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Question: calculate the largest 6 digit number which is exactly divisible by 55 ?
A.999955.
B.999900.
C.999845.
D.999790.
e ) 999735A.
"largest 4 digit number is 999999 after doing 999999 Γ· 55 we get remainder 44 hence largest 4 digit number exactly divisible by 88 = 999999 - 44 = 999955 a" | null |
Question: 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 ?
A.15.
B.11.
C.18.
D.16.
e ) 20D.
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 . | null |
Question: 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 ?
A.$ 60.
B.$ 80.
C.$ 90.
D.$ 120.
e ) $ 180D.
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 | null |
Question: tough and tricky questions : exponents . if 5 ^ ( x + 1 ) * 4 ^ ( y - 1 ) = 25 ^ x * 64 ^ y , then x + y =
A.3 / 2.
B.- 1 / 2.
C.- 1.
D.1 / 2.
e ) 2 / 3D.
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 | null |
Question: what is the remainder of e = 3 ^ 19 when divided by 10 ?
A.0.
B.1.
C.5.
D.7.
e ) 9D.
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 | null |
Question: what no should be subtracted from 92555 to make it a perfect square ?
['A.128', 'B.158', 'C.178', 'D.139', 'e ) 140']D.
root 92555 = 304.228 and 304 ^ 2 = 92416 92555 - 92416 = 139 should be subtracted from 92555 to make it a perfect square answer : d | null |
Question: 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 ) ?
A.96.
B.100.
C.104.
D.108.
e ) 112D.
"2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 108 the answer is d ." | null |
Question: the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 6 . the true discount is
A.rs . 72.
B.rs . 36.
C.rs . 54.
D.rs . 50.
e ) noneD.
"solution t . d = [ b . g x 100 / r x t ] = rs . ( 6 x 100 / 12 x 1 ) = rs . 50 . answer d" | null |
Question: 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 ?
A.( 40,0 ).
B.( 30,0 ).
C.( 0,40 ).
D.( 40,30 ).
e ) ( 0,30 )A.
"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 ." | null |
Question: 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 β s average grade for the entire two - year period ?
A.79.
B.89.
C.95.
D.90.91.
e ) 97.2D.
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 | null |
Question: 8.008 / 2.002
A.0.004.
B.0.04.
C.4.
D.40.
e ) 400C.
"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" | null |
Question: 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 ?
A.17.
B.16.
C.15.
D.14.
e ) 13D.
"7 ^ 2 + 6 ^ 2 + 1 ^ 2 = 49 + 36 + 1 = 86 7 + 6 + 1 = 14 hence answer is d" | null |
Question: 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 ?
A.40.
B.45.
C.50.
D.54.
e ) 60D.
"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" | null |
Question: a 14 % stock yielding 10 % is quoted at :
A.83.33.
B.110.
C.112.
D.140.
e ) 160D.
"solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 14 , money invested = rs . ( 100 / 10 x 14 ) = rs . 140 . Γ’ Λ Β΄ market value of rs . 100 stock = rs . 140 answer d" | null |
Question: 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 .
A.8.
B.10.
C.12.
D.14.
e ) 16C.
"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" | null |
Question: a 25 % stock yielding 20 % is quoted at :
A.s . 83.33.
B.s . 110.
C.s . 112.
D.s . 125.
e ) s . 140D.
"income of rs 20 on investment of rs 100 income of rs 25 on investment of ? = ( 25 * 100 ) / 20 = 125 answer : d" | null |
Question: 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 ?
A.40 days.
B.2 days.
C.4 days.
D.8 days.
e ) 40 daysC.
"c 30 days c = 1 / 3 β 1 / 12 = 1 / 4 = > 4 days" | null |
Question: 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
A.71.5.
B.11.5.
C.81.5.
D.11.5.
e ) 22.5E.
explanation : middle numbers = [ ( 10.5 x 6 + 11.4 x 6 ) - 9.9 x 11 ] = 22.5 . answer : e | null |
Question: 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 ?
A.164.
B.224.
C.280.
D.384.
e ) 476D.
"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 ." | null |
Question: 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 ?
A.26.
B.39.
C.42.
D.144.
e ) 156D.
"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" | null |
Question: the ratio of 3 numbers is 5 : 1 : 4 and their sum is 1000 . the last number of the 3 numbers is ?
A.24.
B.26.
C.27.
D.400.
e ) 30D.
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 | null |
Question: when average age of 21 members are 0 , how many members greater than 0 ?
A.17.
B.20.
C.21.
D.24.
e ) 25B.
"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 )" | null |
Question: 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 ?
A.73.
B.32.
C.34.
D.43.
e ) 96E.
"explanation : a / 72 = 8 * 8 = > a = 8 * 8 * 72 x * 2 x = 8 * 8 * 72 x = 48 = > 2 x = 96 answer : option e" | null |
Question: 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 ?
A.0.
B.1.
C.27.
D.54.
e ) 0E.
"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" | null |
Question: how many times digit 6 is used while writing numbers from 80 to 1000 ?
A.648.
B.300.
C.252.
D.225.
e ) 26D.
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 . | null |
Question: 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 :
A.rs . 65,000.
B.rs . 70,000.
C.rs . 80,000.
D.rs . 90,000.
e ) rs . 60,000D.
"suppose q invested rs . y . then , y = 60,000 / y = 2 / 3 or y = 60000 / 2 * 3 = 90,000 . answer : d" | null |
Question: if m = | | n β 3 | β 2 | , for how many values of n is m = 5 ?
A.5.
B.4.
C.2.
D.3.
e ) 1C.
m = | | n β 3 | β 2 | can be 4 only and only when n - 3 = + / - 7 . so there are 2 values of n answer : c | null |
Question: the average of 30 results is 20 and the average of other 20 results is 30 . what is the average of all the results ?
A.24.
B.25.
C.48.
D.50.
e ) noneA.
"answer sum of 50 result = sum of 30 result + sum of 20 result . = 30 x 20 + 20 x 30 = 1200 correct option : a" | null |
Question: 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 ?
A.5050.
B.5020.
C.5040.
D.5030.
e ) 5075C.
"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 ." | null |
Question: if 5 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ?
A.2 : 5.
B.20 : 3.
C.3 : 7.
D.6 : 11.
e ) 2 : 3B.
"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" | null |
Question: 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 ?
A.28 %.
B.55 %.
C.32 %.
D.36 %.
e ) 72 %B.
"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" | null |
Question: 2 ^ 35 ^ 26 ^ 1 find largest value ?
A.2.
B.3.
C.1.
D.10.
e ) 25E.
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 | null |
Question: what is 35 % of 4 / 13 of 585 ?
A.52.
B.63.
C.74.
D.85.
e ) 96B.
"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 ." | null |
Question: 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 ?
A.15.
B.45.
C.75.
D.125.
e ) 150A.
"( 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 ." | null |
Question: 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 ?
A.5 / 16.
B.3 / 4.
C.9 / 20.
D.7 / 10.
e ) 5 / 7B.
"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" | null |
Question: 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 ?
A.450.
B.310.
C.250.
D.410.
e ) 390A.
"population in 1 year = 500 ( 1 - 10 / 100 ) = 500 * 90 / 100 = 450 answer is a" | null |
Question: if | x | = 7 x - 5 , then x = ?
A.1.
B.1 / 2.
C.1 and 1 / 2.
D.2.
e ) - 1D.
"answer : a approach : substituted option a i . e x = 1 . inequality satisfied . d" | null |
Question: the sum of two numbers is 56 , and one of them is 12 more than the other . what are the two numbers ?
A.36 - 48.
B.22 - 34.
C.60 - 24.
D.42 - 42.
e ) 21 - 63B.
"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 Γ’ Λ β 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" | null |
Question: 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 ?
A.154 cm 2.
B.308 m 2.
C.227 m 2.
D.407 m 2.
e ) none of theseC.
"area of the shaded portion = 1 β 4 Γ Ο Γ ( 17 ) 2 = 227 m 2 answer c" | null |
Question: a person incurs 5 % loss by selling a watch for $ 1140 . at what price should the watch be sold to earn 5 % profit ?
A.$ 1260.
B.$ 1150.
C.$ 1542.
D.$ 1000.
e ) $ 1292A.
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 | null |
Question: if the average of 10 consecutive integers is 22.5 then the 10 th integer is : -
A.15.
B.20.
C.23.
D.27.
e ) 25D.
"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" | null |
Question: find the area of a parallelogram with base 32 cm and height 22 cm ?
A.281.
B.284.
C.704.
D.640.
e ) 920C.
"area of a parallelogram = base * height = 32 * 22 = 704 cm 2 answer : c" | null |
Question: 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 ?
A.$ 1.50.
B.$ 1.88.
C.$ 2.09.
D.$ 2.50.
e ) $ 3.25C.
"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 ." | null |
Question: if 1 = 6 2 = 12 3 = 18 4 = 24 5 = 30 6 = 36 then 12 = ? hint : its a logic riddle not a mathematical riddle
A.1.
B.2.
C.3.
D.4.
e ) 5B.
b 2 as stated 2 = 12 = > 12 = 2 answer is b | null |
Question: what is the number of integers from 1 to 900 ( inclusive ) that are divisible by neither 11 nor by 35 ?
A.884.
B.890.
C.892.
D.910.
e ) 945C.
"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" | null |
Question: 217 + 2.017 + 0.217 + 2.0017 = ?
A.229.3657.
B.229.7563.
C.229.6357.
D.229.5637.
e ) 221.2357E.
217 2.017 0.217 + 2.0017 - - - - - - - - 221.2357 - - - - - - - - - answer is e . | null |
Question: 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
A.3 : 9.
B.3 : 10.
C.3 : 21.
D.3 : 12.
e ) 3 : 14B.
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 | null |
Question: 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 ?
A.6.
B.3.
C.1.
D.4.
e ) 2A.
answer is a ) 6 | null |
Question: a car covers a distance of 624 km in 2 2 / 5 hours . find its speed ?
A.104 kmph.
B.194 kmph.
C.109 kmph.
D.260 kmph.
e ) 271 kmphD.
"624 / 2 2 / 5 = 260 kmph answer : d" | null |
Question: find the perimetri of trapezium with sides 4 , 6,12 and distance between two parallel side is 3 .
['A.27', 'B.26', 'C.28', 'D.25', 'e ) 24']A.
1 / 2 * ( 6 + 12 ) * 3 = 27 answer : a | null |
Question: the average of first five prime numbers greater than 20 is ?
A.32.2.
B.32.98.
C.32.3.
D.32.8.
e ) 32.4A.
"23 + 29 + 31 + 37 + 41 = 161 / 5 = 32.2 answer : a" | null |
Question: 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 ?
A.12.
B.9.
C.15.
D.21.
e ) 30A.
"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 ." | null |
Question: 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 ?
A.80 %.
B.75 %.
C.70 %.
D.65 %.
e ) 60 %A.
"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 ." | null |
Question: 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 ?
A.38.
B.34.
C.58.
D.63.
e ) 73C.
16 + 41 + 1 = 58 answer : c | null |
Question: milk contains 5 % water . what quantity of pure milk should be added to 10 litres of milk to reduce this 2 % ?
A.15 litres.
B.16 litres.
C.17 litres.
D.25 litres.
e ) 35 litresA.
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 | null |
Question: in the set of positive integers from 1 to 80 , what is the sum of all the odd multiples of 5 ?
A.180.
B.245.
C.320.
D.260.
e ) 270C.
"reduce to 1 - 80 5 - 15 - 25 - 35 - 45 - - 55 - - 65 - - 75 are valid multiples . add them - - > 320 c" | null |
Question: dan ' s age after 18 years will be 8 times his age 3 years ago . what is the present age of dan ?
A.4.
B.6.
C.8.
D.10.
e ) 12B.
"let dan ' s present age be x . x + 18 = 8 ( x - 3 ) 7 x = 42 x = 6 the answer is b ." | null |
Question: 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 ?
A.23 %.
B.18.75 %.
C.30 %.
D.30.55 %.
e ) 100 %D.
"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 )" | null |
Question: 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 ?
A.25 %.
B.40 %.
C.50 %.
D.60 %.
e ) 75 %C.
"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 ." | null |
Question: 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 ?
A.33.
B.18.
C.21.
D.12.
e ) 19A.
"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" | null |
Question: a man rows his boat 80 km downstream and 38 km upstream , taking 3 hours each time . find the speed of the stream ?
A.6.
B.9.
C.7.
D.8.
e ) 2B.
"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" | null |
Question: if x β 2 + 5 β 4 = 5 β 4 , what is the value of x ?
A.β 2.
B.β 1.
C.0.
D.1.
e ) 2C.
x β 2 + 5 β 4 = 5 β 4 let ' s multiply both sides by 4 . 2 x + 5 = 5 2 x = 0 x = 0 the answer is c . | null |
Question: at what rate percent per annum will a sum of money double in 7 years .
A.12.5 %.
B.13.5 %.
C.14.2 %.
D.14.5 %.
e ) 21.5 %C.
"let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 8 ) ] % = 14.2 % per annum . answer : c" | null |
Question: 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 ?
A.20.
B.24.
C.19.
D.28.
e ) 30C.
"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 99 + 2 * 131 a + b + c = β 361 = 19 c" | null |
Question: 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 ?
A.2288.
B.2779.
C.2779.
D.3900.
e ) 2600E.
"area = ( l + b Γ’ β¬ β d ) d ( 80 + 60 Γ’ β¬ β 10 ) 10 = > 1300 m 2 1300 * 2 = rs . 2600 answer : e" | null |
Question: 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 ?
A.148.
B.154.
C.156.
D.144.
e ) noneB.
"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" | null |
Question: 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 ?
A.rs . 420000.
B.rs . 180000.
C.rs . 201600.
D.rs . 470400.
e ) none of theseD.
"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" | null |
Question: in the rectangular coordinate system , points ( 2 , 0 ) and ( β 2 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
A.2.
B.4.
C.8.
D.16.
e ) none of the aboveA.
"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" | null |
Question: 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 ?
A.10.
B.5.
C.8.
D.6.
e ) 13D.
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 | null |
Question: trapezoid jklm in the x - y plane has coordinates j = ( β 2 , β 4 ) , k = ( β 2 , 2 ) , l = ( 6 , 8 ) , and m = ( 6 , β 4 ) . what is its perimeter ?
A.34.
B.36.
C.38.
D.40.
e ) ( f ) 42B.
"jk = 6 lm = 12 kl = using distance formula 10 jm = using distance formula 8 sum of all is 36 b" | null |
Question: 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 ?
A.16.
B.17.
C.18.
D.19.
e ) 20D.
11 yellow + 7 purple + after that we have only one option that is to be blue so answer is 19 answer : d | null |
Question: 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 ?
A.18.
B.19.
C.20.
D.22.
e ) 24B.
"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" | null |
Question: 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 )
A.12.
B.15.
C.18.
D.36.
e ) 24D.
the list should be wmwmw . hence , from women 3 ! and men 3 ! , we get ( 3 ! ) ( 3 ! ) = 36 . therefore , the correct answer is d . | null |
Question: 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 ?
['A.24', 'B.26', 'C.28', 'D.30', 'e ) 32']D.
area of first rectangle is 12 * 15 = 180 hence area of second would be 6 x = 180 x x = 30 answer is d | null |
Question: the calendar of the year 2080 can be used again in the year ?
A.2105.
B.1955.
C.1945.
D.1935.
e ) 2108E.
"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" | null |
Question: sum of 42 odd numbers is ?
A.1764.
B.1774.
C.1784.
D.1794.
e ) 1754A.
"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" | null |
Question: 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 ?
A.1.25 %.
B.3.75 %.
C.6.25 %.
D.6.67 %.
e ) 11.11 %E.
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 . | null |
Question: 4 , 25,49 , 121,169 , 289,361 ,
A.149.
B.169.
C.189.
D.529.
e ) 219D.
"23 ^ 2 = 529 because follow sequence of square of the prime numbers answer : d" | null |
Question: 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 β sum of the 8 smaller cubes and the surface area of the larger cube , in square inch ?
['A.24', 'B.64', 'C.81', 'D.108', 'e ) 120']A.
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 | null |
Question: 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 ?
A.5 ..
B.10 ..
C.14 ..
D.15 ..
e ) 20 .B.
"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" | null |
Question: 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 ?
A.4 days.
B.21 days.
C.13 days.
D.12 days.
e ) 3 daysD.
"c = 1 / 3 β 1 / 4 = 1 / 12 = > 12 days answer : d" | null |
Question: 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
A.32 m.
B.22 m.
C.24 m.
D.26 m.
e ) 28 mA.
"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" | null |
Question: 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 ?
A.15.
B.16.
C.18.
D.20.
e ) 24A.
"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 ." | null |
Question: 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 .
A.10.
B.11.
C.12.
D.can not be determined.
e ) none of the aboveC.
"since average price of a pencil = 2 β΄ price of 75 pencils = 150 β΄ price of 30 pens = ( 510 β 150 ) = 360 β΄ average price of a pen = 360 β 60 = 12 answer c" | null |
Question: 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 :
['A.5 m', 'B.12 m', 'C.13 m', 'D.14.5 m', 'e ) 15.5 m']B.
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 | null |
Question: 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 ?
A.44.
B.42.343.
C.50.
D.39.252.
e ) 27.851B.
"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" | null |
Question: 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 ?
A.9.
B.16.
C.18.
D.25 1 / 3.
e ) 28 1 / 2C.
"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" | null |
Question: 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 ?
['A.a 8', 'B.b 22', 'C.c 27', 'D.d 40', 'e ) e 51']A.
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 | null |
Question: the value of ( 0.137 + 0.098 ) Β² - ( 0.137 - 0.098 ) Β² / 0.137 Γ 0.098 is
A.0.039.
B.0.235.
C.0.25.
D.4.
e ) 5D.
solution given expression = ( a + b ) Β² - ( a - b ) Β² / ab = 4 ab / ab = 4 . answer d | null |
Question: 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 ?
A.s . 4991.
B.s . 5991.
C.s . 6001.
D.s . 6991.
e ) s . 7391E.
"total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6900 * 6 ) - 34009 ] = rs . ( 41400 - 34009 ) = rs . 7391 . answer : e" | null |
Question: 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 ?
A.26.4 %.
B.21 %.
C.20 %.
D.19 %.
e ) none of theseA.
"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" | null |
Question: 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 ?
A.1.
B.5.
C.4.
D.6.
e ) 2A.
"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" | null |
Question: boy sells a book for rs . 450 he gets a loss of 10 % , to gain 10 % , at price he should sell ?
A.rs . 400.
B.rs . 450.
C.rs . 550.
D.rs . 600.
e ) rs . 650C.
"find selling price to gain 10 % . now , we are asked to find selling price to gain 10 % profit . hint : selling price = ( 100 + gain % ) Γ c . p . 100 selling price = ( 100 + 10 ) Γ 500 100 selling price = ( 110 ) Γ 500 100 therefore , selling price = rs . 550 c" | null |
Question: how many seconds does sandy take to cover a distance of 700 meters , if sandy runs at a speed of 18 km / hr ?
A.100.
B.120.
C.140.
D.160.
e ) 180C.
"18 km / hr = 18000 m / 3600 s = 5 m / s time = 700 / 5 = 140 seconds the answer is c ." | null |
Question: 5358 x 51 = ?
A.272258.
B.272358.
C.273258.
D.274258.
e ) 274358C.
"5358 x 51 = 5358 x ( 50 + 1 ) = 5358 x 50 + 5358 x 1 = 267900 + 5358 = 273258 . c )" | null |
Question: a company purchased raw material worth 1 / 4 of it capital , 1 / 10 of the remaining is spent on machinery . how much fraction of the capital was left with the company after its expenditures on raw material and machinery ?
A.1 / 5.
B.2 / 8.
C.5 / 9.
D.27 / 40.
e ) 15 / 30D.
the amount spent by the company on raw material is 1 / 4 , so remaining is 3 / 4 . 1 / 10 of the remaining is spent on machinery , 1 / 10 * 3 / 4 = 3 / 40 total amount spent on raw material and machinery is 1 / 4 + 3 / 40 to make the denominator common we use 40 , so 1 / 4 is 10 / 40 10 / 40 + 3 / 40 = 13 / 40 is spent on raw material and machinery remaining 27 / 40 is left with the company answer is d | null |
Question: if x = y = 2 z and xyz = 256 then what is the value of x ?
A.12.
B.8.
C.16.
D.6.
e ) 2B.
given that x = y = z . so , x = y , x = 2 z , y = 2 z . given xyz = 256 = > ( 2 z ) * ( 2 z ) * z = 256 = > 4 z ^ 3 = 256 = > z = 4 then x = 2 z = 2 ( 4 ) = 8 answer : b | null |
Question: danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 5184 , what is the area of the side face of the box ?
A.123.
B.167.
C.178.
D.199.
e ) 288E.
"lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 5184 l * 1.5 l * 2 l = 5184 l = 12 side face area = l * d = l * 2 l = 12 * 2 * 12 = 288 e is the answer" | null |
Question: a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed r of the train .
A.A.45.
B.B.33.
C.C.48.
D.D.55.
e ) e ) 61C.
"let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = r ans = c" | null |
Question: if a Γ£ β b = 2 a - 3 b + ab , then 4 Γ£ β 5 + 5 Γ£ β 4 is equal to :
A.31.
B.32.
C.43.
D.45.
e ) 26A.
"explanation : 4 Γ£ β 5 + 5 Γ£ β 4 = ( 2 Γ£ β 4 - 3 Γ£ β 5 + 4 Γ£ β 5 ) + ( 2 Γ£ β 5 - 3 Γ£ β 4 + 5 Γ£ β 4 ) = ( 8 - 15 + 20 + 10 - 12 + 20 ) = 31 . answer : a" | null |
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