
Problem: the batting average of a particular batsman is 58 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 208 , c ) 210 , d ) 133 , e ) 229
Rationale: "explanation : total runs scored by the batsman = 58 * 46 = 2668 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2668 – 2552 = 116 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 116 2 x = 266 x = 133 runs answer d"
Answer: d
Problem: the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p is ?
Options: a ) rs . 4007 , b ) rs . 4000 , c ) rs . 4028 , d ) rs . 4050 , e ) rs . 4032
Rationale: "let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 * 2 ) = 10100 - - - ( i ) q + r = ( 6250 * 2 ) = 12500 - - - ( ii ) p + r = ( 5200 * 2 ) = 10400 - - - ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 = p + q + r = 16500 - - - ( iv ) subtracting ( ii ) from ( iv ) , we get , p = 4000 . p ' s monthly income = rs . 4000 . answer : b"
Answer: b
Problem: how many integers between 324,700 and 387,600 have tens digit 1 and units digit 3 ?
Options: a ) 438 , b ) 629 , c ) 780 , d ) 879 , e ) 924
Rationale: "the integers are : 324,713 324,813 etc . . . 387,513 the number of integers is 3876 - 3247 = 629 the answer is b ."
Answer: b
Problem: the salary of a , b , c , d , e is rs . 10000 , rs . 5000 , rs . 11000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8400 , c ) rs . 8500 , d ) rs . 9000 , e ) none
Rationale: "answer average salary = 10000 + 5000 + 11000 + 7000 + 9000 / 5 = rs . 8400 correct option : b"
Answer: b
Problem: if ( 1 – 1.25 ) n = 3 , then n =
Options: a ) − 400 , b ) − 140 , c ) − 4 , d ) 4 , e ) - 12
Rationale: ( 1 – 1.25 ) n = 3 simplify to get : - 0.25 n = 3 rewrite as ( - 1 / 4 ) n = 3 multiply both sides by - 4 to get : n = - 12 answer : e
Answer: e
Problem: running at the same constant rate , 6 identical machines can produce a total of 300 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2000 , d ) 10800 , e ) 10900
Rationale: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 300 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 300 x = ( 10 x 4 x 300 ) / ( 6 ) x = 2000 . answer : c"
Answer: c
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along theboundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park is ?
Options: a ) 163600 m , b ) 178600 m , c ) 153600 m , d ) 163600 m , e ) 173600 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m 2 = 153600 m c"
Answer: c
Problem: reema took a loan of rs 1500 with simple interest for as many years as the rate of interest . if she paid rs . 735 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: explanation : let rate = r % then time = r years . = > 1500 ∗ r ∗ r / 100 = 735 = > r 2 = 49 = > r = 7 % option c
Answer: c
Problem: a can do a piece of work in 5 days and b can do it in 7 days how long will they both work together to complete the work ?
Options: a ) 6 / 11 , b ) 8 / 11 , c ) 7 / 12 , d ) 9 / 12 , e ) 10 / 11
Rationale: "explanation : a ’ s one day work = 1 / 5 b ’ s one day work = 1 / 7 ( a + b ) ’ s one day work = 1 / 5 + 1 / 7 = 12 / 35 = > time = 35 / 12 = 2 9 / 12 days answer : option d"
Answer: d
Problem: find the value of m 72519 x 9999 = m ?
Options: a ) 724533811 , b ) 353654655 , c ) 545463251 , d ) 725117481 , e ) 477899932
Rationale: "72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d"
Answer: d
Problem: sandy buys an old scooter for $ 800 and spends $ 200 on its repairs . if sandy sells the scooter for $ 1200 , what is the gain percent ?
Options: a ) 15 % , b ) 18 % , c ) 20 % , d ) 22 % , e ) 25 %
Rationale: selling price / total cost = 1200 / 1000 = 1.2 the gain percent is 20 % . the answer is c .
Answer: c
Problem: a certain bacteria colony doubles in size every day for 21 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
Options: a ) 6.33 , b ) 7.5 , c ) 20 , d ) 15 , e ) 19
Rationale: "if there is one bacteria colony , then it will reach the limit of its habitat in 21 days . if there are two bacteria colonies , then in order to reach the limit of habitat they would need to double one time less than in case with one colony . thus colonies need to double 20 times . answer : c . similar questions to practice : hope it helps ."
Answer: c
Problem: a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ’ s contribution in the capital ?
Options: a ) 6000 , b ) 9000 , c ) 9500 , d ) 12000 , e ) none
Rationale: "sol . let b ’ s capital be rs . x . then , 3500 * 12 / 7 x = 2 / 3 ⇔ 14 x = 126000 ⇔ x = 9000 . answer b"
Answer: b
Problem: how many consecutive zeros are there at the end of 100 ! ( 100 factorial ) ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: number of zeros will be 24 reason 100 / 5 = 20 20 / 5 = 4 so the total number of 5 will be 20 + 4 = 24 answer : d
Answer: d
Problem: the ratio of spinsters to cats is 2 to 7 . if there are 55 more cats than spinsters , how many spinsters are there ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 55 x = 11 and the number of spinsters is 2 ( 11 ) = 22 . the answer is c ."
Answer: c
Problem: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 4000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) s . 375 , b ) s . 400 , c ) s . 500 , d ) s . 800 , e ) s . 850
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 4000 ) = rs . 500 answer = c"
Answer: c
Problem: a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 20 extra yellow balls and making ratio of white balls to yellow balls 8 / 13 . how many tennis balls did the retailer order originally .
Options: a ) 64 , b ) 130 , c ) 140 , d ) 160 , e ) 120
Rationale: "white : yellow = x : ( x + 20 ) = 8 : 13 - - > 13 x = 8 x + 160 - - > x = 32 . the total # of balls originally x + x = 32 + 32 = 64 . answer : a ."
Answer: a
Problem: ramu bought an old car for rs . 42000 . he spent rs . 10000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) 17 % , b ) 19 % , c ) 24.8 % , d ) 14 % , e ) 16 %
Rationale: "total cp = rs . 42000 + rs . 10000 = rs . 52000 and sp = rs . 64900 profit ( % ) = ( 64900 - 52000 ) / 52000 * 100 = 24.8 % answer : c"
Answer: c
Problem: find the average of all numbers between 5 and 45 which are divisible by 6
Options: a ) 26 , b ) 24 , c ) 28 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 6 + 12 + 18 + 24 + 30 + 36 + 42 / 6 ) = 168 / 6 = 28 option c"
Answer: c
Problem: a group of men decided to do a work in 40 days , but 5 of them became absent . if the rest of the group did the work in 60 days , find the original number of men ?
Options: a ) 60 , b ) 15 , c ) 40 , d ) 10 , e ) 25
Rationale: "original number of men = 5 * 60 / ( 60 - 40 ) = 15 answer is b"
Answer: b
Problem: if an object travels at nine feet per second , how many feet does it travel in one hour ?
Options: a ) 30 , b ) 300 , c ) 720 , d ) 1800 , e ) 32400
Rationale: "speed = 9 feet per second . 1 hour = 60 x 60 seconds = 3600 seconds . total no of feet traveled in 1 hour = 3600 x 9 = 32400 answer e"
Answer: e
Problem: the youngest of 4 children has siblings who are 3 , 6 , and 7 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 30 , what is the age of the youngest sibling ?
Options: a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "x + ( x + 3 ) + ( x + 6 ) + ( x + 7 ) = 120 4 x + 16 = 120 4 x = 104 x = 26 the answer is e ."
Answer: e
Problem: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 126 grams of water ?
Options: a ) 110 , b ) 112 , c ) 114 , d ) 116 , e ) 118
Rationale: "( 16 / 18 ) * 126 = 112 grams the answer is b ."
Answer: b
Problem: in what ratio p : q should the mixture p of milk and water in the ratio of 6 : 1 be mixed with another mixture q of milk and water in the ratio 3 : 4 so that the resultant mixture contains equal quantities of milk and water ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 2 : 5 , e ) 3 : 4
Rationale: "( 6 / 7 ) * p + ( 3 / 7 ) * q = ( 1 / 7 ) * p + ( 4 / 7 ) * q 5 p = q p / q = 1 / 5 the answer is c ."
Answer: c
Problem: sum of two numbers prime to each other is 8 and their l . c . m . is 15 . what are the numbers ?
Options: a ) 3 and 5 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 10 , e ) 6 and 8
Rationale: "as two numbers are prime , only options satisfy ie option a and b and c but option d will not make the product of numbers i . e 15 answer : a"
Answer: a
Problem: when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 12 - inch boxes . if the university pays $ 0.40 for every box , and if the university needs 2.16 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 120 , b ) $ 180 , c ) $ 310 , d ) $ 450 , e ) $ 640
Rationale: "the volume of each box is 20 * 20 * 12 = 4800 cubic inches . number of boxes = 2 , 160,000 / 4800 = 450 boxes total cost = 450 × $ 0.4 = $ 180 the answer is b ."
Answer: b
Problem: the sector of a circle has radius of 21 cm and central angle 90 o . find its perimeter ?
Options: a ) 91.5 , b ) 75 , c ) 93 , d ) 94 , e ) 95
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 90 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 75 cm answer : option b"
Answer: b
Problem: in what ratio should a variety of rice costing rs . 5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 1 / 2 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 3 , e ) 7 / 6
Rationale: let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 5 ) = 1 / 2 answer : a
Answer: a
Problem: 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 160 kg then find the average weight of all the 7 rounds ?
Options: a ) 91.4 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs
Rationale: average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 160 / 7 = 91.4 kgs answer : a
Answer: a
Problem: bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 10 minutes 30 seconds and his sister ’ s time is currently 9 minutes 36 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
Options: a ) 3 % , b ) 5 % , c ) 9 % , d ) 10 % , e ) 12 %
Rationale: "bob ' s time = 630 secs . his sis ' time = 576 secs . percent increase needed = ( 630 - 576 / 630 ) * 100 = 54 / 640 * 100 = 9 % . ans ( c ) ."
Answer: c
Problem: sum of two numbers is 20 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
Options: a ) a ) 5 , b ) b ) 9 , c ) c ) 11 , d ) d ) 13 , e ) e ) 15
Rationale: "explanation : x + y = 20 2 x – 3 y = 5 x = 13 y = 7 d )"
Answer: d
Problem: with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity e of the pool ?
Options: a ) 9000 cubic meters , b ) 10500 cubic meters , c ) 11750 cubic meters , d ) 12000 cubic meters , e ) 12500 cubic meters
Rationale: d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters .
Answer: d
Problem: if p # q denotes the least common multiple of p and q , then t = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?
Options: a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72
Rationale: "there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , t = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c ."
Answer: c
Problem: how many seconds will it take for a car that is traveling at a constant rate of 90 miles per hour to travel a distance of 22 yards ? ( 1 mile = 1,160 yards )
Options: a ) 0.8 , b ) 0.5 , c ) 1.0 , d ) 1.1 , e ) 1.2
Rationale: speed = 90 miles / hr = 44 yard / s distance = 22 yards time = distance / speed = 22 / 44 = 0.5 sec ans - b
Answer: b
Problem: if 4 men and 1 boy working together , can do two times as much work per hour as a man and a boy together . find the ratio of the work done by a man and that of a boy for a given time ?
Options: a ) 3 : 2 , b ) 2 : 1 , c ) 3 : 3 , d ) 1 : 2 , e ) 6 : 1
Rationale: 4 m + 1 b = 2 ( 1 m + 1 b ) 4 m + 1 b = 2 m + 2 b 2 m = 1 b the required ratio of work done by a man and a boy = 1 : 2 d
Answer: d
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 1.15 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 65 sec , b ) 54 sec , c ) 48 sec , d ) 33 sec , e ) 12 sec
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 1.15 = 2.25 km = 2250 m . required time = 2250 * 3 / 125 = 54 sec . answer : b"
Answer: b
Problem: two carpenters , working in the same pace , can build 2 desks in two hours and a half . how many desks can 4 carpenters build in 5 hours ?
Options: a ) 2.4 . , b ) 3.6 . , c ) 4.2 . , d ) 8 . , e ) 6.4
Rationale: w = 2 desks t = 2.5 hrs rate of 2 carpenters = 2 × r rate = work done / time 2 xr = 2 / 2.5 r = 1 / 2.5 = 2 / 5 ( this is the rate of each carpenter ) work done by 4 carpenters in 5 hrs = 4 × rate of each carpenter x time = 4 × 2 / 5 × 5 = 8 desks d is the correct answer .
Answer: d
Problem: a retailer buys 60 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ?
Options: a ) 40 , b ) 65 , c ) 72 , d ) 78 , e ) 20
Rationale: let the market price of each pen be $ 1 then , cost price of 60 pens = $ 36 selling price of 60 pens = 99 % of $ 60 = $ 59.40 profit % = ( ( 23.40 * 100 ) / 36 ) % = 65 % answer b
Answer: b
Problem: if 65 percent of a class answered the first question on a certain test correctly , 55 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 45 % , b ) 40 % , c ) 35 % , d ) 30 % , e ) 25 %
Rationale: "65 % answered the first question correctly and 20 % answered neither correctly . then 15 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 55 % - 15 % = 40 % . the answer is b ."
Answer: b
Problem: a person starts walking at a speed of 5 km / hr through half the distance , rest of the distance he covers with aspeed 4 km / hr . total time of travel is 6 hours . what is the maximum distance he can cover ?
Options: a ) 20 km , b ) 40 km , c ) 60 km , d ) 80 km , e ) 26.6 km
Rationale: t = d / s , so 6 = x / 2 * 1 / 5 + x / 2 * 1 / 4 ( because half distance with 5 km / ph , and remaining half with 4 km / hr ) 6 = x ( 18 / 80 ) x = 26.6 km answer : e
Answer: e
Problem: the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 1 year ?
Options: a ) 12300 , b ) 12350 , c ) 12000 , d ) 12500 , e ) 12600
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 ã — 120 / 100 = 12000 c"
Answer: c
Problem: two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every third , starting with the third , how many of the 95 widgets produced in the first hour of operation are not inspected by either inspector ?
Options: a ) 50 , b ) 43 , c ) 45 , d ) 55 , e ) 60
Rationale: "widgets inspected by lauren : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by steven : ( ( 93 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both : ( ( 90 / 15 ) + 1 = 6 total : 19 + 32 - 6 = 45 hence , widgets not inspected : 95 - 45 = 50 option a"
Answer: a
Problem: what percent is 10 gm of 1 kg ?
Options: a ) 0.5 % , b ) 1 % , c ) 1.5 % , d ) 2 % , e ) 3 %
Rationale: "1 kg = 1000 gm 10 / 1000 × 100 = 1000 / 1000 = 1 % b )"
Answer: b
Problem: 7 people went to a restaurant for dinner . 6 of them spent $ 11 each on their meals and the seventh person spent $ 6 more than the average expenditure of all 7 people . what was the total amount of money that the 7 people spent ?
Options: a ) $ 80 , b ) $ 81 , c ) $ 82 , d ) $ 83 , e ) $ 84
Rationale: let t be the total amount of money spent . 6 * 11 + ( t / 7 + 6 ) = t 72 = 6 t / 7 t = ( 7 * 72 ) / 6 = 84 the answer is e .
Answer: e
Problem: on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on september 1 than were in stock on january 1 ?
Options: a ) 8 , b ) 12 , c ) 20 , d ) 32 , e ) 36
Rationale: "jan 1 = c feb 1 = c - 4 march 1 = c - 8 april 1 = c - 12 may 1 = c - 16 june 1 = c - 20 july 1 = c - 24 aug 1 = c - 28 sept 1 = c - 32 difference between stock on september 1 than were in stock on january 1 will be - c - ( c - 32 ) = 32 hence answer will be ( d )"
Answer: d
Problem: there are 15 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 272 , b ) 167 , c ) 157 , d ) 352 , e ) 380
Rationale: "the total number of stations = 17 from 17 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 17 p ₂ ways . 17 p ₂ = 17 * 16 = 272 . answer : a"
Answer: a
Problem: how long will it take a train travelling at 68 kmph to pass an electric pole if the train is 170 m long
Options: a ) 6.99 , b ) 5.99 , c ) 8.99 , d ) 4.99 , e ) 9.99
Rationale: "sol . speed = [ 68 x 5 / 18 ] m / sec = 18.9 m / sec . time taken = ( 170 / 18.9 ) sec = 8.99 sec . answer c"
Answer: c
Problem: a , b and c rents a pasture for rs . 1073 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 289 , c ) 267 , d ) 255 , e ) 333
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 1073 = 333 answer : e"
Answer: e
Problem: during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 15 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 100 % , c ) 116.7 % , d ) 120 % , e ) 160 %
Rationale: "kim purchased 20 gallons of gas . she paid for 15 + 0.9 * 5 = 19.5 gallons , so the overall discount she got was 0.5 / 20 = 0.025 . isabella purchased 25 gallons of gas . she paid for 15 + 0.9 * 10 = 24 gallons , so the overall discount she got was 1 / 25 = 0.04 . 4 / 2.5 * 100 = 160 % answer : e ."
Answer: e
Problem: a batsman makes a score of 100 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .
Options: a ) 40 , b ) 50 , c ) 62 , d ) 45 , e ) 56
Rationale: "let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 100 = 11 x x = 100 - 50 = 50 answer is b"
Answer: b
Problem: sam wrote 7 letters on tuesday and 3 letters on wednesday . how many letters did he write on average per day ?
Options: a ) 10 , b ) 4 , c ) 21 , d ) 3 , e ) 5
Rationale: ( 7 + 3 ) / 2 = 5 the correct answer is e
Answer: e
Problem: on a trip covering 250 km , a bicyclist travels the first 100 km at 20 km per hour and the remainder of the distance at 15 km per hour . what is the average speed , in km per hour , for the entire trip ?
Options: a ) 15.8 , b ) 16.3 , c ) 16.7 , d ) 17.2 , e ) 17.5
Rationale: "time 1 = 100 / 20 = 5 hours time 2 = 150 / 15 = 10 hours total time = 15 hours average speed = 250 / 15 = 16.7 km / hr the answer is c ."
Answer: c
Problem: the mean of 20 observations was 36 . it was found later that an observation 25 was wrongly taken as 40 . the corrected new mean is
Options: a ) 30 , b ) 25.4 , c ) 40 , d ) 35.25 , e ) 26.55
Rationale: "explanation : correct sum = ( 36 * 20 + 25 - 40 ) = 705 correct mean = = 705 / 20 = 35.25 answer : d"
Answer: d
Problem: an outlet pipe can empty 2 / 3 of a cistern in 12 minutes . in 4 minutes , what part of the cistern will be emptied ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 2 / 7 , d ) 2 / 9 , e ) 3 / 10
Rationale: "4 / 12 * 2 / 3 = 2 / 9 the answer is d ."
Answer: d
Problem: an engineer undertakes a project to build a road 15 km long in 300 days and employs 30 men for the purpose . after 100 days , he finds only 2.5 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) a . 43 , b ) b . 45 , c ) c . 55 , d ) d . 68 , e ) e . 60
Rationale: "30 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 75 thus , more men needed to finish the task = 75 - 30 = 45 hence answer is b"
Answer: b
Problem: how many of the positive factors of 24 are not factors of 26
Options: a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 6
Rationale: "factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12,24 factors of 26 - 1 , 2 , 13 , 26 comparing both , we have 6 factors of 24 which are not factors of 26 - 3 , 4 , 6 , 8 , 12,24 answer : e"
Answer: e
Problem: he average weight of 6 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 55 kg , c ) 45 kg , d ) 80 kg , e ) 25 kg
Rationale: "explanation : total weight increased = ( 6 x 2.5 ) kg = 15 kg . weight of new person = ( 65 + 15 ) kg = 80 kg . answer : d"
Answer: d
Problem: there are 500 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of managers to 98 % ?
Options: a ) 150 , b ) 200 , c ) 250 , d ) 350 , e ) 400
Rationale: "there are 495 managers and 5 others . the 5 others would compose 2 % of the total number of people if there were 250 people in the room . thus 250 managers must leave . the answer is c ."
Answer: c
Problem: the speed at which a woman can row a boat in still water is 30 kmph . if he rows downstream , where the speed of current is 6 kmph , what time will he take to cover 100 metres ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "speed of the boat downstream = 30 + 6 = 36 kmph = 36 * 5 / 18 = 10 m / s hence time taken to cover 100 m = 100 / 10 = 10 seconds . answer : c"
Answer: c
Problem: how many batteries will remain unboxed if in a factory that manufactures batteries 2 types of boxes are used to store batteries . the bigger box can store 25 batteries while the smaller box can store 18 batteries . the total number of batteries to be stored is 217 .
Options: a ) 0 , b ) 1 , c ) 2 , d ) 7 , e ) 5
Rationale: total batteries to be stored 218 the big box can store 25 small box can store 18 storing 217 batteries in big box 218 / 25 = 8 r 18 store remainder in small box 18 / 18 = 1 r 0 least number of batteries that will be left unboxed = 0 answer : a
Answer: a
Problem: a company decreased the price of its main product by 30 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?
Options: a ) 1.26 , b ) 2.54 , c ) 5.23 , d ) 4.23 , e ) 3.33
Rationale: for the total revenue to remain the same when the price is 3 / 10 , the number of products sold must 3 / 10 times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 30 % = 3.33 answer : e
Answer: e
Problem: a train 110 m long is running with a speed of 80 km / h . in how many seconds will the train pass a man who is running at 8 km / h in the direction opposite to that in which the train is going ?
Options: a ) 3.5 , b ) 4.5 , c ) 5.5 , d ) 6.5 , e ) 7.5
Rationale: "the speed of the train relative to the man = 80 + 8 = 88 km / h . 88000 m / h * 1 h / 3600 s = ( 880 / 36 ) m / s ( 110 m ) / ( 880 / 36 m / s ) = ( 110 * 36 ) / 880 = 36 / 8 = 4.5 seconds the answer is b ."
Answer: b
Problem: after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 5265 . what was the number of original inhabitants ?
Options: a ) 7500 , b ) 7800 , c ) 8100 , d ) 8400 , e ) 8700
Rationale: "let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 5265 ( 27 / 40 ) * x = 5265 x = 5265 * 40 / 27 = 7800 the answer is b ."
Answer: b
Problem: a merchant has 1000 kg of sugar part of which he sells at 8 % profit and the rest at 18 % profit . he gains 14 % on the whole . the quantity sold at 18 % profit is ?
Options: a ) 700 kg , b ) 500 kg , c ) 600 kg , d ) 800 kg , e ) 900 kg
Rationale: "by the rule of alligation : profit of first part profit of second part so , ratio of 1 st and 2 nd parts = 4 : 6 = 2 : 3 . quantity of 2 nd kind = ( 3 / 5 x 1000 ) kg = 600 kg answer : c"
Answer: c
Problem: a rower whose speed is 8 km / hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 4 km / hr . what is the rower ' s average speed ( in km / hr ) for the total journey ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "time upstream = d / 4 time downstream = d / 12 total time = d / 4 + d / 12 = d / 3 average speed = 2 d / ( d / 3 ) = 6 km / hr the answer is b ."
Answer: b
Problem: how many pounds of salt at 50 cents / lb must be mixed with 40 lbs of salt that costs 25 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 20 , b ) 15 , c ) 40 , d ) 60 , e ) 25
Rationale: "selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 25 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 50 - 40 ) / ( 40 - 25 ) = 2 / 3 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 60 lbs . answer ( d )"
Answer: d