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Question: the average weight of a group of boys is 20 kg . after a boy of weight 32 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
A.12.
B.11.
C.18.
D.24.
e ) 10B.
"let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 32 kg joins the group , total weight of boys = 20 x + 32 so 20 x + 32 = 21 ( x + 1 ) = > x = 11 . answer : b" | null |
Question: a football team lost 5 yards and then gained 11 . what is the team ' s progress ?
A.2.
B.4.
C.5.
D.6.
e ) 8D.
"for lost , use negative . for gain , use positive . progress = - 5 + 11 = 6 yards d" | null |
Question: two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 160 m , in what time will they cross other travelling in opposite direction ?
A.17 sec.
B.12 sec.
C.16 sec.
D.15 sec.
e ) 18 secC.
"speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 160 + 160 ) / 20 = 16 sec . answer : c" | null |
Question: last year a worker saved 10 % of her annual salary . this year , she made 10 % more money than last year and she saved 12 % of her salary . the amount she saved this year was what percent of the amount she saved last year ?
A.126 %.
B.128 %.
C.130 %.
D.132 %.
e ) 134 %D.
"let x be the worker ' s salary last year . last year , she saved 0.1 x . this year , she saved 0.12 ( 1.1 x ) = 0.132 x 0.132 x / 0.1 x = 132 % the answer is d ." | null |
Question: what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 120 ?
A.60.
B.25.
C.50.
D.75.
e ) 100A.
"surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 120 / 2 = 60 answer is a" | null |
Question: how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | ≤ 14 ?
A.15.
B.12.
C.17.
D.18.
e ) 19B.
"so i can write this as in - 3 i + 4 < = 14 or in - 3 i < = 10 so n can have - 7 to 13 = 12 true values . . . . b" | null |
Question: a sum of money at simple interest amounts to 815 in 3 years and to 854 in 4 years . the sum is :
A.698.
B.387.
C.373.
D.593.
e ) 372A.
"a 698 s . i . for 1 year = ( 854 - 815 ) = 39 . s . i . for 3 years = ( 39 x 3 ) = 117 . principal = ( 815 - 117 ) = 698 ." | null |
Question: a woman spends 15 % of her income in house rent , 15 % of the rest on his children ’ s education , 10 % of the rest miscellaneous causes and 15 % in medical expenses . if she now posses rs . 5548 then her income is ?
A.10058.
B.10068.
C.10078.
D.10088.
e ) 10038E.
x * ( 85 / 100 ) * ( 85 / 100 ) * ( 90 / 100 ) * ( 85 / 100 ) = 5548 x * 0.85 * 0.85 * 0.9 * 0.85 = 5548 x = 5548 / 0.5527 x = 10038 answer : e | null |
Question: a student got twice as many sums wrong as he got right . if he attempted 48 sums in all , how many did he solve correctly ?
A.12.
B.16.
C.18.
D.24.
e ) 26B.
"explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 48 3 x = 48 x = 16 . answer : b" | null |
Question: a worker is paid a regular rate of rs . 20 for completing a survey . the worker completes 50 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 10 % higher than her regular rate . if she completed 35 surveys involving the use of her cellphone , how much did she get that week ?
A.570.
B.670.
C.1070.
D.470.
e ) 2070C.
"amount earned by using her cell phone = 35 * 22 = 770 amount earned as usual = 15 * 20 = 300 total = 770 + 300 = 1070 answer : c" | null |
Question: reeya obtained 50 , 60 , 70 , 80 and 80 out of 100 in different subjects , what will be the average
A.70.
B.75.
C.80.
D.85.
e ) 68E.
"explanation : ( 50 + 60 + 70 + 80 + 80 / 5 ) = 68 option e" | null |
Question: 5 goats ’ s and 10 hens are brought for rs . 2500 . if the average price of a hen be rs . 50 . what is the average price of a goat .
A.425.
B.375.
C.350.
D.400.
e ) 500D.
explanation : average price of a hen = rs . 50 total price of 10 hens = 10 * 50 = rs . 500 but total price of 5 goats and 10 hens = rs . 2500 total price of 5 goats is = 2500 - 500 = 2000 average price of a goat = 2000 / 5 = rs . 400 answer : d | null |
Question: kareena , saif , and a puppy start walking down a road . they start at the same time , from the same point , in the same direction . the saif walks at 5 miles / hour kareena at 6 miles / hour . the puppy runs from saif to kareena and back again with a constant speed of 10 miles / hour . the puppy does not slow down on the turn . how far does the puppy travel in 1 hour ?
A.10 miles.
B.14 miles.
C.12 miles.
D.20 miles.
e ) 30 milesA.
a 10 miles speed us 10 miles / hour | null |
Question: if m is a positive integer and m ^ 2 is divisible by 39 , then the largest positive integer that must divide m is ?
A.3.
B.6.
C.8.
D.12.
e ) 13E.
"m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 13 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is e but if m = 39 then answer should be 16 . is the question right ? or am i missing some thing ? e" | null |
Question: a man can row 6 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?
A.7.76 kms.
B.8.76 kms.
C.5.76 kms.
D.3.76 kms.
e ) 4.76 kmsC.
"explanation : speed in still water = 6 kmph stream speed = 1.2 kmph down stream = 7.2 kmph up stream = 4.8 kmph x / 7.2 + x / 4.8 = 1 x = 2.88 total distance = 2.88 x 2 = 5.76 kms answer : c" | null |
Question: for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 315 what is the least possible value of k ?
A.5.
B.7.
C.9.
D.11.
e ) 13B.
315 = 3 * 3 * 5 * 7 thus k must include numbers at least up to the number 7 . the answer is b . | null |
Question: find the value of a from ( 15 ) ^ 2 x 8 ^ 3 ã · 256 = a .
A.250.
B.420.
C.440.
D.650.
e ) 450E.
given exp . = ( 15 ) ^ 2 x 8 ^ 3 ã · 256 = a = 225 x 512 ã · 256 = 450 e | null |
Question: the sum of two prime numbers is 85 . what is the product of these two prime numbers ?
A.85.
B.91.
C.115.
D.133.
e ) 166E.
since there is only one even prime number ( 2 ) , and the sum of two odd numbers is even , the product of these two numbers must be even . correct answer e | null |
Question: a and b can do a work in 15 days , b and c in 30 days , c and a in 45 days . if a , b and c work together , they will complete the work in ?
A.10 days.
B.16 days.
C.20 days.
D.25 days.
e ) 22 daysB.
"a + b 1 day work = 1 / 15 b + c 1 day work = 1 / 30 c + a 1 day work = 1 / 45 adding we get 2 ( a + b + c ) = 1 / 15 + 1 / 30 + 1 / 45 = 11 / 90 a + b + c 1 day work = 11 / 180 a , b , c can finish the work in 180 / 11 days = 16 days approximately answer is b" | null |
Question: a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,053 . how much did she invest at 5 % ?
A.$ 500.
B.$ 600.
C.$ 700.
D.$ 900.
e ) $ 950C.
"et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1053 / 1000 ) - 1 = 0.053 = 5.3 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.053 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.053 - 0.01 x = - 0.007 x = - 0.007 / - 0.01 = 7 / 10 = 70 % so x = 70 % of the 1000 which is 700 answer : c" | null |
Question: 6 ! / ( 6 - 3 ) ! = ?
A.120.
B.346.
C.356.
D.366.
e ) 396A.
6 ! / 6 - 3 ) ! = 6 ! / 3 ! = 6 * 5 * 4 = 120 . hence , the correct answer is a . | null |
Question: x is a positive integer less than 500 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
A.21.
B.22.
C.23.
D.24.
e ) 25D.
"when x divided by 7 and leave reminder 1 . x could be 1 , 8,15 , . . . . when divided by 3 and leave reminder 2 - x could be 2 , 5,8 , . . . . so x must be of the form 21 m + 8 where m = 0 , 1,2 , . . . . . first no will be 8 and last no will be 491 . so total no . less than 500 will be 24 . answer : d" | null |
Question: the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 27 ?
A.6.
B.7.
C.8.
D.9.
e ) 10D.
"first , let ' s translate the expression 21 # 27 , using the definition given : 21 # 27 = 21 × 24 × 27 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 27 = 3 ^ 3 ( 7 × 8 × 9 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 27 = 3 ^ 3 ( 7 × 2 ^ 3 × 3 ^ 2 ) let ' s group the prime bases : 21 # 27 = 2 ^ 3 × 3 ^ 5 × 7 the sum of the exponents is 3 + 5 + 1 = 9 the answer is d ." | null |
Question: the average age of the boys in a class is 16 years and that of the girls is 15 years . the average age for the whole class is
A.27.
B.29.
C.11.
D.data inadequate.
e ) 28D.
clearly , to find the average , we ought to know the number of boys , girls or students in the class , neither of which has been given . so , the data provided is inadequate answer : d | null |
Question: the length of the bridge , which a train 170 meters long and travelling at 45 km / hr can cross in 30 seconds , is :
A.239.
B.277.
C.205.
D.88.
e ) 232C.
"speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 170 + x ) / 30 = 25 / 2 = = > 2 ( 170 + x ) = 750 = = > x = 205 m . answer : c" | null |
Question: a collection of books went on sale , and 2 / 3 of them were sold for $ 3 each . if none of the 36 remaining books were sold , what was the total amount received for the books that were sold ?
A.$ 216.
B.$ 135.
C.$ 90.
D.$ 60.
e ) $ 54A.
"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 ( $ 3 ) or $ 216 . the best answer is therefore a . answer : a ." | null |
Question: the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 9 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
A.23 years.
B.24 years.
C.25 years.
D.26 years.
e ) 27 yearsD.
"explanation let the average age of the whole team by x years . 11 x â € “ ( 26 + 38 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 52 2 x = 52 x = 26 . so , average age of the team is 26 years . answer d" | null |
Question: if ( 2 ^ 12 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?
A.12.
B.8.
C.15.
D.16.
e ) 23A.
"given 2 ^ 12 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 12 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans a on comparing the power of 2 = > m = 12" | null |
Question: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 125 resolutions ?
A.794 m.
B.704 m.
C.454 m.
D.186 m.
e ) 176 mE.
"in one resolution , the distance covered by the wheel is its own circumference . distance covered in 125 resolutions . = 125 * 2 * 22 / 7 * 22.4 = 17600 cm = 176 m answer : e" | null |
Question: if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 160 pounds . what is leo ' s current weight ?
A.80.
B.86.
C.92.
D.98.
e ) 104C.
"l + k = 160 and so k = 160 - l l + 10 = 1.5 k = 1.5 ( 160 - l ) 2.5 l = 230 l = 92 the answer is c ." | null |
Question: if 40 % of a certain number is 160 , then what is 60 % of that number ?
A.270.
B.380.
C.260.
D.360.
e ) 240E.
"explanation : 40 % = 40 * 4 = 160 60 % = 60 * 4 = 240 answer : option e" | null |
Question: if 22 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
A.95.
B.90.
C.88.
D.80.
e ) 75C.
"let x be the number of students in the school . 0.22 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.22 x / 0.25 = 0.88 x students went to the camping which is 88 % . the answer is c" | null |
Question: if a : b : c = 3 : 4 : 7 , then the ratio ( a + b + c ) : c is equal to
A.2 : 1.
B.14 : 3.
C.7 : 2.
D.1 : 2.
e ) noneA.
solution : ( a + b + c ) = 3 + 4 + 7 = 14 and c = 7 then , ( a + b + c ) : c = 2 : 1 . answer : option a | null |
Question: a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.05 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fifth day it is overdue ?
A.$ 0.60.
B.$ 0.70.
C.$ 0.80.
D.$ 0.90.
e ) $ 1.00B.
1 st day fine - 0.05 2 nd day fine - 0.05 * 2 = 0.1 ( as doubling gives lower value ) 3 rd day fine - 0.1 * 2 = 0.2 ( as doubling gives lower value ) 4 th day fine - 0.2 * 2 = 0.4 ( as doubling gives lower value we add 0.3 this time ) 5 th day fine - 0.4 + 0.3 = 0.7 ( as doubling gives higher value we add 0.3 this time ) answer : b . | null |
Question: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 230 , what were her original savings ?
A.$ 900.
B.$ 800.
C.$ 1000.
D.$ 920.
e ) $ 1500D.
"if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 230 . so 1 / 4 of her savings is $ 230 . so her original savings are 4 times $ 230 = $ 920 correct answer d" | null |
Question: 45 x ? = 10 % of 900
A.2.
B.4.
C.5.
D.500.
e ) noneA.
answer let 45 x a = ( 10 x 900 ) / 100 ∴ a = ( 10 x 9 ) / 45 = 2 correct option : a | null |
Question: a circle graph shows how the budget of a certain company was spent : 20 percent for transportation , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for salaries . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent salaries ?
['A.90 °', 'B.135 °', 'C.216 °', 'D.240 °', 'e ) 270 °']C.
the percent of the budget for salaries is 100 - ( 20 + 9 + 5 + 4 + 2 ) = 60 % 100 % of the circle is 360 degrees . then ( 60 % / 100 % ) * 360 = 216 degrees the answer is c . | null |
Question: sales price is $ 44 , gross profit is 120 % of cost , what is the value of gross profit ?
A.24.
B.33.
C.39.
D.40.
e ) 42A.
cost + profit = sales cost + ( 120 / 100 ) cost = 44 cost = 20 profit = 44 - 20 = 24 answer ( a ) | null |
Question: seed mixture x is 40 % ryegrass and 60 % bluegrass by weight ; seed mixture y is 25 % ryegrass and 75 % fescue . if a mixture of x and y contains 30 % ryegrass , what percent of the weight of the mixture is x ?
A.10 %.
B.33.33 %.
C.40 %.
D.50 %.
e ) 66.67 %B.
"x - wt of mix x added y - wt of mix y added 0.4 x + 0.25 y = 0.3 ( x + y ) 0.1 x = 0.05 y x / y = 5 / 10 = 1 / 2 y / x = 2 ( y + x ) / x = 3 = > x / ( y + x ) * 100 = 100 / 3 = 33.33 % answer : b" | null |
Question: a circular road runs around a circular garden . if the sum of the circumferences of the inner and outer circles is 88 metres and the radius of the inner circle is one - third of the outer circle , then the width of the road is :
A.4 metres.
B.5 metres.
C.7 metres.
D.6 metres.
e ) 8 metresC.
let radius of inner circle = r 1 radius of outer circle = r 2 also r 1 = 1 / 3 * r 2 3 * r 1 = r 2 circumference of inner circle = 2 * pi * r 1 circumference of outer circle = 2 * pi * r 2 = 6 * pi * r 1 ( since r 2 = 3 * r 1 ) 2 * pi * r 1 + 6 * pi * r 1 = 88 ( as per question ) r 1 = 3.5 m r 2 = 3 * 3.5 = 10.5 m width of road = 10.5 - 3.5 = 7 m ans . answer : c | null |
Question: in a multiple choice test comprising 5 questions , each with 4 choices , what is the probability of a student getting 3 or more questions correct ? each question has only one correct answer and the student is equally likely to choose any of the 4 choices .
A.24 / 256.
B.53 / 512.
C.105 / 512.
D.459 / 512.
e ) 47 / 256B.
probability for choosing correct answer is 1 / 4 and incorrect answer is 3 / 4 for 3 correct answers , c ( 5,3 ) * ( 1 / 4 ) ^ 3 * ( 3 / 4 ) ^ 2 = 90 / ( 4 ^ 5 ) for 4 correct answers , c ( 5,4 ) * ( 1 / 4 ) ^ 4 * ( 3 / 4 ) ^ 1 = 15 / ( 4 ^ 5 ) for 5 correct answers , c ( 5,5 ) * ( 1 / 4 ) ^ 5 * ( 3 / 4 ) ^ 0 = 1 / ( 4 ^ 5 ) so total probability = 106 / 1024 = 53 / 512 ans b | null |
Question: p and q together can do a work in 6 days . if p alone can do it in 15 days . in how many days can q alone do it ?
A.5.
B.4.
C.10.
D.11.
e ) 12C.
1 / 6 - 1 / 15 = = > 1 / 10 = = > 10 answer c | null |
Question: in a certain animal shelter , the ratio of the number of catsto the number of dogs is 15 to 7 . if 12 additional dogs were to be taken in by the shelter , the ratio of the number of cats to the number of dogs would be 15 to 11 . how many cats are in the shelter ?
A.15.
B.45.
C.30.
D.45.
e ) 60B.
this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of cats to the number of dogs is 15 : 7 . we ' re then told that 12 more dogs are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of cats . algebraically , since the number of cats is a multiple of 15 and the number of dogs is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 12 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 12 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 12 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 12 ) ( 1 ) 11 x = 7 x + 12 4 x = 12 x = 3 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 3 ) = 45 final answer : b | null |
Question: the ratio between the sale price and the cost price of an article is 9 : 5 . what is the ratio between the profit and the cost price of that article ?
A.23.
B.1 : 2.
C.4 : 5.
D.3 : 5.
e ) 25C.
"c . p . = rs . 5 x and s . p . = rs . 9 x . then , gain = rs . 4 x required ratio = 4 x : 5 x = 4 : 5 c" | null |
Question: a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 300 , find the original price per kg ?
A.s . 7.7.
B.s . 7.4.
C.s . 7.5.
D.s . 7.1.
e ) s . 7.9C.
"100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 300 - - - 80 ? - - - 2 = > rs . 7.5 answer : c" | null |
Question: 8 is 6 % of a , and 6 is 8 % of b . c equals b / a . what is the value of c ?
A.3 / 8.
B.8 / 15.
C.9 / 16.
D.12 / 25.
e ) 16 / 27C.
"6 a / 100 = 8 a = 400 / 3 8 b / 100 = 6 b = 75 c = b / a = 75 * 3 / 400 = 9 / 16 the answer is c ." | null |
Question: of the 65 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?
A.10.
B.15.
C.20.
D.25.
e ) 30A.
neither car nor garage = total - garage - ( swim - common ) = 65 - 50 - ( 40 - 35 ) = 65 - 55 = 10 answer a | null |
Question: exactly 3 / 8 of the people in the room are under the age of 21 , and exactly 5 / 12 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
A.21.
B.36.
C.39.
D.60.
e ) 65B.
"the total number of the people in the room must be a multiple of both 8 and 12 ( in order 3 / 7 and 5 / 13 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 8 and 12 , which is 96 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 96 people in the room . therefore there are 3 / 8 * 96 = 36 people in the room under the age of 21 . answer : b ." | null |
Question: we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 10 , and the difference between the total number of strawberries and the total number of blueberries would increase by 50 . each blue box contains how many blueberries ?
A.10.
B.15.
C.20.
D.25.
e ) 30C.
"let x be the number of blueberries in each blue box . then there are x + 10 strawberries in each red box . x + ( x + 10 ) = 50 x = 20 the answer is c ." | null |
Question: if x / y = 3 and ( 2 a - x ) / ( 3 b - y ) = 3 , then the value of a / b is ?
A.– 3.
B.9 / 2.
C.1.
D.2.
e ) 3B.
x = 3 y 2 a - 3 y = 3 ( 3 b - y ) 2 a - 3 y = 9 b - 3 y 2 a = 9 b a / b = 9 / 2 answer : b | null |
Question: if z is a multiple of 9702 , what is the remainder when z ^ 2 is divided by 4 ?
A.0.
B.1.
C.2.
D.3.
e ) it depends on z .A.
"2 is a factor of 9702 , so 2 is a factor of z . then 2 ^ 2 = 4 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 4 is 0 . the answer is a ." | null |
Question: a man buys a cycle for rs . 1400 and sells it at a loss of 15 % . what is the selling price of the cycle ?
A.rs . 1200.
B.rs . 890.
C.rs . 600.
D.rs . 1190.
e ) rs . 450D.
"explanation : s . p . = 85 % of rs . 1400 = rs . ( 85 / 100 * 1400 ) = rs . 1190 answer : d" | null |
Question: a and b can finish a work in 12 days while a alone can do the same work in 24 days . in how many days b alone will complete the work ?
A.76 days.
B.48 days.
C.98 days.
D.31 days.
e ) 24 daysE.
"b = 1 / 12 – 1 / 24 = 1 / 24 = > 24 days answer : e" | null |
Question: when n is divided by 5 the remainder is 3 . what is the remainder when ( n + 2 ) ^ 2 is divided by 5 ?
A.0.
B.1.
C.2.
D.3.
e ) 4A.
"n = 5 x + 3 , for some integer x ( n + 2 ) ^ 2 = ( 5 x + 5 ) ^ 2 = 5 y , for some integer y when we divide this by 5 , the remainder is 0 . the answer is a ." | null |
Question: if an average hard drive had a capacity of 0.3 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
A.3072.
B.512.
C.768.
D.1024.
e ) 1536A.
"0.3 * 2 ^ 10 = 0.3 * 1024 = 307.2 the answer is a ." | null |
Question: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 250 resolutions ?
A.277 m.
B.704 m.
C.352 m.
D.288 m.
e ) 378 mC.
"in one resolution , the distance covered by the wheel is its own circumference . distance covered in 250 resolutions . = 250 * 2 * 22 / 7 * 22.4 = 35200 cm = 352 m answer : c" | null |
Question: if grapes are 93 % water and raisins are 16 % water , then how many kilograms did a quantity of raisins , which currently weighs 8 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )
A.92.
B.96.
C.100.
D.104.
e ) 108B.
let x be the original weight . the weight of the grape pulp was 0.07 x . since the grape pulp is 84 % of the raisins , 0.07 x = 0.84 ( 8 ) . then x = 12 * 8 = 96 kg . the answer is b . | null |
Question: find the slope of the line perpendicular to the line y = x - 7
A.1.
B.2.
C.- 1.
D.4.
e ) 5C.
two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 . if m is the slope of the line perpendicular to the given line , then m × 1 = - 1 solve for m m = - 1 correct answer c ) - 1 | null |
Question: set a consists of all the prime numbers between 10 and 25 . what is the range of set a ?
A.12.
B.13.
C.16.6.
D.17.
e ) 23A.
"the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 23 lowest number = 11 range = highest - lowest = 23 - 11 = 12 option a" | null |
Question: a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 370 m long platform ?
A.19.
B.27.
C.29.
D.47.
e ) 49E.
let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 370 ) / 36 * 5 / 18 = 49 min . answer : e | null |
Question: a train of 25 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 2.5 km long ?
A.4.
B.3.
C.5.
D.7.
e ) 9A.
"d = 25 * 60 + 2500 = 4000 m t = 4000 / 60 * 18 / 5 = 240 sec = 4 mins answer : a" | null |
Question: the length of a rectangle is halved , while its breadth is tripled . what is the % change in area ?
A.30 %.
B.40 %.
C.50 %.
D.60 %.
e ) 65 %C.
"let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c" | null |
Question: there were two candidates in an election . winner candidate received 60 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
A.776.
B.864.
C.299.
D.257.
e ) 125B.
"w = 60 % l = 40 % 60 % - 40 % = 20 % 20 % - - - - - - - - 288 60 % - - - - - - - - ? = > 864 answer : b" | null |
Question: in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( − 2 , − 3 ) ?
A.4.
B.2.
C.0.
D.− 2.
e ) − 4A.
"slope = rise / run = 6 / 12 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a ." | null |
Question: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
A.276.
B.299.
C.322.
D.345.
e ) 355C.
"clearly , the numbers are ( 23 x 13 ) and ( 23 x 14 ) . larger number = ( 23 x 14 ) = 322 . answer : option c" | null |
Question: a and b undertake to do a piece of work for rs . 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . ! find the share of b .
A.225.
B.500.
C.75.
D.800.
e ) none 0 of themA.
"c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 » ) = rs . 75 . answer is a" | null |
Question: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 500 resolutions
A.700.
B.704.
C.704.
D.706.
e ) 707B.
"in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.4 = 70400 cm = 704 m answer : option b" | null |
Question: a 220 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
A.280.
B.270.
C.260.
D.250.
e ) 240A.
"relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 220 ) / 9 = 500 / 9 = > x = 280 . answer : option a" | null |
Question: the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 402 to 500 inclusive ?
A.14,550.
B.18,550.
C.22,550.
D.26,550.
e ) 30,550C.
"2 + 4 + 6 + 8 + . . . + 100 = 2550 402 + 404 + . . . + 500 = 50 ( 400 ) + ( 2 + 4 + . . . + 100 ) = 20,000 + 2550 = 22,550 the answer is c ." | null |
Question: we run a business that rents out canoes and kayaks . a canoe rental costs $ 9 per day , and a kayak rental costs $ 12 dollars per day . one day , our business rents out 4 canoes for every 3 kayaks and receives a total of $ 432 in revenue . how many more canoes than kayaks were rented out ?
A.10.
B.9.
C.8.
D.7.
e ) 6E.
"let x be the number of canoes . then 3 x / 4 is the number of kayaks . 9 x + ( 3 x / 4 ) * 12 = 432 9 x + 9 x = 432 18 x = 432 x = 24 ( canoes ) 3 x / 4 = 18 ( kayaks ) there were 24 - 18 = 6 more canoes rented out . the answer is e ." | null |
Question: ramu bought an old car for rs . 48000 . he spent rs . 14000 on repairs and sold it for rs . 72900 . what is his profit percent ?
A.16 %.
B.17.5 %.
C.18.2 %.
D.58.5 %.
e ) 13 %B.
"total cp = rs . 48000 + rs . 14000 = rs . 62000 and sp = rs . 72900 profit ( % ) = ( 72900 - 62000 ) / 62000 * 100 = 17.5 % answer : b" | null |
Question: rs . 2600 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 140 . how much was lent at 5 % ?
A.1600.
B.1700.
C.1800.
D.1900.
e ) 2000A.
"( x * 5 * 1 ) / 100 + [ ( 2600 - x ) * 6 * 1 ] / 100 = 140 x = 1600 answer : a" | null |
Question: a bag contains 6 white marbles and 6 black marbles . if each of 6 girls and 6 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
A.1 / 35.
B.1 / 10.
C.1 / 3.
D.1 / 462.
e ) 1 / 252D.
"first , total ways to select for all boys and girls , i . e 12 ! / ( 6 ! * 6 ! ) = 12 * 11 * 10 * 9 * 8 * 7 / 6 * 5 * 4 * 3 * 2 = 924 then there are one two way girls can have all same colors , either white or black . the number of ways in which 6 girls can select 6 white balls = 6 c 6 = 1 the number of ways in which 6 girls can select 6 black balls = 6 c 6 = 1 therefore , total favorable outcomes / total outcomes = 2 / 924 = 1 / 462 d" | null |
Question: the average weight of 7 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?
A.74 kg.
B.78.5 kg.
C.99.5 kg.
D.data inadequate.
e ) none of theseC.
"total weight increased = ( 7 x 3.5 ) kg = 24.5 kg . weight of new person = ( 75 + 24.5 ) kg = 99.5 kg . answer : option c" | null |
Question: in a group of people , if 30 people were made to stand in each column , 16 columns could be formed . if 32 people were made to stand in a column , how many columns could be formed ?
A.15.
B.20.
C.25.
D.30.
e ) 35A.
"16 * 30 = 32 * n n = 15 the answer is a ." | null |
Question: what least number must be subtracted from 427398 so that remaining no . is divisible by 10
A.3.
B.5.
C.6.
D.7.
e ) 8E.
"explanation : on dividing 427398 by 10 we get the remainder 8 , so 8 should be subtracted answer : option e" | null |
Question: the average age of applicants for a new job is 10 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?
A.8.
B.16.
C.17.
D.18.
e ) 34C.
minimum age = average - 1 standard deviation = 10 - 8 = 2 maximum age = average + 1 standard deviation = 10 + 8 = 18 maximum number of different ages of the applicants = 18 - 2 + 1 = 17 answer c | null |
Question: ajay can ride 50 km in 1 hour . in how many hours he can ride 900 km ?
A.10 hrs.
B.15 hrs.
C.20 hrs.
D.25 hrs.
e ) 18 hrsE.
1 hour he ride 50 km he ride 900 km in = 900 / 50 * 1 = 18 hours answer is e | null |
Question: a and b invests rs . 6000 and rs . 12000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
A.32 : 99.
B.8 : 21.
C.32 : 45.
D.34 : 89.
e ) 35 : 21B.
"a : b ( 6000 * 4 ) + ( 3000 * 8 ) : ( 12000 * 6 ) + ( 9000 * 6 ) 48000 : 126000 8 : 21 answer : b" | null |
Question: tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 7 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
A.80.
B.90.
C.56.
D.70.
e ) 60C.
"c 56 sum = ( n x n ) + n hence , 7 x 7 = 49 + 7 = 56" | null |
Question: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 80 metres ?
A.16 seconds.
B.76 seconds.
C.26 seconds.
D.12 seconds.
e ) 18 secondsA.
"speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 80 m = 80 / 5 = 16 seconds . answer : a" | null |
Question: a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 44 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
A.a . 72.
B.b . 50.
C.c . 92.
D.d . 46.
e ) e . 44C.
at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 44 seconds . thus x = 4 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 92 seconds . answer c | null |
Question: each week , harry is paid x dollars per hour for the first 21 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
A.35.
B.36.
C.37.
D.38.
e ) 39A.
"42 x = 21 x + 1.5 x ( h - 21 ) = = > 42 = 21 + 1.5 ( h - 21 ) = = > h - 21 = 21 / 1.5 = 14 = > h = 35 answer is a" | null |
Question: the volume of a cube is 729 cc . find its surface .
A.486.
B.556.
C.255.
D.287.
e ) 267A.
"a 3 = 729 = > a = 9 6 a 2 = 6 * 9 * 9 = 486 answer : a" | null |
Question: a bag contains 4 white marbles and 4 black marbles . if each of 4 girls and 4 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
A.1 / 35.
B.1 / 9.
C.1 / 10.
D.1 / 20.
e ) 1 / 30A.
"first , total ways to select for all boys and girls , i . e 8 ! / ( 4 ! * 4 ! ) = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1 * 4 * 3 * 2 * 1 = 70 then there are one two way girls can have all same colors , either white or black . the number of ways in which 4 girls can select 4 white balls = 4 c 4 = 1 the number of ways in which 4 girls can select 4 black balls = 4 c 4 = 1 therefore , total favorable outcomes / total outcomes = 2 / 70 = 1 / 35 a" | null |
Question: a can knit a pair of socks in 3 days . b can knit the same thing in 6 days . if they are knitting together , in how many days will they knit two pairs of socks ?
A.4 days.
B.2 days.
C.4 1 ⁄ 2 days.
D.3 days.
e ) none of theseA.
explanationa ’ s one day ’ s work = 1 ⁄ 3 rd work . b ’ s one day ’ s work = 1 ⁄ 6 rd work . ( a + b ) ’ s one day ’ s work = 1 ⁄ 3 + 1 ⁄ 6 = 1 ⁄ 2 nd work . ∴ a and b together can complete the work ( knit a pair of socks ) in 2 days . ∴ they together knit two pair of socks in 4 days . answer a | null |
Question: the difference between c . i . and s . i . on an amount of $ 20,000 for 2 years is $ 72 . what is the rate of interest per annum ?
A.5 %.
B.6 %.
C.7 %.
D.8 %.
e ) 9 %B.
"$ 72 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 20000 * x . the interest on the first year ' s interest is 20000 * x * x 20000 * x ^ 2 = 72 x = 0.06 the answer is b ." | null |
Question: running at their respective constant rates , machine x takes 6 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 2 w widgets ?
A.8.
B.6.
C.4.
D.10.
e ) 12A.
"together they make 5 / 4 w widgets in 3 days . so they make w widgets in 3 * 4 / 5 = 12 / 5 days . 1 / ( t + 2 ) + 1 / t = 5 / 12 now , calculating this is really cumbersome so try to plug in options to get to the answer . if machine x takes 12 days to produce 2 w widgets , it would take 6 days to make w widgets , t would be 4 . 1 / 6 + 1 / 4 = 5 / 12 it works so t = 4 . answer : a" | null |
Question: find the ones digit of 73 ^ 353
A.3.
B.5.
C.6.
D.7.
e ) 9A.
"the units digit of 73 ^ 353 will be the same as the units digit of 3 ^ 353 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 353 = 352 + 1 = ( multiple of 4 ) + 1 , then the units digit of 3 ^ 353 will be the first number in the pattern thus 3 . answer : a ." | null |
Question: if 2 x + y = 26 and x + 2 y = 10 , then ( x + y ) / 3 =
A.1.
B.4 / 3.
C.17 / 5.
D.18 / 5.
e ) 4E.
"we have two equations : 2 x + y = 26 x + 2 y = 10 notice that something nice happens when we add them . we get : 3 x + 3 y = 36 divide both sides by 3 to get : x + y = 12 so , ( x + y ) / 3 = 12 / 3 = 4 answer : e" | null |
Question: find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 16 per cubic meter ?
A.2998.
B.2799.
C.2890.
D.1485.
e ) 1584E.
"22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 16 = 1584 answer : e" | null |
Question: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1015 . find the cost of each ice - cream cup ?
A.34.
B.76.
C.29.
D.12.
e ) 20A.
"explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1015 96 + 225 + 490 + 6 x = 1015 6 x = 204 = > x = 34 . answer : a" | null |
Question: a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more thanc . out of a total profit of rs . 35000 , a receives :
A.14700.
B.14703.
C.37798.
D.13777.
e ) 14778A.
explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 35000 * 21 / 50 ) = rs . 14,700 . answer : a ) 14700 | null |
Question: a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 2,000 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?
A.$ 18,400.
B.$ 19,500.
C.$ 20,200.
D.$ 20,700.
e ) $ 21,100D.
"price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 1500 net price of the car in 02 = 18700 + 2000 = $ 20700 correct option : d" | null |
Question: a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 6 days before the completion of the work . in how many days was the work completed ?
A.12 days.
B.16 days.
C.18 days.
D.11.5 days.
e ) 38 daysD.
"one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 6 days = 6 * ( 1 / 24 + 1 / 30 ) = 9 / 20 remaining work = 11 / 20 the number of days required for this initial work = 5.5 days . the total number of days required = 6 + 5.5 = 11.5 days . answer : d" | null |
Question: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 300 , what were her original savings ?
A.$ 1200.
B.$ 1300.
C.$ 1400.
D.$ 1800.
e ) $ 1900A.
"if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 300 . so 1 / 4 of her savings is $ 300 . so her original savings are 4 times $ 300 = $ 1200 correct answer a" | null |
Question: walking 7 / 6 of his usual rate , a boy reaches his school 6 min early . find his usual time to reach the school ?
A.22.
B.28.
C.99.
D.42.
e ) 66D.
"speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 6 - - - - - - - - - ? = 42 m answer : d" | null |
Question: a jogger running at 9 kmph along side a railway track is 230 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
A.3.6 sec.
B.18 sec.
C.35 sec.
D.72 sec.
e ) none of theseC.
"speed of train relative to jogger = ( 45 – 9 ) km / h = 36 km / h = ( 36 × 5 ⁄ 18 ) m / sec = 10 m / sec distance to be covered = ( 230 + 120 ) m = 350 m . ∴ time taken = ( 350 ⁄ 10 ) sec = 35 sec . answer c" | null |
Question: a train covers a distance of 36 km in 12 min . if it takes 10 sec to pass a telegraph post , then the length of the train is ?
A.300 m.
B.1000 m.
C.120 m.
D.200 m.
e ) 500 mE.
"speed = ( 36 / 12 * 60 ) km / hr = ( 180 * 5 / 18 ) m / sec = 50 m / sec . length of the train = 50 * 10 = 500 m . answer : e" | null |
Question: 8 people decided to split the restaurant bill evenly . if the bill was $ 214.18 dollars , how much money did they 1 cent is the smallest unit ?
A.$ 214.16.
B.$ 214.17.
C.$ 214.18.
D.$ 214.19.
e ) $ 214.24E.
"if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 418 not divisible by a hence , we need to add 6 to this number for it to be divisible by 8 correct option : e" | null |
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