regisss/math_qa huggingface dataset:
Problem: how many times are the hands of a clock at right angles in a day ?
Options: a ) 42 , b ) 44 , c ) 49 , d ) 41 , e ) 47
Rationale: in 12 hours , they are at right angles 22 times . = = > in 24 hours , they are at right angles 44 times . answer is b .
Answer: b
Problem: a cyclist traveled for two days . on the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day . if during the two days she traveled a total of 240 miles and spent a total of 12 hours traveling , what was her average speed on the second day ?
Options: a ) 5 mph , b ) 10 mph , c ) 20 mph , d ) 30 mph , e ) 40 mph
Rationale: solution : d = 280 mi t = 12 hrs đ â y 1 time = t 1 d â y 2 time = t 2 t 2 - t 1 = 4 hrs - - - - - ( i ) t 1 + t 2 = 12 hrs - - - - - ( ii ) adding i and ii , t 2 = 8 hrs and t 1 = 4 hrs d à y 1 rate = r 1 d â y 2 rate = r 2 r 1 - r 2 = 10 mph í . ẹ . r 1 = 10 + r 2 280 = 8 r 2 + 4 r 1 í . ẹ . 280 = 8 r 2 + 4 ( 10 + r 2 ) í . ẹ . r 2 = 20 mph answer : b
Answer: b
Problem: a is twice as good as workman as b and together they finish a piece of work in 18 days . in how many days will b alone finish the work .
Options: a ) 27 days , b ) 54 days , c ) 56 days , d ) 68 days , e ) none of these
Rationale: explanation : as per question , a do twice the work as done by b . so a : b = 2 : 1 also ( a + b ) one day work = 1 / 18 to get days in which b will finish the work , lets calculate work done by b in 1 day = = ( 118 ∗ 13 ) = 154 [ please note we multiplied by 1 / 3 as per b share and total of ra ɵ o is 1 / 3 ] so b will finish the work in 54 days answer : b
Answer: b
Problem: in the xy - coordinate system , what is the slope of the line that goes through the origin and is equidistant from the two points p = ( 4 , 6 ) and q = ( 6 , 2 ) ?
Options: a ) 0.8 , b ) 1.0 , c ) 1.2 , d ) 1.4 , e ) 1.6
Rationale: first , get the middle coordinate between ( 46 ) and ( 62 ) . x = 4 + ( 6 - 4 ) / 2 = 5 y = 2 + ( 6 - 2 ) / 2 = 4 second , get the slope of ( 54 ) and ( 00 ) . m = 4 - 0 / 5 - 0 = 4 / 5 = 0.8 answer : a
Answer: a
Problem: an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 15 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 80.00
Rationale: "without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 23 % , thus he must pay slightly more than $ 77 . answer : e ."
Answer: e
Problem: the perimeter of a rectangle is 60 mete ( 132 ) 7 × ( 132 ) ? = ( 132 ) 11.5 .
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "7 + x = 11.5 x = 11.5 - 7 x = 4.5 answer : d"
Answer: d
Problem: the youngest of 4 children has siblings who are 3 , 5 , and 8 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 21 , what is the age of the youngest sibling ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 21 , e ) 22
Rationale: "total age of the 4 sibling is 21 x 4 = 84 years . . we already have the total age of all the children is 4 y + 16 so , 4 y + 16 = 84 or , 4 y = 68 or , y = 17 so , age of the youngest child is 17 years . answer : a"
Answer: a
Problem: a can do a piece of work in 15 days and b can do it in 15 days and c can do it 20 days . they started the work together and a leaves after 2 days and b leaves after 4 days from the beginning . how long will work lost ?
Options: a ) 15 , b ) 10 , c ) 12 , d ) 11 , e ) 13
Rationale: "2 / 15 + 4 / 15 + x / 20 = 1 x = 12 answer : c"
Answer: c
Problem: the speed of a boat in still water is 36 kmph . what is the speed of the stream if the boat can cover 80 km downstream or 40 km upstream in the same time ?
Options: a ) 10 kmph , b ) 14 kmph , c ) 12 kmph , d ) 16 kmph , e ) 15 kmph
Rationale: "x = the speed of the stream ( 36 + x ) / ( 36 - x ) = 2 / 1 36 + x = 72 - 2 x 3 x = 36 x = 12 km / hour if the speed of the stream is 12 km / hour , then the ' downstream ' speed of the boat is 36 + 12 = 48 km / hour and the ' upstream ' speed of the boat is 36 - 12 = 24 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 48 = 96 km downstream and 2 x 24 = 48 km / hour upstream . answer : c"
Answer: c
Problem: a man buys a cycle for rs . 1800 and sells it at a loss of 10 % . what is the selling price of the cycle ?
Options: a ) 1410 , b ) 1620 , c ) 1430 , d ) 1440 , e ) 1540
Rationale: "s . p . = 90 % of rs . 1800 = 90 / 100 x 1800 = rs . 1620 answer : b"
Answer: b
Problem: if n divided by 11 has a remainder of 1 , what is the remainder when 5 times n is divided by 11 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 9 , e ) 5
Rationale: "as per question = > n = 11 p + 1 for some integer p hence 5 n = > 55 q + 5 = > remainder = > 5 for some integer q hence e"
Answer: e
Problem: an artist wishes to paint a circular region on a square poster that is 3.4 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ?
Options: a ) 1 / pi
b ) sqrt ( 2 / pi )
c ) 1
d ) 2 / sqrt ( pi )
e ) sqrt ( 5.78 / pi )
Rationale: area of the poster is 3.4 x 3.4 = 11.56 1 / 2 the area = 5.78 pi * r ^ 2 = 5.78 r ^ 2 = 5.78 / pi r = sqrt ( 5.78 / pi ) answer ( e )
Answer: e
Problem: the value of ( 34.31 * 0.473 * 1.567 ) / ( 0.0673 * 23.5 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.05 , d ) 2.12 , e ) 2.35
Rationale: "( 34.31 * 0.473 * 1.567 ) / ( 0.0673 * 23.5 * 7.57 ) = 25.4303 / 11.972 = 2.12 answer : d"
Answer: d
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 47 , then how old is b ?
Options: a ) 17 years , b ) 19 years , c ) 18 years , d ) 10 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 47 5 x = 45 = > x = 9 hence , b ' s age = 2 x = 18 years . answer : c"
Answer: c
Problem: find the value of 658217 x 99999 = m ?
Options: a ) 65842158943 , b ) 65839570421 , c ) 65821141683 , d ) 66821785904 , e ) 65821041783
Rationale: "658217 x 99999 = 658217 x ( 100000 - 1 ) = 658217 x 100000 - 658217 x 1 = 65821700000 - 658217 = 65821041783 e"
Answer: e
Problem: a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1251 . find the number to be multiplied .
Options: a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 139
Rationale: "let the required number be x . then , 43 x – 34 x = 1251 or 9 x = 1251 or x = 139 . required number = 139 . answer : e"
Answer: e
Problem: calculate the largest 6 digit number which is exactly divisible by 55 ?
Options: a ) 999955 , b ) 999900 , c ) 999845 , d ) 999790 , e ) 999735
Rationale: "largest 4 digit number is 999999 after doing 999999 ÷ 55 we get remainder 44 hence largest 4 digit number exactly divisible by 88 = 999999 - 44 = 999955 a"
Answer: a
Problem: 10 years ago , the age of peter was one - third the age of jacob at that time . the present age of jacob is 12 years more than the present age of peter . find the present age of peter ?
Options: a ) 15 , b ) 11 , c ) 18 , d ) 16 , e ) 20
Rationale: d 16 let the present ages of peter and jacob be ' a ' and ' b ' respectively . a - 10 = 1 / 3 ( b - 10 ) - - - ( 1 ) b = a + 12 substituting b = a + 12 in first equation , a - 10 = 1 / 3 ( a + 2 ) = > 3 a - 30 = a + 2 = > 2 a = 32 = > a = 16 .
Answer: d
Problem: at a supermarket , john spent 1 / 2 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 8 on candy , how much did john spend at the supermarket ?
Options: a ) $ 60 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 180
Rationale: let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 2 of his money on fresh fruits and vegetables , or ( 1 / 2 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 8 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 2 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 8 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 15 t + 10 t + 3 t + 240 = 30 t 28 t + 240 = 30 t 240 = 2 t t = 120 john spent $ 90 at the supermarket . answer : d
Answer: d
Problem: tough and tricky questions : exponents . if 5 ^ ( x + 1 ) * 4 ^ ( y - 1 ) = 25 ^ x * 64 ^ y , then x + y =
Options: a ) 3 / 2 , b ) - 1 / 2 , c ) - 1 , d ) 1 / 2 , e ) 2 / 3
Rationale: here is my solution . 5 ^ ( x + 1 ) * 4 ^ ( y - 1 ) = 25 ^ x * 64 ^ y here rhs 25 ^ x * 64 ^ y = 5 ^ ( 2 x ) * 4 ^ ( 3 y ) equating powers on both sides - - > x + 1 = 2 x , thus x = 1 and 2 y - 1 = 3 y giving y = - 1 / 2 so , x + y = 1 / 2 option : d
Answer: d
Problem: what is the remainder of e = 3 ^ 19 when divided by 10 ?
Options: a ) 0 , b ) 1 , c ) 5 , d ) 7 , e ) 9
Rationale: i looked for patterns : ^ 2 - units digit 9 ^ 3 - units digit 7 ^ 4 - units digit 1 ^ 5 - units digit 3 hence , we can see that when raised to a power which is multiple of 4 , the units digit is 1 , and when to an even power not multiple of 4 , the units digit is 9 and we can then see : ^ 16 - units digit 1 , or ^ 18 - units digit 9 and ^ 19 - units digit 7 therefore , e = when divided by 10 , the remainder must be 7 . d
Answer: d
Problem: what no should be subtracted from 92555 to make it a perfect square ?
Options: a ) 128
b ) 158
c ) 178
d ) 139
e ) 140
Rationale: root 92555 = 304.228 and 304 ^ 2 = 92416 92555 - 92416 = 139 should be subtracted from 92555 to make it a perfect square answer : d
Answer: d
Problem: a hall is 6 meters long and 6 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?
Options: a ) 96 , b ) 100 , c ) 104 , d ) 108 , e ) 112
Rationale: "2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 108 the answer is d ."
Answer: d
Problem: the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 6 . the true discount is
Options: a ) rs . 72 , b ) rs . 36 , c ) rs . 54 , d ) rs . 50 , e ) none
Rationale: "solution t . d = [ b . g x 100 / r x t ] = rs . ( 6 x 100 / 12 x 1 ) = rs . 50 . answer d"
Answer: d
Problem: a line has a slope of 3 / 4 and intersects the point q ( - 12 , - 39 ) . at which point does this line intersect the x - axis ?
Options: a ) ( 40,0 ) , b ) ( 30,0 ) , c ) ( 0,40 ) , d ) ( 40,30 ) , e ) ( 0,30 )
Rationale: "assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point q of intersection is ( 40,0 ) . a is the correct answer ."
Answer: a
Problem: a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 80 points . to the nearest tenth of a point , what was the student ’ s average grade for the entire two - year period ?
Options: a ) 79 , b ) 89 , c ) 95 , d ) 90.91 , e ) 97.2
Rationale: let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 80 * 5 = 400 student ' s average = ( 600 + 400 ) / 11 = 90.91 answer d
Answer: d
Problem: 8.008 / 2.002
Options: a ) 0.004 , b ) 0.04 , c ) 4 , d ) 40 , e ) 400
Rationale: "answer is 4 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 8008 / 2002 = 4 answer c"
Answer: c
Problem: the number 86 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "7 ^ 2 + 6 ^ 2 + 1 ^ 2 = 49 + 36 + 1 = 86 7 + 6 + 1 = 14 hence answer is d"
Answer: d
Problem: a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 50 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 54 , e ) 60
Rationale: "a - b = 120 miles b - c = 60 miles avg speed = 50 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 50 = 180 / 4 t t = 54 b - c = 54 mph answer d"
Answer: d
Problem: a 14 % stock yielding 10 % is quoted at :
Options: a ) 83.33 , b ) 110 , c ) 112 , d ) 140 , e ) 160
Rationale: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 14 , money invested = rs . ( 100 / 10 x 14 ) = rs . 140 . â ˆ ´ market value of rs . 100 stock = rs . 140 answer d"
Answer: d
Problem: subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 30 pages .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 30 / 2.5 ) = 12 hrs answer : c"
Answer: c
Problem: a 25 % stock yielding 20 % is quoted at :
Options: a ) s . 83.33 , b ) s . 110 , c ) s . 112 , d ) s . 125 , e ) s . 140
Rationale: "income of rs 20 on investment of rs 100 income of rs 25 on investment of ? = ( 25 * 100 ) / 20 = 125 answer : d"
Answer: d
Problem: a and b can do a piece of work in 12 days . with the help of c they finish the work in 3 days . c alone can do that piece of work in ?
Options: a ) 40 days , b ) 2 days , c ) 4 days , d ) 8 days , e ) 40 days
Rationale: "c 30 days c = 1 / 3 – 1 / 12 = 1 / 4 = > 4 days"
Answer: c
Problem: the average of 11 numbers is 9.9 . if the average of the first 6 numbers is 10.5 and that of the last 6 numbers is 11.4 , then the middle number is
Options: a ) 71.5 , b ) 11.5 , c ) 81.5 , d ) 11.5 , e ) 22.5
Rationale: explanation : middle numbers = [ ( 10.5 x 6 + 11.4 x 6 ) - 9.9 x 11 ] = 22.5 . answer : e
Answer: e
Problem: in how many ways can an answer key for a quiz be written if the quiz contains 3 true - false questions followed by 3 multiple - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 164 , b ) 224 , c ) 280 , d ) 384 , e ) 476
Rationale: "there are 2 ^ 3 = 8 possibilities for the true - false answers . however we need to remove two cases for ttt and fff . there are 4 * 4 * 4 = 64 possibilities for the multiple choice questions . the total number of possibilities is 6 * 64 = 384 . the answer is d ."
Answer: d
Problem: if 2 ^ 5 , 3 ^ 3 , and 12 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 26 , b ) 39 , c ) 42 , d ) 144 , e ) 156
Rationale: "here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 12 * 3 * 4 = 144 smash d"
Answer: d
Problem: the ratio of 3 numbers is 5 : 1 : 4 and their sum is 1000 . the last number of the 3 numbers is ?
Options: a ) 24 , b ) 26 , c ) 27 , d ) 400 , e ) 30
Rationale: 5 : 1 : 4 total parts = 10 10 parts - - > 1000 1 part - - - - > 100 the last number of the three numbers is = 4 * 100 = 400 answer : d
Answer: d
Problem: when average age of 21 members are 0 , how many members greater than 0 ?
Options: a ) 17 , b ) 20 , c ) 21 , d ) 24 , e ) 25
Rationale: "average of 21 numbers = 0 . sum of 21 numbers ( 0 x 21 ) = 0 . it is quite possible that 20 of these numbers may be positive and if their sum is a then 21 st number is ( - a ) answer is 20 ( b )"
Answer: b
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 72 of the area of the field . what is the length of the field ?
Options: a ) 73 , b ) 32 , c ) 34 , d ) 43 , e ) 96
Rationale: "explanation : a / 72 = 8 * 8 = > a = 8 * 8 * 72 x * 2 x = 8 * 8 * 72 x = 48 = > 2 x = 96 answer : option e"
Answer: e
Problem: for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.367 ] = 1 and [ 1.899 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
Options: a ) 0 , b ) 1 , c ) 27 , d ) 54 , e ) 0
Rationale: "k = [ lcm of 80 and 45 ] * ( any integer ) however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer for value of k ( 60 ) * any integer unit value will be always zero . e"
Answer: e
Problem: how many times digit 6 is used while writing numbers from 80 to 1000 ?
Options: a ) 648 , b ) 300 , 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 225 . hence d .
Answer: d
Problem: p and q invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if p invested rs . 60 , 000 , the amount invested by q is :
Options: a ) rs . 65,000 , b ) rs . 70,000 , c ) rs . 80,000 , d ) rs . 90,000 , e ) rs . 60,000
Rationale: "suppose q invested rs . y . then , y = 60,000 / y = 2 / 3 or y = 60000 / 2 * 3 = 90,000 . answer : d"
Answer: d
Problem: if m = | | n – 3 | – 2 | , for how many values of n is m = 5 ?
Options: a ) 5 , b ) 4 , c ) 2 , d ) 3 , e ) 1
Rationale: m = | | n – 3 | – 2 | can be 4 only and only when n - 3 = + / - 7 . so there are 2 values of n answer : c
Answer: c
Problem: the average of 30 results is 20 and the average of other 20 results is 30 . what is the average of all the results ?
Options: a ) 24 , b ) 25 , c ) 48 , d ) 50 , e ) none
Rationale: "answer sum of 50 result = sum of 30 result + sum of 20 result . = 30 x 20 + 20 x 30 = 1200 correct option : a"
Answer: a
Problem: when an amount was distributed among 14 boys , each of them got $ 80 more than the amount received by each boy when the same amount is distributed equally among 18 boys . what was the amount ?
Options: a ) 5050 , b ) 5020 , c ) 5040 , d ) 5030 , e ) 5075
Rationale: "let the total amount be rs . x the , x / 14 - x / 18 = 80 = = > 2 x / 126 = 80 = = > x / 63 = 63 x 80 = 5040 . hence the total amount is 5040 . answer c ."
Answer: c
Problem: if 5 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ?
Options: a ) 2 : 5 , b ) 20 : 3 , c ) 3 : 7 , d ) 6 : 11 , e ) 2 : 3
Rationale: "let 5 % of a = 1 / 3 b then 5 a / 100 = 1 b / 3 a / 20 = b / 3 a / b = 20 / 3 a : b = 20 : 3 answer is b"
Answer: b
Problem: a baseball card decreased in value 50 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 55 % , c ) 32 % , d ) 36 % , e ) 72 %
Rationale: "let the initial value of baseball card = 100 after first year , value of baseball card = ( 1 - 50 / 100 ) * 100 = 50 after second year , value of baseball card = ( 1 - 10 / 100 ) * 50 = 45 total percent decrease of the card ' s value over the two years = ( 100 - 45 ) / 100 * 100 % = 55 % answer b"
Answer: b
Problem: 2 ^ 35 ^ 26 ^ 1 find largest value ?
Options: a ) 2 , b ) 3 , c ) 1 , d ) 10 , e ) 25
Rationale: explanation : 2 ^ 3 = 2 * 2 * 2 = 8 5 ^ 2 = 5 * 5 = 25 6 ^ 1 = 6 * 1 = 6 hence 5 ^ 2 is the largest one answer : e
Answer: e
Problem: what is 35 % of 4 / 13 of 585 ?
Options: a ) 52 , b ) 63 , c ) 74 , d ) 85 , e ) 96
Rationale: "this problem can be solved easily if we just use approximation : 35 % is a little over 1 / 3 , while 4 / 13 is a little less than 4 / 12 , which is 1 / 3 . thus , the answer is about 1 / 3 of 1 / 3 of 585 , or 1 / 9 of 585 . since the first 1 / 3 is a slight underestimate and the second 1 / 3 is a slight overestimate , the errors will partially cancel each other out . our estimate will be relatively accurate . the number 585 is between 540 and 630 , so ( 1 / 9 ) * 585 will be about 65 . keeping track not only of your current estimate , but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently . the closest answer is 63 , so this is the answer to choose . the answer is b ."
Answer: b
Problem: if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ) , 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 one appearance of 5 ( in the 10 ) . thus n must include at least 3 * 5 = 15 the answer is a ."
Answer: a
Problem: at a small company , 64 percent of the employees are women , and 60 percent of the employees are married . if 2 / 3 of the men are single , what fraction of the women are married ?
Options: a ) 5 / 16 , b ) 3 / 4 , c ) 9 / 20 , d ) 7 / 10 , e ) 5 / 7
Rationale: "lets take total employees are 100 . given that , total women = 64 and total married = 60 . total men = 100 - 64 = 36 and single men = 2 / 3 * 36 = 24 . married men = total men - single men = 36 - 24 = 12 . married women = total married - married men = 60 - 12 = 48 . fraction of women are married = married women / total women = 48 / 64 = 3 / 4 . ans b"
Answer: b
Problem: if annual decrease in the population of a town is 10 % and the present number of people is 500 what will the population be in 1 year ?
Options: a ) 450 , b ) 310 , c ) 250 , d ) 410 , e ) 390
Rationale: "population in 1 year = 500 ( 1 - 10 / 100 ) = 500 * 90 / 100 = 450 answer is a"
Answer: a
Problem: if | x | = 7 x - 5 , then x = ?
Options: a ) 1 , b ) 1 / 2 , c ) 1 and 1 / 2 , d ) 2 , e ) - 1
Rationale: "answer : a approach : substituted option a i . e x = 1 . inequality satisfied . d"
Answer: d
Problem: the sum of two numbers is 56 , and one of them is 12 more than the other . what are the two numbers ?
Options: a ) 36 - 48 , b ) 22 - 34 , c ) 60 - 24 , d ) 42 - 42 , e ) 21 - 63
Rationale: "in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 56 : word problem = 56 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 56 â ˆ ’ 12 = 44 . x = 44 / 2 = 22 . this is the first number . therefore the other number is x + 12 = 22 + 12 = 34 . the sum of 22 + 34 is 56 . b"
Answer: b
Problem: a horse is tethered to one corner of a rectangular grassy field 46 m by 20 m with a rope 17 m long . over how much area of the field can it graze ?
Options: a ) 154 cm 2 , b ) 308 m 2 , c ) 227 m 2 , d ) 407 m 2 , e ) none of these
Rationale: "area of the shaded portion = 1 ⁄ 4 × π × ( 17 ) 2 = 227 m 2 answer c"
Answer: c
Problem: a person incurs 5 % loss by selling a watch for $ 1140 . at what price should the watch be sold to earn 5 % profit ?
Options: a ) $ 1260 , b ) $ 1150 , c ) $ 1542 , d ) $ 1000 , e ) $ 1292
Rationale: let the new selling price be $ x ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) ( 100 - 5 ) / 1140 = ( 100 + 5 ) / x x = 105 * 1140 / 95 = 1260 answer is a
Answer: a
Problem: if the average of 10 consecutive integers is 22.5 then the 10 th integer is : -
Options: a ) 15 , b ) 20 , c ) 23 , d ) 27 , e ) 25
Rationale: "the average falls between the 5 th and 6 th integers , integer 5 = 22 , integer 6 = 23 . counting up to the tenth integer we get 27 . answer : d"
Answer: d
Problem: find the area of a parallelogram with base 32 cm and height 22 cm ?
Options: a ) 281 , b ) 284 , c ) 704 , d ) 640 , e ) 920
Rationale: "area of a parallelogram = base * height = 32 * 22 = 704 cm 2 answer : c"
Answer: c
Problem: sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 350 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 4 of the days were hot , then what was the price of 1 cup on a hot day ?
Options: a ) $ 1.50 , b ) $ 1.88 , c ) $ 2.09 , d ) $ 2.50 , e ) $ 3.25
Rationale: "6 regular days - - > sales = 6 * 32 * x = 192 x ; 4 hot days - - > sales = 4 * 32 * ( 1.25 x ) = 160 x ; total sales = 192 x + 160 x = 352 x . total cost = 10 * 32 * 0.75 = 240 . profit = 352 x - 240 = 350 - - > x = 1.676 . 1.25 x = ~ 2.09 . answer : c ."
Answer: c
Problem: if 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 6 = 36 then 12 = ? hint : its a logic riddle not a mathematical riddle
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: b 2 as stated 2 = 12 = > 12 = 2 answer is b
Answer: b
Problem: what is the number of integers from 1 to 900 ( inclusive ) that are divisible by neither 11 nor by 35 ?
Options: a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945
Rationale: "normally , i would use the method used by bunuel . it ' s the most accurate . but if you are looking for a speedy solution , you can use another method which will sometimes give you an estimate . looking at the options ( most of them are spread out ) , i wont mind trying it . ( mind you , the method is accurate here since the numbers start from 1 . ) in 1000 consecutive numbers , number of multiples of 11 = 1000 / 11 = 90 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 11 * 35 i . e . 385 = 1000 / 385 = 2 number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - ( 90 + 28 - 2 ) { using the concept of sets here ) = 892 think : why did i say the method is approximate in some cases ? think what happens if the given range is 11 to 1010 both inclusive ( again 1000 numbers ) what is the number of multiples in this case ? c"
Answer: c
Problem: 217 + 2.017 + 0.217 + 2.0017 = ?
Options: a ) 229.3657 , b ) 229.7563 , c ) 229.6357 , d ) 229.5637 , e ) 221.2357
Rationale: 217 2.017 0.217 + 2.0017 - - - - - - - - 221.2357 - - - - - - - - - answer is e .
Answer: e
Problem: two men amar and bhuvan have the ratio of their monthly incomes as 6 : 5 . the ratio of their monthly expenditures is 3 : 2 . if bhuvan saves one - fourth of his income , find the ratio of their monthly savings ? a . 3 : 5
Options: a ) 3 : 9 , b ) 3 : 10 , c ) 3 : 21 , d ) 3 : 12 , e ) 3 : 14
Rationale: let the monthly incomes of amar and bhuvan be 6 x and 5 x respectively . let the monthly expenditure of amar and bhuvan be 3 y and 2 y respectively . savings of bhuvan every month = 1 / 4 ( 5 x ) = ( his income ) - ( his expenditure ) = 5 x - 2 y . = > 5 x = 20 x - 8 y = > y = 15 x / 8 . ratio of savings of amar and bhuvan = 6 x - 3 y : 1 / 4 ( 5 x ) = 6 x - 3 ( 15 x / 8 ) : 5 x / 4 = 3 x / 8 : 5 x / 4 = 3 : 10 . answer : option b
Answer: b
Problem: if 3 cm of a pencil is purple , 2 cm of the remaining is black and the remaining 1 cm is blue , what is the total length of the pencil ?
Options: a ) 6 , b ) 3 , c ) 1 , d ) 4 , e ) 2
Rationale: answer is a ) 6
Answer: a
Problem: a car covers a distance of 624 km in 2 2 / 5 hours . find its speed ?
Options: a ) 104 kmph , b ) 194 kmph , c ) 109 kmph , d ) 260 kmph , e ) 271 kmph
Rationale: "624 / 2 2 / 5 = 260 kmph answer : d"
Answer: d
Problem: find the perimetri of trapezium with sides 4 , 6,12 and distance between two parallel side is 3 .
Options: a ) 27
b ) 26
c ) 28
d ) 25
e ) 24
Rationale: 1 / 2 * ( 6 + 12 ) * 3 = 27 answer : a
Answer: a
Problem: the average of first five prime numbers greater than 20 is ?
Options: a ) 32.2 , b ) 32.98 , c ) 32.3 , d ) 32.8 , e ) 32.4
Rationale: "23 + 29 + 31 + 37 + 41 = 161 / 5 = 32.2 answer : a"
Answer: a
Problem: a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 6 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?
Options: a ) 12 , b ) 9 , c ) 15 , d ) 21 , e ) 30
Rationale: "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 6 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 6 ) = 0.08 t - - > 60 + 6 ( t - 6 ) = 8 t - - > t = 12 . answer : a ."
Answer: a
Problem: solution x is 10 % chemical a and 90 % chemical b by volume . solution y is 20 % chemical a and 80 % chemical b by volume . if a mixture of x and y is 12 % chemical a , what percent of the mixture is solution x ?
Options: a ) 80 % , b ) 75 % , c ) 70 % , d ) 65 % , e ) 60 %
Rationale: "the volume of the mixture be x + y . 0.1 x + 0.2 y = 0.12 ( x + y ) x = 4 y x / ( x + y ) = 4 / 5 = 80 % . the answer is a ."
Answer: a
Problem: the flowerman sale , all of the prices of the flowers sold were different . if the price of a radio sold at the flowerman sale was both the 17 th highest price and the 42 th lowest price among the prices of the slowers sold , how many flowers were sold at the flowerman sale ?
Options: a ) 38 , b ) 34 , c ) 58 , d ) 63 , e ) 73
Rationale: 16 + 41 + 1 = 58 answer : c
Answer: c
Problem: milk contains 5 % water . what quantity of pure milk should be added to 10 litres of milk to reduce this 2 % ?
Options: a ) 15 litres , b ) 16 litres , c ) 17 litres , d ) 25 litres , e ) 35 litres
Rationale: present ration of milk to water is 95 : 5 amount of milk is 10 litres hence , pure milk content is 9.5 litre and water content is 0.5 litres now , we should not disturb the water content so , 0.5 litres of water is equivalent to 2 % so 100 % mixture is : ( 0.5 / 2 ) * 100 = 25 litre thus , milk should be added = 25 - 10 = 15 litres of pure milk answer : a
Answer: a
Problem: in the set of positive integers from 1 to 80 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 245 , c ) 320 , d ) 260 , e ) 270
Rationale: "reduce to 1 - 80 5 - 15 - 25 - 35 - 45 - - 55 - - 65 - - 75 are valid multiples . add them - - > 320 c"
Answer: c
Problem: dan ' s age after 18 years will be 8 times his age 3 years ago . what is the present age of dan ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "let dan ' s present age be x . x + 18 = 8 ( x - 3 ) 7 x = 42 x = 6 the answer is b ."
Answer: b
Problem: the wages earned by robin is 44 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?
Options: a ) 23 % , b ) 18.75 % , c ) 30 % , d ) 30.55 % , e ) 100 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 144 and $ 160 respectively . charles earns $ 44 more than robin who earns $ 144 . therefore , charles ' wage is 44 / 144 * 100 = 30.55 % . the correct choice is ( d )"
Answer: d
Problem: solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 67.5 % percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 25 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "67.5 % is 12.5 % - points below 80 % and 12.5 % - points above 55 % . so the ratio of solution p to solution q is 1 : 1 . mixture p is 1 / 2 = 50 % of the volume of mixture pq . the answer is c ."
Answer: c
Problem: the average age of a family of 6 members is 40 years . if the age of the youngest member is 7 years , what was the average age of the family at the birth of the youngest member ?
Options: a ) 33 , b ) 18 , c ) 21 , d ) 12 , e ) 19
Rationale: "present age of total members = 6 x 40 = 240 7 yrs back their ages were = 6 x 7 = 42 ages at the birth of youngest member = 240 - 42 = 198 therefore , avg age at the birth of youngest member = 198 / 6 = 33 . answer : a"
Answer: a
Problem: a man rows his boat 80 km downstream and 38 km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 9 , c ) 7 , d ) 8 , e ) 2
Rationale: "speed downstream = d / t = 80 / ( 3 ) = 27 kmph speed upstream = d / t = 38 / ( 3 ) = 9 kmph the speed of the stream = ( 27 - 9 ) / 2 = 9 kmph answer : b"
Answer: b
Problem: if x ⁄ 2 + 5 ⁄ 4 = 5 ⁄ 4 , what is the value of x ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: x ⁄ 2 + 5 ⁄ 4 = 5 ⁄ 4 let ' s multiply both sides by 4 . 2 x + 5 = 5 2 x = 0 x = 0 the answer is c .
Answer: c
Problem: at what rate percent per annum will a sum of money double in 7 years .
Options: a ) 12.5 % , b ) 13.5 % , c ) 14.2 % , d ) 14.5 % , e ) 21.5 %
Rationale: "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 8 ) ] % = 14.2 % per annum . answer : c"
Answer: c
Problem: sum of the squares of 3 no . ' s is 99 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 24 , c ) 19 , d ) 28 , e ) 30
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 99 + 2 * 131 a + b + c = √ 361 = 19 c"
Answer: c
Problem: a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 2 per sq m ?
Options: a ) 2288 , b ) 2779 , c ) 2779 , d ) 3900 , e ) 2600
Rationale: "area = ( l + b â € “ d ) d ( 80 + 60 â € “ 10 ) 10 = > 1300 m 2 1300 * 2 = rs . 2600 answer : e"
Answer: e
Problem: the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 150 . what is the number of frogs in the pond ?
Options: a ) 148 , b ) 154 , c ) 156 , d ) 144 , e ) none
Rationale: "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 150 . so , total number of ducks and frogs in the pond , = 2 * 150 = 300 . therefore , number of frogs , = ( 300 * 39 ) / 76 = 154 . answer : option b"
Answer: b
Problem: the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 14000 , then find the annual income of a ?
Options: a ) rs . 420000 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 470400 , e ) none of these
Rationale: "b ' s monthly income = 14000 * 112 / 100 = rs . 15680 b ' s monthly income = 2 parts - - - - > rs . 15680 a ' s monthly income = 5 parts = 5 / 2 * 15680 = rs . 39200 a ' s annual income = rs . 39200 * 12 = rs . 470400 answer : d"
Answer: d
Problem: in the rectangular coordinate system , points ( 2 , 0 ) and ( – 2 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) none of the above
Rationale: "the answer is a it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 2"
Answer: a
Problem: if ram and gohul can do a job in 10 days and 15 days independently , how many days would they take to complete the same job working simultaneously ?
Options: a ) 10 , b ) 5 , c ) 8 , d ) 6 , e ) 13
Rationale: if total work is x . ram working rate = x / 10 per day . working rate of gohul = x / 15 per day . rate of work = ( x / 10 ) + ( x + 15 ) = 30 x / 5 x = 6 days the answer is option d
Answer: d
Problem: trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 4 ) , k = ( – 2 , 2 ) , l = ( 6 , 8 ) , and m = ( 6 , – 4 ) . what is its perimeter ?
Options: a ) 34 , b ) 36 , c ) 38 , d ) 40 , e ) ( f ) 42
Rationale: "jk = 6 lm = 12 kl = using distance formula 10 jm = using distance formula 8 sum of all is 36 b"
Answer: b
Problem: a box contains 7 purple , 5 blue and 11 yellow balls . what is the minimum number of tries required to get one blue and one yellow ball ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: 11 yellow + 7 purple + after that we have only one option that is to be blue so answer is 19 answer : d
Answer: d
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 361 is required to paint the floor at the rate of rs . 3.00001 / sq m , what would be the length of the floor ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 22 , e ) 24
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 361 / 3 = 120.33 sq m l b = 120.33 i . e . , l * l / 3 = 120.33 l ^ 2 = 361 = > l = 19 . b"
Answer: b
Problem: 3 men and 3 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )
Options: a ) 12 , b ) 15 , c ) 18 , d ) 36 , e ) 24
Rationale: the list should be wmwmw . hence , from women 3 ! and men 3 ! , we get ( 3 ! ) ( 3 ! ) = 36 . therefore , the correct answer is d .
Answer: d
Problem: carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 12 inches by 15 inches and jordan ' s rectangle is 6 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 24
b ) 26
c ) 28
d ) 30
e ) 32
Rationale: area of first rectangle is 12 * 15 = 180 hence area of second would be 6 x = 180 x x = 30 answer is d
Answer: d
Problem: the calendar of the year 2080 can be used again in the year ?
Options: a ) 2105 , b ) 1955 , c ) 1945 , d ) 1935 , e ) 2108
Rationale: "explanation : given year 2080 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2080 + 28 = 2108 answer : e"
Answer: e
Problem: sum of 42 odd numbers is ?
Options: a ) 1764 , b ) 1774 , c ) 1784 , d ) 1794 , e ) 1754
Rationale: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 42 odd numbers = 42 ^ 2 = 1764 answer : a"
Answer: a
Problem: a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 5,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 3.75 % , c ) 6.25 % , d ) 6.67 % , e ) 11.11 %
Rationale: the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 5,500 = 4,500 gallons and sodium chloride is 500 gallons ( 5 % of initial solution of 10,000 gallons ) then sodium chloride is 500 / 4,500 * 100 = ~ 11.11 % of the remaining solution of 4,500 gallons . answer : e .
Answer: e
Problem: 4 , 25,49 , 121,169 , 289,361 ,
Options: a ) 149 , b ) 169 , c ) 189 , d ) 529 , e ) 219
Rationale: "23 ^ 2 = 529 because follow sequence of square of the prime numbers answer : d"
Answer: d
Problem: a larger cube has 8 cubic inch as a volume and in the cube there are 8 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 8 smaller cubes and the surface area of the larger cube , in square inch ?
Options: a ) 24
b ) 64
c ) 81
d ) 108
e ) 120
Rationale: volume of larger cube = 8 = 2 ^ 3 side of larger cube = 2 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 2 ^ 2 = 24 surface area of 27 smaller cubes = 8 * 6 * 1 = 48 difference = 48 - 24 = 24 answer : a
Answer: a
Problem: the distance from steve ' s house to work is 20 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 20 .
Rationale: "time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 20 km = > speed = 10 kmph b"
Answer: b
Problem: a and b can do a piece of work in 4 days . with the help of c they finish the work in 3 days . c alone can do that piece of work in ?
Options: a ) 4 days , b ) 21 days , c ) 13 days , d ) 12 days , e ) 3 days
Rationale: "c = 1 / 3 – 1 / 4 = 1 / 12 = > 12 days answer : d"
Answer: d
Problem: in a garden , there are 10 rows and 16 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 32 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m
Rationale: "explanation : each row contains 16 plants . there are 15 gapes between the two corner trees ( 15 x 2 ) metres and 1 metre on each side is left . therefore length = ( 30 + 2 ) m = 32 m . answer : a"
Answer: a
Problem: on a certain date , pat invested $ 9,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 36,000 , in how many years total will the total value of the investment plus interest increase to $ 72,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "36,000 = 9,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 72,000 = 9,000 ( 1 + x ) ^ n 8 = ( 1 + x ) ^ n 2 ^ 3 = ( 1 + x ) ^ n ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."
Answer: a
Problem: 30 pens and 75 pencils were purchased for 510 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 10 , b ) 11 , c ) 12 , d ) can not be determined , e ) none of the above
Rationale: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 510 – 150 ) = 360 ∴ average price of a pen = 360 ⁄ 60 = 12 answer c"
Answer: c
Problem: a rectangular carpet has an area of 60 sq . m . if its diagonal and longer side together equal 5 times the shorter side , the length of the carpet is :
Options: a ) 5 m
b ) 12 m
c ) 13 m
d ) 14.5 m
e ) 15.5 m
Rationale: let , length = x meters and breadth = y meters then xy = 60 and ( x 2 + y 2 ) + x = 5 therefore , x = 60 and ( x 2 + y 2 ) = ( 5 y - x ) 2 or xy = 60 and 24 y 2 - 10 xy = 0 . therefore , 24 y 2 - 10 * 60 = 0 or y 2 = 25 or = 5 . therefore , x = ( 60 / 5 ) m = 12 m . so , length of the carpet = 12 m answer : b
Answer: b
Problem: a train is 357 meter long is running at a speed of 42 km / hour . in what time will it pass a bridge of 137 meter length ?
Options: a ) 44 , b ) 42.343 , c ) 50 , d ) 39.252 , e ) 27.851
Rationale: "speed = 42 km / hr = 42 * ( 5 / 18 ) m / sec = 35 / 3 m / sec total distance = 357 + 137 = 494 meter time = distance / speed = 494 * ( 3 / 35 ) = 42.343 seconds . answer : b"
Answer: b
Problem: a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 34 pints of perfect pink paint ?
Options: a ) 9 , b ) 16 , c ) 18 , d ) 25 1 / 3 , e ) 28 1 / 2
Rationale: "3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 34 pints will require 9 / 17 * 34 = 18 points . . second way . . get both red and white paints in same denominator . . . 3 / 4 + 2 / 3 = ( 9 / 12 ) + ( 8 / 12 ) pints . . from here we get the ratio of red : white = 9 : 8 . . so in 34 pints red will be 9 / ( 9 + 8 ) * 34 = 18 . . answer : c"
Answer: c
Problem: in a rectangular metallic piece of paper that covers exactly the area of a cube . the length of the piece of paper is 48 inches and the width is 72 inches . what is the volume of the cube in cubic feet is 1 feet is 12 inches ?
Options: a ) a 8
b ) b 22
c ) c 27
d ) d 40
e ) e 51
Rationale: l = 48 / 12 = 4 ft w = 72 / 12 = 6 ft area of paper = 24 area of cube = 4 * side ^ 2 side of cube = 2 v of cube = 8
Answer: a
Problem: the value of ( 0.137 + 0.098 ) ² - ( 0.137 - 0.098 ) ² / 0.137 × 0.098 is
Options: a ) 0.039 , b ) 0.235 , c ) 0.25 , d ) 4 , e ) 5
Rationale: solution given expression = ( a + b ) ² - ( a - b ) ² / ab = 4 ab / ab = 4 . answer d
Answer: d
Problem: a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6900 ?
Options: a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6991 , e ) s . 7391
Rationale: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6900 * 6 ) - 34009 ] = rs . ( 41400 - 34009 ) = rs . 7391 . answer : e"
Answer: e
Problem: mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 457 ?
Options: a ) 26.4 % , b ) 21 % , c ) 20 % , d ) 19 % , e ) none of these
Rationale: "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 457 , discount = 621 - 457 = 164 discount % = 164 / 621 * 100 = 26.4 % answer : a"
Answer: a
Problem: a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 8 cubic feet . if a small block has half the width , half the depth , and half the length of a normal block , what is the volume of cheese in a small block in cubic feet ?
Options: a ) 1 , b ) 5 , c ) 4 , d ) 6 , e ) 2
Rationale: "volume of cube = lbh = 8 new cube l , b , h are decreases of . 5 l , . 5 b , . 5 h new volume of cube = . 5 l * . 5 b * . 5 h = . 125 * lbh = . 125 * 8 = 1 answer : a"
Answer: a
Problem: boy sells a book for rs . 450 he gets a loss of 10 % , to gain 10 % , at price he should sell ?
Options: a ) rs . 400 , b ) rs . 450 , c ) rs . 550 , d ) rs . 600 , e ) rs . 650
Rationale: "find selling price to gain 10 % . now , we are asked to find selling price to gain 10 % profit . hint : selling price = ( 100 + gain % ) × c . p . 100 selling price = ( 100 + 10 ) × 500 100 selling price = ( 110 ) × 500 100 therefore , selling price = rs . 550 c"
Answer: c
Problem: how many seconds does sandy take to cover a distance of 700 meters , if sandy runs at a speed of 18 km / hr ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 160 , e ) 180
Rationale: "18 km / hr = 18000 m / 3600 s = 5 m / s time = 700 / 5 = 140 seconds the answer is c ."
Answer: c
Problem: 5358 x 51 = ?
Options: a ) 272258 , b ) 272358 , c ) 273258 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 1 ) = 5358 x 50 + 5358 x 1 = 267900 + 5358 = 273258 . c )"
Answer: c