regisss/math_qa huggingface dataset:
Problem: if x = 1 - 4 t and y = 2 t - 2 , then for what value of t does x = y ?
Options: a ) 5 / 2 , b ) 1 / 2 , c ) 2 / 3 , d ) 2 / 5 , e ) 0
Rationale: we are given x = 1 – 4 t and y = 2 t – 2 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 – 4 t for x and 2 t – 2 for y in the equation x = y . this gives us : 1 – 4 t = 2 t – 2 3 = 6 t 1 / 2 = t the answer is b .
Answer: b
Problem: the sum of two numbers is 528 and their h . c . f is 33 . the number of pairs of numbers satisfying the above conditions is :
Options: a ) 4 , b ) 5 , c ) 6 , d ) 6 , e ) 1
Rationale: "let the required numbers be 33 a and 33 b . then , 33 a + 33 b = 528 = > a + b = 16 . now , co - primes with sum 16 are ( 1 , 15 ) , ( 3 , 13 ) , ( 5 , 11 ) and ( 7 , 9 ) . required numbers are ( 33 * 1 , 33 * 15 ) , ( 33 * 3 , 33 * 13 ) , ( 33 * 5 , 33 * 11 ) , ( 33 * 7 , 33 * 9 ) . the number of such pairs is 4 . answer : a"
Answer: a
Problem: what is the last digit in ( 7 ^ 95 - 3 ^ 58 ) ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 9 , e ) 5.5
Rationale: explanation : unit digit in 795 = unit digit in [ ( 74 ) 23 x 73 ] = unit digit in [ ( unit digit in ( 2401 ) ) 23 x ( 343 ) ] = unit digit in ( 123 x 343 ) = unit digit in ( 343 ) = 3 unit digit in 358 = unit digit in [ ( 34 ) 14 x 32 ] = unit digit in [ unit digit in ( 81 ) 14 x 32 ] = unit digit in [ ( 1 ) 14 x 32 ] = unit digit in ( 1 x 9 ) = unit digit in ( 9 ) = 9 unit digit in ( 795 - 358 ) = unit digit in ( 343 - 9 ) = unit digit in ( 334 ) = 4 . so , answer c
Answer: c
Problem: how many cuboids of length 5 m , width 4 m and height 3 m can be farmed from a cuboid of 16 m length , 10 m width and 12 m height .
Options: a ) 32 , b ) 28 , c ) 36 , d ) 40 , e ) 50
Rationale: ( 16 ã — 10 ã — 12 ) / ( 5 ã — 4 ã — 3 ) = 32 answer is a .
Answer: a
Problem: one night 10 percent of the female officers on a police force were on duty . if 200 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 90 , b ) 180 , c ) 270 , d ) 500 , e ) 1,000
Rationale: "let total number of female officers in the police force = f total number of officers on duty on that night = 200 number of female officers on duty on that night = 200 / 2 = 100 ( 10 / 100 ) * f = 100 = > f = 1000 answer e"
Answer: e
Problem: a furniture dealer purchased a desk for $ 140 and then set the selling price equal to the purchase price plus a markup that was 30 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) $ 40 , b ) $ 60 , c ) $ 80 , d ) $ 90 , e ) $ 100
Rationale: "purchase price = 140 selling price = x 140 + 0.3 * x = x 0.7 * x = 140 x = 200 profit = 200 - 140 = 60 answer : b"
Answer: b
Problem: find 96 × × 97
Options: a ) 91 / 198 , b ) 91 / 12 , c ) 91 / 13 , d ) 91 / 10 , e ) 91 / 11
Rationale: "here both numbers are less than 100 . so they are deficient of - 4 and - 3 compared with 100 . so answer : b"
Answer: b
Problem: of 3 numbers , the third is twice the first and the second is 4 times the first . if their average is 77 , the smallest of the 3 numbers is :
Options: a ) 18 , b ) 25 , c ) 20 , d ) 32 , e ) 33
Rationale: explanation : let first number be x . so , 2 nd no . = 4 x & 3 rd no . = 2 x . so , x + 4 x + 2 x = 77 × 3 = 231 7 x = 231 x = 231 / 7 hence , smallest number x = 33 answer : e
Answer: e
Problem: the slant height of a cone is 21 cm and radius of the base is 10 cm , find the curved surface of the cone .
Options: a ) 330 , b ) 770 , c ) 660 , d ) 100 , e ) 600
Rationale: "π * 21 * 10 = 660 answer : c"
Answer: c
Problem: a store reported total sales of $ 400 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?
Options: a ) 2 % , b ) 17 % , c ) 25 % , d ) 65 % , e ) 83 %
Rationale: "new value – old value ) / old value x 100 we are given : february sales this year = 400 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 400 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 400 – 320 ) / 320 ] x 100 = 25 % . the answer is c ."
Answer: c
Problem: two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 20 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
Options: a ) 3 : 5 , b ) 9 : 25 , c ) 5 : 2 , d ) 25 : 9 , e ) can not be determined from the information provided
Rationale: "same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 10 / speed b since the times are same , 50 pi / speed a = 20 pi / speed b speeda / speed b = 50 pi / 30 pi = 5 / 2 correct option : c"
Answer: c
Problem: in a company , 56 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
Options: a ) 45 % , b ) 50 % , c ) 55 % , d ) 60 % , e ) 65 %
Rationale: "the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 44 % of all employees are women , so non - union women are 44 % - 18 % = 26 % 40 % of all employees are non - union . the percent of non - union employees who are women is 26 % / 40 % = 65 % the answer is e ."
Answer: e
Problem: in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 15 and the other one , that is cheaper , costs $ 10 . the factory holds a $ 140 worth stock of 13 modules . how many of the modules in the stock are of the cheaper kind ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 11 , e ) 35
Rationale: "so the number of $ 10 modules must be 11 so that the leftover 2 modules are of $ 15 which will give a total value $ 140 . 11 * 10 + 2 * 15 = 110 + 30 = 140 answer : d"
Answer: d
Problem: in a two digit number it is known that its unit ' s digit exceeds its 10 ' s digit by 4 and that the product of the given number and the sum of its digits is equal to 208 , what is the number ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: xy is 2 digit no . y - x = 4 ; ( 10 x + y ) * ( 2 x + 4 ) = 208 ; sub y = x + 4 ; we get 26 answer : c
Answer: c
Problem: if a fills a tank in 30 mins , and b fills the same tank in 20 mins , and c emptys it in 40 min , if a , b , c works together how much time will the tank take to fill ?
Options: a ) 15.14 mins , b ) 16.14 mins , c ) 17.14 mins , d ) 18.14 mins , e ) 19.14 mins
Rationale: 1 / 30 + 1 / 20 - 1 / 40 = 7 / 120 so total time = 120 / 7 = 17.14 mins answer : c
Answer: c
Problem: an article is bought for rs . 560 and sold for rs . 340 , find the loss percent ?
Options: a ) 36 % , b ) 38 % , c ) 16 % , d ) 39 % , e ) 12 %
Rationale: 560 - - - - 220 100 - - - - ? = > 39 % answer : d
Answer: d
Problem: jennifer had $ 180 to spend on herself . she spent 1 / 5 of the money on a sandwich , 1 / 6 for a ticket to a museum , and 1 / 2 of it on a book . how much money does jennifer have left over ?
Options: a ) $ 4 , b ) $ 14 , c ) $ 5 , d ) $ 15 , e ) $ 24
Rationale: 1 / 5 x $ 180 = $ 36 for sandwich 1 / 6 x $ 180 = $ 30 for museum 1 / 2 x $ 180 = $ 90 for book $ 36 + $ 30 + $ 90 = $ 156 spent $ 180 - $ 156 = $ 24 left over correct answer e
Answer: e
Problem: a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 12 miles per gallon , and from town b to town c , the car averaged 16 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 13 , b ) 13.5 , c ) 14.4 , d ) 14.5 , e ) 15
Rationale: "ans is c given d _ ab = 2 * d _ bc let d _ ab = d and d _ bc = x so d = 2 x for average miles per gallon = ( d + x ) / ( ( d / 12 ) + ( x / 16 ) ) = 14.4 ( formula avg speed = total distance / total time )"
Answer: c
Problem: the greater of two numbers is twice the less , and the sum of the numbers is 96 . what are the numbers ?
Options: a ) 64 , b ) 68 , c ) 70 , d ) 79 , e ) 80
Rationale: let x = the less number 2 x = the greater number the sum of the numbers is 96 x + 2 x = 96 3 x = 96 x = 32 2 x = 64 option a
Answer: a
Problem: pipe p can fill a tank in 3 hours , pipe q in 9 hours and pipe r in 24 hours . if all the pipes are open , in how many hours will the tank be filled ?
Options: a ) 2 hours , b ) 2.1 hours , c ) 3 hours , d ) 3.5 hours , e ) 4.5 hours
Rationale: "explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 3 + 1 / 9 + 1 / 24 ) = 35 / 72 all the three pipes together will fill the tank = 72 / 35 = 2.1 hours answer b"
Answer: b
Problem: a boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes . how long will it take to go 8 km in stationary water ?
Options: a ) 2 hours , b ) 1 hour , c ) 1 hour 15 min , d ) 1 hour 30 min , e ) 1 hour 10 min
Rationale: "speed ( upstream ) = 2 / 1 = 2 kmhr speed ( downstream ) = 1 / ( 10 / 60 ) = 6 kmhr speed in still water = 1 / 2 ( 2 + 6 ) = 4 kmhr time taken in stationary = 8 / 4 = 2 hrs answer : a"
Answer: a
Problem: one woman and one man can build a wall together in five hours , 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 nine 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 ) 55 / 7 , b ) 1 , c ) 135 / 32 , d ) 222 / 37 , e ) 252 / 58
Rationale: solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 5 - - > ( 1 ) , w + 2 g = 1 / 5 - - > ( 2 ) and m + g = 1 / 9 - - > ( 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 / 27 , m = 2 / 27 and w = 17 / 135 . so , n = 1 / ( 32 / 135 ) = 135 / 32 option , c
Answer: c
Problem: a trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 35 per metre of cloth . how much profit will the trder earn on 40 metres of cloth ?
Options: a ) rs . 950 , b ) rs . 1500 , c ) rs . 1000 , d ) rs . 1400 , e ) none of these
Rationale: "explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 35 = rs . 170 cp on 40 metres = 170 x 40 = rs . 6800 profit earned on 40 metres cloth = rs . 8200 – rs . 6800 = rs . 1400 . answer : option d"
Answer: d
Problem: a reduction of 25 % in the price of apples would enable a man to obtain 36 more for rs . 25 , what is reduced price per dozen ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 7 , e ) 10
Rationale: "a 25 * ( 25 / 100 ) = 6 - - - 36 ? - - - 12 = > rs . 2"
Answer: a
Problem: the ratio between the present age of p and q is 6 : 7 . if q is 4 years old than p , what will be the ratio of the ages of p and q after 4 years ?
Options: a ) 8 : 7 , b ) 7 : 8 , c ) 8 : 6 , d ) 6 : 7 , e ) 6 : 8
Rationale: let p and q ' s age is 6 x and 7 x years respectively . 7 x - 6 x = 4 x = 4 required ratio = ( 6 x + 4 ) : ( 7 x + 4 ) = 28 : 32 = 7 : 8 option a is answer
Answer: a
Problem: what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 60 ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 105 , e ) 115
Rationale: "put in simple words , we need to find the highest power of 2 in 100 ^ 60 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 60 = ( 2 ^ 2 * 5 ^ 2 ) ^ 60 = 2 ^ 120 * 5 ^ 120 answer : c"
Answer: c
Problem: if both 5 ^ 3 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ^ 2 ) , what is the smallest possible positive value of n ?
Options: a ) 15 , b ) 45 , c ) 75 , d ) 125 , e ) 150
Rationale: "( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ) has two appearances of 3 ( in 12 ^ 2 ) and two appearances of 5 ( in 10 ^ 2 ) . thus n must include at least 3 * 5 = 15 the answer is a ."
Answer: a
Problem: in one hour , a boat goes 8 km along the stream and 2 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 8 + 2 ) kmph . = 5 kmph . answer b"
Answer: b
Problem: the sale price sarees listed for rs . 200 after successive discount is 20 % and 10 % is ?
Options: a ) 187 , b ) 124 , c ) 172 , d ) 144 , e ) 175
Rationale: "200 * ( 80 / 100 ) * ( 90 / 100 ) = 144 answer : d"
Answer: d
Problem: sandy is younger than molly by 20 years . if the ratio of their ages is 7 : 9 , how old is sandy ?
Options: a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70
Rationale: "let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 20 x = 10 sandy is 70 years old . the answer is e ."
Answer: e
Problem: 5 times a number equals one 100 . the number is
Options: a ) 50 , b ) 10 , c ) 15 , d ) 25 , e ) 20
Rationale: since five times the number equals one hundred , then the number equals one hundred divided by five . therefore the number is 100 / 5 = 20 . correct answer e
Answer: e
Problem: the manufacturing cost of a shoe is rs . 200 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) s 222 , b ) s 246 , c ) s 220 , d ) s 210 , e ) s 217
Rationale: "explanation : total cost of a watch = 200 + ( 500 / 100 ) = 205 . gain = 20 % = > sp = 1.2 cp = 1.2 x 205 = 246 answer : b"
Answer: b
Problem: find the compound interest on $ 10,000 in 2 years at 4 % per annum , the interest being compounded half - yearly
Options: a ) 824 , b ) 824.36 , c ) 824.32 , d ) 824.24 , e ) 824.26
Rationale: "principal = $ 10000 ; rate = 2 % per half - year ; time = 2 years = 4 half - years . amount = $ [ 10000 * ( 1 + ( 2 / 100 ) ) 4 ] = $ ( 10000 * ( 51 / 50 ) * ( 51 / 50 ) * ( 51 / 50 ) * ( 51 / 50 ) ) = $ 10824.32 . : . c . i . = $ ( 10824.32 - 10000 ) = $ 824.32 . answer c ."
Answer: c
Problem: in how many years will a sum of money doubles itself at 30 % per annum on simple interest ?
Options: a ) 7 % , b ) 3 % , c ) 5 % , d ) 8 % , e ) 2 %
Rationale: "p = ( p * 30 * r ) / 100 r = 3 % answer : b"
Answer: b
Problem: a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 25 paise per sq m is
Options: a ) rs . 186 , b ) rs . 258 , c ) rs . 486 , d ) rs . 586 , e ) none of these
Rationale: "explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 25 / 100 ) = rs . 186 answer : a"
Answer: a
Problem: a collection of books went on sale , and 2 / 3 of them were sold for $ 2.00 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 144 , b ) $ 135 , c ) $ 90 , d ) $ 60 , e ) $ 54
Rationale: since 2 / 3 of the books in the collection were sold , 1 / 3 were not sold . the 36 unsold books represent 1 / 3 of the total number of books in the collection , and 2 / 3 of the total number of books equals 2 ( 36 ) or 72 . the total proceeds of the sale was 72 ( $ 2.00 ) or $ 144 . the best answer is therefore a . answer : a .
Answer: a
Problem: in some quantity of ghee , 50 % is pure ghee and 50 % is vanaspati . if 20 kg of pure ghee is added , then the strength of vanaspati ghee becomes 30 % . the original quantity was ?
Options: a ) 25 , b ) 15 , c ) 30 , d ) 45 , e ) 20
Rationale: "let the original quantity be x then , vanaspati ghee in xkg = 50 x / 100 kg = x / 2 kg ( x / 2 ) / ( x + 20 ) = 30 / 100 x / ( 2 x + 40 ) = 3 / 10 x = 30 answer is c"
Answer: c
Problem: the roof of an apartment building is rectangular and its length is 4 times longer than its width . if the area of the roof is 1024 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 40 . , c ) 42 . , d ) 48 . , e ) 46 .
Rationale: "let the width = x x * 4 x = 1024 x ^ 2 = 256 x = 16 length = 4 * 16 = 64 difference = 64 - 16 = 48 d is the answer"
Answer: d
Problem: at what price must an article costing rs . 38 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 52.5 , b ) 50 , c ) 62.3 , d ) 62.1 , e ) 62.4
Rationale: "cp = 38 sp = 38 * ( 125 / 100 ) = 38 mp * ( 95 / 100 ) = 47.5 mp = 50 answer : b"
Answer: b
Problem: if the given two numbers are respectively 6 % and 18 % of a third number , then what percentage is the first of the second ?
Options: a ) 20 % , b ) 25 % , c ) 18 % , d ) 33 1 / 3 % , e ) none of these
Rationale: "here , l = 6 and m = 18 therefore , first number = l / m x 100 % of second number = 6 / 18 x 100 % of second number = 33 1 / 3 % of second number answer : d"
Answer: d
Problem: a 4 % stock yield 5 % . the market value of the stock is ?
Options: a ) rs . 125 , b ) rs . 80 , c ) rs . 99 , d ) rs . 109 , e ) rs . 101
Rationale: "for an income of rs . 5 , investment = rs . 100 for an income of rs . 4 , investment = rs . ( 100 / 5 ) x 4 = rs . 80 answer : b"
Answer: b
Problem: a train is 288 meter long is running at a speed of 29 km / hour . in what time will it pass a bridge of 101 meter length ?
Options: a ) 48.29 , b ) 50 , c ) 26.8 , d ) 45.29 , e ) 30
Rationale: "speed = 29 km / hr = 29 * ( 5 / 18 ) m / sec = 145 / 18 m / sec total distance = 288 + 101 = 389 meter time = distance / speed = 389 * ( 18 / 145 ) = 48.29 seconds . answer : a"
Answer: a
Problem: rani bought more apples than oranges . she sells apples at ₹ 23 apiece and makes 15 % profit . she sells oranges at ₹ 10 apiece and makes 25 % profit . if she gets ₹ 653 after selling all the apples and oranges , find her profit percentage c .
Options: a ) 16.8 % , b ) 17.4 % , c ) 17.9 % , d ) 18.5 % , e ) 19.1 %
Rationale: "given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % c = ( 97 / 556 ) * 100 = 17.4 % answer : b"
Answer: b
Problem: john had a stock of 1100 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?
Options: a ) 50.4 % , b ) 63.4 % , c ) 66.5 % , d ) 34.9 % , e ) 43.5 %
Rationale: "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1100 - n = 1100 - 402 = 698 percentage books not sold / total number of books = 698 / 1100 = 0.634 = 63.4 % correct answer b"
Answer: b
Problem: in the third grade of windblown school there are 108 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 , e ) 12
Rationale: "one third of them failed the math test = 1 / 3 of 108 = 36 . passed in math test = 82 . and 1 / 6 failed that literature test = 18 . it is a possible scenario that these 18 ( failed in literature ) were the ones who passed the math test . so in this case , no one failed in both . hence a ."
Answer: a
Problem: if a ( a - 4 ) = 21 and b ( b - 4 ) = 21 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 4 , d ) 46 , e ) 48
Rationale: "a ( a - 4 ) = 21 and b ( b - 4 ) = 21 = > a , b must be integers and if a is - 3 or 7 , b will be 7 and - 3 respectively = > a + b = 4 ans : c"
Answer: c
Problem: a housing society has been allotted a square piece of land measuring 2550.25 sq . m . what is the side of the plot ?
Options: a ) 50.25 m
b ) 50.5 m
c ) 50.65 m
d ) 50.85
e ) none
Rationale: solution side = √ 2550.25 = √ 255025 / 100 = 505 / 10 = 50.5 m . answer b
Answer: b
Problem: in a certificate by mistake a candidate gave his height as 10 % more than actual height . in the interview panel , he clarified that his height was 5 feet 5 nches . find the % correction made by the candidate from his stated height to his actual height ?
Options: a ) 6.5 , b ) 7 , c ) 8 , d ) 9 , e ) 5
Rationale: "his height was = 5 feet 5 inch = 5 + 60 = 65 inch . required % correction = 65 * ( 1.10 - 1 ) = 6.5 a"
Answer: a
Problem: rs . 900 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 900 become in 3 years ?
Options: a ) rs . 1020.80 , b ) rs . 1025 , c ) rs . 1064 , d ) data inadequate , e ) none of these
Rationale: "solution s . i . = rs . ( 956 - 900 ) = rs . 56 rate = ( 100 x 56 / 900 x 3 ) = 56 / 27 % new rate = ( 56 / 27 + 4 ) % = 164 / 27 % new s . i . = rs . ( 900 x 164 / 27 x 3 / 100 ) rs . 164 . ∴ new amount = rs . ( 900 + 164 ) = rs . 1064 . answer c"
Answer: c
Problem: if the population of a certain country increases at the rate of one person every 20 seconds , by how many persons does the population increase in 30 minutes ?
Options: a ) 55 , b ) 20 , c ) 96 , d ) 90 , e ) 40
Rationale: answer = 3 * 30 = 90 answer = d
Answer: d
Problem: jake took a bus from home to market , that travels at 10 kmph . while walking back at 2 kmph , halfway through , he suddenly realized he was getting late and he cycled back the remaining distance in 50 kmph . find the average speed .
Options: a ) 1.17 kmph , b ) 1.67 kmph , c ) 0.69 kmph , d ) 1.45 kmph , e ) none of these
Rationale: let the distance be 2 x ( one way ) time taken by bus = 2 x / 10 , by walking = x / 2 , by cycling = x / 50 hours : . average speed = total distance / total time = 2 x / x / 5 + x / 2 + x / 50 = 2 * 60 / 12 + 30 + 1.2 = 1.67 answer : b
Answer: b
Problem: a survey reveals that the average income of a company ’ s customers is $ 45000 per year . if 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $ 55000 , what is the average income of the other 40 customers ? is there a way to solve this using weighted average concept instead of doing tedious calculations ?
Options: a ) $ 27,500 , b ) $ 35,000 , c ) $ 37,500 , d ) $ 42,500 , e ) $ 50,000
Rationale: let x be the average of 40 customers 40 * x + 10 * 55000 = 50 * 45000 solving this we have x = 42500 answer is d .
Answer: d
Problem: hcf of two numbers is 11 and the product of these numbers is 363 , what is the the greater number ?
Options: a ) 28 , b ) 31 , c ) 33 , d ) 35 , e ) 38
Rationale: the numbers be 11 a and 11 b 11 a × 11 b = 363 ab = 3 co - primes with product 3 are ( 1 , 3 ) hence the numbers with hcf 11 and product 363 = ( 11 × 1 , 11 × 3 ) = ( 11 , 33 ) numbers are 11 and 33 the greater number = 33
Answer: c
Problem: if n divided by 7 has a remainder of 2 , what is the remainder when 4 times n is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8
Rationale: "as per question = > n = 7 p + 2 for some integer p hence 4 n = > 28 q + 8 = > remainder = > 6 for some integer q alternatively = > n = 2 > 3 n = > 8 = > 8 divided by 7 will leave a remainder 1 hence a"
Answer: a
Problem: running at the same rate , 8 identical machines can produce 560 paperclips a minute . at this rate , how many paperclips could 12 machines produce in 6 minutes ?
Options: a ) 1344 , b ) 3360 , c ) 8400 , d ) 5040 , e ) 67200
Rationale: "8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 12 machine produce 560 * 6 * ( 12 / 8 ) in 6 minutes 560 * 6 * 12 / 8 = 5040 answer is d ."
Answer: d
Problem: if 8 workers can build 8 cars in 8 days , then how many days would it take 5 workers to build 5 cars ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 10 , e ) 12
Rationale: "8 workers can build 1 car per day on average . 1 worker can build 1 / 8 of a car per day . 5 workers can build 5 / 8 car per day . the time required to build 5 cars is 5 / ( 5 / 8 ) = 8 days the answer is c ."
Answer: c
Problem: square m is inscribed in circle n . if the perimeter of m is 20 , what is the circumference of n ?
Options: a ) 33 √ 2 π
b ) 2 √ 2 π
c ) 6 √ 2 π
d ) 7 √ 2 π
e ) 5 √ 2 π
Rationale: square forms two right angled triangles . any time we have a right angle triangle inside a circle , the hypotenuse is the diameter . hypotenuse here = diagonal of the square = 5 sqrt ( 2 ) = diameter = > radius = 2.5 sqrt ( 2 ) circumference of the circle = 2 pi r = 5 pi sqrt ( 2 ) answer is e .
Answer: e
Problem: if both 7 ^ 2 and 3 ^ 4 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ?
Options: a ) 120 , b ) 256 , c ) 343 , d ) 441 , e ) 512
Rationale: "the number a must include at least 3 ^ 2 * 7 ^ 2 = 441 the answer is d ."
Answer: d
Problem: how many times digit 6 is used while writing numbers from 100 to 1400 ?
Options: a ) 648 , b ) 350 , c ) 252 , d ) 225 , e ) 26
Rationale: "there are 100 numbers which begin with 600 next , in every 10 numbers such as 100 to 110 , 110 to 120 , 120 to 130 6 comes at least once . number of such intervals = end limit - first no . / interval . our range of numbers is 100 - 1000 1000 - 100 = 900 / 10 = 90 number of 10 s interval in this is 90 . so 90 ' 6 s ' so far we have calculated 190 . the total now comes to 280 . the nearest to which is 350 . hence b ."
Answer: b
Problem: a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 25 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 300 . , b ) 412 . , c ) 432 . , d ) 502 . , e ) 522 .
Rationale: "pastry is divided in 25 customers equally . so , total number of pastry must be a multiple of 25 only option a satisfies the condition , and hence is the answer"
Answer: a
Problem: the sum of the non - prime numbers between 40 and 50 , non - inclusive , is
Options: a ) 131 , b ) 176 , c ) 274 , d ) 405 , e ) 495
Rationale: "the sum of the non - prime numbers between 40 and 50 , non - inclusive , are { 42 , 44 , 45 , 46 , 48 , 49 } . 6 times 40 something is approx north of 240 hence the answer is ( c ) 274"
Answer: c
Problem: fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 20 kg of fresh grapes ?
Options: a ) 2 kg , b ) 2.4 kg , c ) 2.5 kg , d ) 10 kg , e ) none of these
Rationale: "the weight of non - water in 20 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 20 ∗ 0.1 = x ∗ 0.8 - - > x = 2.5 answer : c ."
Answer: c
Problem: there are 9 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 36 , d ) 60 , e ) 90
Rationale: "9 players are there . two players play one game with one another . so 9 c 2 = 9 x 8 / 2 = 36 so option c is correct"
Answer: c
Problem: in order to obtain an income of rs . 680 from 10 % stock at rs . 120 , one must make an investment of
Options: a ) 5363 , b ) 8160 , c ) 2368 , d ) 1987 , e ) 2732
Rationale: "to obtain rs . 10 , investment = rs . 120 . to obtain rs . 680 , investment = = rs . 8160 . answer : b"
Answer: b
Problem: in a party every person shakes hands with every other person . if there are 105 hands shakes , find the number of person in the party
Options: a ) 14 , b ) 12 , c ) 13 , d ) 15 , e ) 16
Rationale: "let n be the number of persons in the party . number of hands shake = 105 ; total number of hands shake is given by nc 2 . now , according to the question , nc 2 = 105 ; or , n ! / [ 2 ! * ( n - 2 ) ! ] = 105 ; or , n * ( n - 1 ) / 2 = 105 ; or , n 2 - n = 210 ; or , n 2 - n - 210 = 0 ; or , n = 15 , - 14 ; but , we can not take negative value of n . so , n = 15 i . e . number of persons in the party = 15 . answer d"
Answer: d
Problem: the price of stock decreased by 8 % last year and rose by 10 % this year . what is the net percentage change in the price of the stock ?
Options: a ) 0.2 % , b ) 0.8 % , c ) 1.2 % , d ) 1.6 % , e ) 2 %
Rationale: ( 100 % - 8 % ) * ( 100 % + 10 % ) = 0.92 * 1.10 = 1.012 = 101.2 % . the net percentage change in the price of the stock is ( + ) 1.2 % the answer is c
Answer: c
Problem: two men and three women working 7 hours a day finish a work in 5 days . four men and four women working 3 hours a day complete the work in 7 days . the number of days in which only 7 men working 4 hours a day will finish the work is ?
Options: a ) 5 days , b ) 3 days , c ) 2 days , d ) 9 days , e ) 10 days
Rationale: answer : option a 2 m + 3 w - - - - - 35 h 4 m + 4 w - - - - - - - 21 h 7 m - - - - - - - ? d 70 m + 105 w = 84 m + 84 m 21 w = 14 m = > 2 m = 3 w 4 * 35 = 7 * x = > x = 20 hours 20 / 4 = 5 days
Answer: a
Problem: a train is running at a speed of 40 km / hr and it crosses a post in 19.8 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 220 metres , e ) 250 metres
Rationale: "speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 19.8 s distance covered , d = vt = ( 400 / 36 ) ã — 19.8 = 220 m distance covered is equal to the length of the train = 220 m correct answer is 220 metres d"
Answer: d
Problem: the average age of 20 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?
Options: a ) 79 , b ) 86 , c ) 95 , d ) 72 , e ) 80
Rationale: "age of the 15 th student = 20 * 15 - ( 14 * 5 + 16 * 9 ) = 300 - 214 = 86 years answer is b"
Answer: b
Problem: in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 8 , 1 ) , ( 1 , 1 ) , ( 1 , - 7 and ( - 8 , - 7 ) ?
Options: a ) 144 , b ) 36 , c ) 72 , d ) 56 , e ) 112
Rationale: "length of side 1 = 8 + 1 = 9 length of side 2 = 7 + 1 = 8 area of rectangle = 9 * 8 = 72 c is the answer"
Answer: c
Problem: on a certain farm the ratio of horses to cows is 6 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 3 : 1 . after the transaction , how many more horses than cows would the farm own ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "originally , there were 6 k horses and k cows . ( 6 k - 15 ) = 3 ( k + 15 ) 6 k - 3 k = 45 + 15 3 k = 60 k = 20 the difference between horses and cows is ( 6 k - 15 ) - ( k + 15 ) = 5 k - 30 = 70 the answer is d ."
Answer: d
Problem: if a * b * c = 195 , b * c * d = 65 , c * d * e = 1000 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) none of these
Rationale: explanation : a â ˆ — b â ˆ — c / b â ˆ — c â ˆ — d = 195 / 65 = > a / d = 3 d â ˆ — e â ˆ — f / c â ˆ — d â ˆ — e = 250 / 1000 = > f / c = 1 / 4 a / d * f / c = 3 * 1 / 4 = 3 / 4 answer : c
Answer: c
Problem: a circular well with a diameter of 2 metres , is dug to a depth of 4 metres . what is the volume of the earth dug out ?
Options: a ) 26 m ³ , b ) 28 m ³ , c ) 44 m ³ , d ) 46 m ³ , e ) none
Rationale: "sol . volume = ∏ r ² h = [ 22 / 7 * 1 * 1 * 14 ] m ³ = 44 m ³ answer c"
Answer: c
Problem: what is the least value of x , so that 2 x 5478 is divisible by 9
Options: a ) 7 , b ) 8 , c ) 9 , d ) 1 , e ) 2
Rationale: "explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 5 + 4 + 7 + 8 = 26 + x least value of x may be ' 1 ' , so that the total 26 + 1 = 27 is divisible by 9 . answer : option d"
Answer: d
Problem: the jogging track in a sports complex is 594 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 5.29 min , b ) 4.32 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min
Rationale: "clearly , the two will meet when they are 594 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 594 m apart , they take ( 100 / 825 * 594 / 1000 ) hrs = ( 594 / 8250 * 60 ) min = 4.32 min . answer : b"
Answer: b
Problem: a can do a job in 45 days and b can do it in 30 days . a and b working together will finish 4 times the amount of work in - - - - - - - days ?
Options: a ) 30 days , b ) 45 days , c ) 80 days , d ) 72 1 / 2 days , e ) 72 days
Rationale: 1 / 45 + 1 / 30 = 5 / 90 = 1 / 18 18 / 1 = 18 * 4 = 72 days answer : e
Answer: e
Problem: on dividing a number by 357 , we get 37 as remainder . on dividing the same number by 17 , what will be the remainder ?
Options: a ) 4 , b ) 3 , c ) 8 , d ) 7 , e ) 2
Rationale: "let x be the number and y be the quotient . then , x = 357 * y + 37 = ( 17 * 21 * y ) + ( 17 * 2 ) + 3 = 17 * ( 21 y + 2 ) + 3 . required number = 3 . answer is b"
Answer: b
Problem: a certain social security recipient will receive an annual benefit of $ 12,000 provided he has annual earnings of $ 9,360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9,360 . what amount of total annual earnings would result in a 55 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 25,560 , d ) $ 21,360 , e ) $ 27,360
Rationale: "for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.55 * 12000 = 12000 - 6600 x = 5400 earning becomes 9360 + 3 x = 9360 + 3 * 5400 = 25560 ans : c"
Answer: c
Problem: a vessel of capacity 45 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ?
Options: a ) 28.8 , b ) 72.9 , c ) 38.3 , d ) 78.3 , e ) 79.3
Rationale: "explanation : let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] ^ n * t for the given problem , t = 45 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 45 - 9 ) / 45 ] ^ 2 ( 45 ) = 28.8 litres . answer : option a"
Answer: a
Problem: if circles x and y have the same area and circle x has a circumference of 12 π , half of the radius of circle y is :
Options: a ) 16 , b ) 8 , c ) 3 , d ) 2 , e ) 1
Rationale: "x be radius of circle x y be radius of circle y given : pi * x ^ 2 = pi * y ^ 2 also , 2 * pi * x = 12 * pi x = 6 thus y = 6 y / 2 = 3 ans : c"
Answer: c
Problem: convert the 18 / 42 m / s into kilometers per hour ?
Options: a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1.2 kmph . , d ) 1.54 kmph . , e ) 1.9 kmph .
Rationale: "18 / 42 m / s = 18 / 42 * 18 / 5 = 1 ( 27 / 50 ) = 1.54 kmph . answer : d"
Answer: d
Problem: if a man lost 1 % by selling oranges at the rate of 16 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 12 , b ) 14 , c ) 7 , d ) 11 , e ) 10
Rationale: "99 % - - - - 16 144 % - - - - ? 99 / 144 * 16 = 11 answer : d"
Answer: d
Problem: a certain car uses one gallon of gasoline every 34 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ?
Options: a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 35 % , e ) 50 %
Rationale: 4 miles on the highway = 4 / 34 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 34 + 4 / 20 = 27 / 85 gallons . 8 miles on the highway = 4 / 17 gallons . the % change = ( 27 / 85 - 4 / 17 ) / ( 4 / 17 ) = 0.35 . answer : d .
Answer: d
Problem: in measuring the sides of a rectangle , one side is taken 9 % in excess , and the other 8 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.11 % , b ) 0.7 % , c ) 0.4 % , d ) 0.6 % , e ) 0.28 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 12 / 11 ) x ( 23 / 25 ) y = ( 358 / 357 ) ( xy ) error in measurement = ( 358 / 357 ) xy - xy = ( 1 / 357 ) xy error percentage = [ ( 1 / 357 ) xy ( 1 / xy ) 100 ] % = ( 7 / 25 ) % = 0.28 % . answer is e ."
Answer: e
Problem: there is 50 % increase in an amount in 6 years at s . i . what will be the c . i . of rs . 12,000 after 3 years at the same rate ?
Options: a ) 2160 , b ) 3120 , c ) 17988 , d ) 6240 , e ) 5240
Rationale: "let p = rs . 100 . then , s . i . rs . 50 and t = 6 years . r = ( 100 * 50 ) / ( 100 * 6 ) = 10 % p . a . now , p = rs . 12000 , t = 3 years and r = 8.33 % p . a . c . i . = [ 12000 * { ( 1 + 8.33 / 100 ) 3 - 1 } ] = rs . 17988 answer : c"
Answer: c
Problem: if the cost price is 86 % of the selling price , then what is the profit percent ?
Options: a ) 5 % , b ) 11 % , c ) 16 % , d ) 21 % , e ) 19 %
Rationale: "let s . p . = $ 100 c . p . = $ 86 profit = $ 14 profit % = 14 / 86 * 100 = 25 / 6 = 16 % approximately answer is c"
Answer: c
Problem: find the length of the wire required to go 15 times round a square field containing 69696 m ^ 2 .
Options: a ) 1250 , b ) 2489 , c ) 6398 , d ) 15840 , e ) 2487
Rationale: "explanation : a 2 = 69696 = > a = 264 4 a = 1056 1056 * 15 = 15840 answer : d"
Answer: d
Problem: the average of 5 quantities is 8 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 14 , b ) 10 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: "answer : a ( 5 x 8 - 3 x 4 ) / 2 = 14"
Answer: a
Problem: the perimeter of one square is 48 cm and that of another is 20 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 5 cm
b ) 13 √ 2 cm
c ) 12 cm
d ) 6 cm
e ) 8 cm
Rationale: explanation : 4 a = 48 4 a = 20 a = 12 a = 5 a ^ 2 = 144 a ^ 2 = 25 combined area = a ^ 2 = 169 = > a = 13 d = 13 √ 2 cm answer : b
Answer: b
Problem: in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 14 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: the class borrowed a total of 40 * 2 = 80 books . the 28 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 14 * 2 = 40 . to maximize the number of books borrowed by 1 student , let ' s assume that 11 students borrowed 3 books and 1 student borrowed the rest . 80 - 40 - 3 * 11 = 7 the maximum number of books borrowed by any student is 7 . the answer is e .
Answer: e
Problem: a picnic attracts 240 persons . there are 30 more men than women , and 30 more adults than children . how many men are at this picnic ?
Options: a ) 240 , b ) 75 , c ) 85 , d ) 130 , e ) 200
Rationale: "adult + children = 240 let , children = y then , adult = y + 30 i . e . y + ( y + 30 ) = 210 i . e . y = 115 i . e . adult = 115 + 30 = 145 adults include only men and women i . e . men + women = 145 let women , w = x then men , m = x + 30 i . e . x + ( x + 30 ) = 2 x + 30 = 145 i . e . x = 55 i . e . men , m = 55 + 30 = 85 answer : option c"
Answer: c
Problem: find 80 / ? = ? / 20
Options: a ) 40 , b ) 400 , c ) 800 , d ) 1600 , e ) none
Rationale: "answer let 80 / y = y / 20 then , y 2 = 80 x 20 = 1600 ∴ y = √ 1600 = 40 . option : a"
Answer: a
Problem: what is the greatest positive integer r such that 3 ^ r is a factor of 9 ^ 10 ?
Options: a ) r = 5 , b ) r = 9 , c ) r = 10 , d ) r = 20 , e ) 30
Rationale: "what is the greatest positive integer r such that 3 ^ r is a factor of 9 ^ 10 ? 9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 d . 20"
Answer: d
Problem: find the average of all the numbers between 40 and 80 which are divisible by 3 .
Options: a ) 15 , b ) 70 , c ) 20 , d ) 60 , e ) none
Rationale: "sol . average = ( 42 + 45 + 48 + 51 + 54 + 57 + 60 + 63 + 66 + 69 + 72 + 75 + 78 / 13 ) = 780 / 5 = 60 . answer d"
Answer: d
Problem: a can do a job in 18 days and b can do it in 30 days . in how many days will they finish it together ?
Options: a ) 1 / 9 , b ) 4 / 45 , c ) 2 / 7 , d ) 6 / 3 , e ) 5 / 2
Rationale: explanation : 1 / 18 + 1 / 30 = 8 / 90 = 4 / 45 so , both together will finish the work in 4 / 45 days . answer : b
Answer: b
Problem: in the xy - plane the point ( - 2 - 3 ) is the centre of a circle , the point ( - 2 , 1 ) lies inside the circle and the point ( 4 , - 3 ) lies outside the circle . if the radius r of the circle r is an integer then diameter ?
Options: a ) 6 , b ) 10 , c ) 4 , d ) 3 , e ) 2
Rationale: "can be solved without much calculations . you are given that ( - 2 , - 3 ) is the center of the circle . point ( 4 , - 3 ) lies inside the circle - - - > the radius is lesser than distance of ( - 2 , - 3 ) from ( 4 , - 3 ) - - - > lesser than 6 units but the radius will also be greater than the distance of ( - 2 , - 3 ) from ( - 2,1 ) - - - - > greater than 4 units . thus the radius is > 4 but < 6 and as it is an integer , the only possible value of radius = 5 units . diameter = 2 r = 10 b is the correct answer ."
Answer: b
Problem: the mass of 1 cubic meter of a substance is 300 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 1.33
b ) 1.25
c ) 8.0
d ) 12.5
e ) 80.0
Rationale: density is mass divided by volume . so density of the given substance will be mass / volume = 800 kg / 1 m ^ 3 = 300 kg / m ^ 3 or 1 g / 1.33 cm ^ 3 = 0.3 g / cm ^ 3 . next , ask yourself if 300,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 000,000 / 300,000 = 10 / 3 = 1.33 cubic centimeters . answer is a
Answer: a
Problem: in a 300 member association consisting of men and women , exactly 80 % of men and exactly 15 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: "solution simple out of 300 80 % are male i . e 240 and 15 % are female i . e 45 , so total homeowner is 295 . now min number homeowner is 45 and max is 240 so question ask us to find least and 46 has least value among all option . so ans is 46 . ans : a"
Answer: a
Problem: mark has a rectangular driveway with a line painted diagonally across . the length of the driveway is 5 feet longer than its width . if the total area of the driveway is 36 square feet , what is the length of the painted line ( in feet ) ?
Options: a ) between 9 and 10
b ) between 10 and 11
c ) between 11 and 12
d ) between 12 and 13
e ) between 13 and 14
Rationale: to solve this , we first need to set up an equation for the area of the room . if x is the width , then we have x ( x + 5 ) = 36 . by putting the equation in standard form , we get x ^ 2 + 5 x - 36 = 0 . by using the quadratic formula , we get roots of 4 and - 9 . we know that x is the width , and x + 5 is the length , so by using the roots , we get 4 as the width ( x ) , and 9 as the length ( x + 5 ) . once we have this , we can use the pythagorean theorem to solve for the diagonal . plugging in the length and width , we will get d ^ 2 = 4 ^ 2 + 9 ^ 2 = 16 + 81 = 97 the square root of 97 is less than 10 , since 10 ^ 2 = 100 . going down a number , we can compute 9 ^ 2 = 81 < 97 . therefore , the length of the diagonal must be between 9 and 10 . the correct answer is a .
Answer: a
Problem: tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 41 pages per hour . if tom starts reading a novel at 3 : 20 , and jan begins reading an identical copy of the same book at 4 : 26 , at what time will they be reading the same page ?
Options: a ) 6 : 26 , b ) 6 : 56 , c ) 7 : 26 , d ) 7 : 56 , e ) 8 : 26
Rationale: since tom reads an average of 1 page every 2 minutes , tom will read 33 pages in the first 66 minutes . jan can catch tom at a rate of 11 pages per hour , so it will take 3 hours to catch tom . the answer is c .
Answer: c
Problem: a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 355 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 115 , c ) 120 , d ) 130 , e ) 220
Rationale: "orchestra seats - a balcony seats - b a + b = 355 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 355 = 3320 - 2840 = 480 i . e . a = 120 and b = 355 - 120 = 235 more seats in balcony than orchestra = b - a = 235 - 120 = 115 answer : option b"
Answer: b
Problem: a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 6 years ago ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let ' s say age of richard isr age of david isd age of scott iss now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 6 years ago ? i . e . d - 6 = 14 - 6 = 8 years answer : option a"
Answer: a
Problem: a type t machine can complete a job in 5 hours and a type b machine can complete the job in 7 hours . how many hours will it take 2 type t machines and 3 type b machines working together and independently to complete the job ?
Options: a ) 1 / 5 , b ) 29 / 35 , c ) 5 / 6 , d ) 35 / 29 , e ) 35 / 12
Rationale: now d should be the answer . t need 5 hours to complete and b needs 7 hours to compete so 2 t + 3 b will complete 2 / 5 + 3 / 7 or 29 / 35 portion of the job in 1 hour so the whole job will take 35 / 29 hours . . . . = d
Answer: d
Problem: on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 120,000 ?
Options: a ) 15 , b ) 21 , c ) 18 , d ) 20 , e ) 24
Rationale: "if i were to choose during the test , would go for 18 or 20 . probably 18 cuz it wont take too long to get the value doubled . . . . i found a method : rule of 72 . given an x % return , it takes 10,000 to quadralope 12 years . so according to the rule : 72 / x is the no of years 10 , 000.00 took to double 20 , 000.00 . again , 20 , 000.00 took to double 40 , 000.00 same ( 72 / x ) no of years . 72 / x + 72 / x = 12 x = 12 % ( though rate here is not very much required ) . again , 40 , 000.00 takes the same ( 72 / x ) no of years to double 120 , 000.00 . 72 / x = 6 years . so altogather : 10,000 - 20,000 = 6 years 20,000 - 40,000 = 6 years 40,000 - 80,000 = 6 years 80,000 - 120,000 = 3 years total 21 years . answer b"
Answer: b