regisss/math_qa huggingface dataset:
Problem: bill and jane play a simple game involving two fair dice , each of which has 6 sides numbered from 1 to 6 ( with an equal chance of landing on any side ) . bill rolls the dice and his score is the total of the two dice . jane then rolls the dice and her score is the total of her two dice . if jane ’ s score is higher than bill ’ s , she wins the game . what is the probability the jane will win the game ?
Options: a ) 15 / 36 , b ) 175 / 432 , c ) 575 / 1296 , d ) 583 / 1296 , e ) 1 / 2
Rationale: there are three possible outcomes in the game : 1 . b wins 2 . j wins 3 . draw so , 1 = p ( j ) + p ( b ) + p ( draw ) 1 = p ( j ) + p ( b ) + p ( draw ) the probability of b winning or j winning the game is same . so , 1 = 2 ∗ p ( j ) + p ( draw ) 1 = 2 ∗ p ( j ) + p ( draw ) so , we need to calculate the probability of a draw . a draw can happen when both will have the same sum . the possible sums are - 2 , 34 , 56 , 78 , 910 , 1112 prob . of each sum is - 2 - 11 - 1 / 36 3 - 1 2 , 2 1 - 2 / 36 4 - 1 3 , 2 2 , 3 1 - 3 / 36 5 - 1 4 , 2 3 , 3 2 , 41 - 4 / 36 6 - 1 5 , 2 4 , 3 3 , 4 2 , 5 1 - 5 / 36 7 - 1 6 , 2 5 , 3 4 , 4 3 , 5 2 , 61 - 6 / 36 8 - 2 6 , 3 5 , 4 4 , 5 3 , 6 2 , - 5 / 36 9 - 3 6 , 4 5 , 5 4 , 63 - 4 / 36 10 - 4 6 , 5 5 , 6 4 - 3 / 36 11 - 5 6 , 6 5 - 2 / 36 12 - 6 6 - 1 / 36 now , since both have to get the same sum , the probability will be same for both and the combined probability will be the square of the probabilities i . e . 2 - ( 1 / 36 ) ^ 2 3 - ( 2 / 36 ) ^ 2 etc . squaring the probabilities and adding them will give 146 / 1296 so , p ( d ) = 146 / 1296 1 = 2 * p ( j ) + p ( d ) 2 * p ( j ) = 1150 / 1296 p ( j ) = 575 / 1296 ans . c
Answer: c
Problem: the total age of a and b is 11 years more than the total age of b and c . c is how many year younger than a
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : given that a + b = 11 + b + c = > a ? c = 11 + b ? b = 11 = > c is younger than a by 11 years answer : option a"
Answer: a
Problem: if the sides of a triangle are 30 cm , 40 cm and 50 cm , what is its area ?
Options: a ) 400 , b ) 500 , c ) 550 , d ) 600 , e ) 700
Rationale: "the triangle with sides 30 cm , 40 cm and 50 cm is right angled , where the hypotenuse is 50 cm . area of the triangle = 1 / 2 * 40 * 30 = 600 cm 2 answer : option d"
Answer: d
Problem: the area of an equilateral triangle is subtracted from its base , and the perimeter is then added to this total , the result is 4 . what is the height of the equilateral triangle if its base is 2 ?
Options: a ) 2
b ) 3
c ) 4
d ) 5
e ) 6
Rationale: an eqilateral triangle means all sides are equal ; therefore , base = side . the equation is ; base - area + perimeter = b - a + p = b - 1 / 2 bh + 3 b , and b = 2 . so , 2 - 2 / 2 h + 6 = 4 , and 8 - h = 4 . by plugging in the answers we can test the answers quickly ; then , 4 is the only possible answer . answer : c
Answer: c
Problem: ( 6 ! - 4 ! ) / 5 ! = ?
Options: a ) 29 / 5 , b ) 28 / 3 , c ) 27 / 6 , d ) 25 / 4 , e ) 29 / 6
Rationale: ( 6 ! - 4 ! ) / 5 ! ( 4 ! * 5 * 6 - 4 ! ) / 5 ! 4 ! ( 5 * 6 - 1 ) / 4 ! * 5 29 / 5 answer a
Answer: a
Problem: a sum of money is sufficient to pay p ' s wages for 24 days and q ' s wages for 40 days . the same money is sufficient to pay the wages of both for ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: let the total money be $ x p ' s 1 day work = $ x / 24 q ' s 1 day work = $ x / 40 p + q 1 day work = $ x / 15 money is sufficient to pay the wages of both for 15 days answer is d
Answer: d
Problem: if i walk at 5 km / h , i miss the bus by 9 minutes . if i walk at 3 km / h , i reach 6 minutes before the arrival of the bus . how far i walk to reach the bus stand ?
Options: a ) 1.99 km , b ) 1.55 km , c ) 1.82 km , d ) 2.87 km , e ) 1.87 km
Rationale: "d = product of speed difference of time / difference of speed d = 5 x 3 / 60 [ 9 â ˆ ’ ( â ˆ ’ 6 ) / 5 - 3 ] [ here , â € “ ve sign indicates before the schedule time ] â ‡ ’ d = 1.87 km answer e"
Answer: e
Problem: tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 27000 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 20000 , b ) 15000 , c ) 25000 , d ) 34000 , e ) 30000
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 27000 = 15000 b"
Answer: b
Problem: how many numbers from 10 to 50 are exactly divisible by 9 ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "10 / 9 = 1 and 50 / 9 = 5 = = > 5 - 1 = 4 . therefore 4 answer : e"
Answer: e
Problem: a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 7 years ago ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 7
Rationale: "let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e . r = 2 s + 8 but r = d + 6 = ( s + 8 ) + 6 = s + 14 therefore , 2 s + 8 = s + 14 i . e . s = 6 i . e . r = 20 i . e . d = 14 now , how old was david 7 years ago ? i . e . d - 7 = 14 - 7 = 7 years answer : e"
Answer: e
Problem: in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 84 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 7000 , b ) 8400 , c ) 6000 , d ) 5000 , e ) 4000
Rationale: "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 84 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 84 = > total appeared candidates in state b = 84 x 100 = 8400 = > total appeared candidates in state a = total appeared candidates in state b = 8400"
Answer: b
Problem: find the area of a parallelogram with base 34 cm and height 18 cm ?
Options: a ) 198 cm 2 , b ) 384 cm 2 , c ) 510 cm 2 , d ) 612 cm 2 , e ) 680 cm 2
Rationale: "area of a parallelogram = base * height = 34 * 18 = 612 cm 2 answer : d"
Answer: d
Problem: a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey ?
Options: a ) 288 , b ) 390 , c ) 287 , d ) 266 , e ) 161
Rationale: "the total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = sum of 10 terms in ap whose first term is 30 and last term is 48 = 10 / 2 [ 30 + 48 ] = 390 km . answer : b"
Answer: b
Problem: in a sports club with 35 members , 15 play badminton and 18 play tennis and 5 do not play either . how many members play both badminton and tennis ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "15 + 18 = 33 but where as total number is 35 - 5 = 30 therefore answer is 33 - 30 = 3 hence answer is a"
Answer: a
Problem: on day one , a store sold 96 pens . on each of the next d days , the company sold 44 pens . if the average daily sales of pens over this time period ( including day one ) is 48 pens , what is the value of d ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: 96 + 44 d = 48 ( d + 1 ) . 4 d = 48 . d = 12 . the answer is d .
Answer: d
Problem: walking 7 / 6 of his usual rate , a boy reaches his school 5 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 28 , c ) 99 , d ) 35 , e ) 66
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 5 - - - - - - - - - ? = 35 m answer : d"
Answer: d
Problem: carrie likes to buy t - shirts at the local clothing store . they cost $ 9.15 each . one day , she bought 22 t - shirts . how much money did she spend ?
Options: a ) $ 150 , b ) $ 248.75 , c ) $ 200 , d ) $ 201.3 , e ) $ 190
Rationale: $ 9.15 * 22 = $ 201.3 . answer is d .
Answer: d
Problem: there were two candidates in an election . winner candidate received 56 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
Options: a ) 776 , b ) 1344 , c ) 299 , d ) 257 , e ) 125
Rationale: "w = 56 % l = 44 % 56 % - 44 % = 12 % 12 % - - - - - - - - 288 56 % - - - - - - - - ? = > 1344 answer : b"
Answer: b
Problem: 243 has been divided into 3 parts such that half of the first part , one - third of the second part and one - fourth of the third part are equal . the largest part is ?
Options: a ) 12628 , b ) 23488 , c ) 26688 , d ) 26667 , e ) 12672
Rationale: explanation : ratio of their shares = ( 35000 * 8 ) : ( 42000 * 10 ) = 2 : 3 . reena ' s share rs . 31570 * ( 2 / 5 ) = rs . 12628 . answer : a ) 12628
Answer: a
Problem: in the rectangular coordinate system , points ( 8 , 0 ) and ( – 8 , 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 c 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 8 c
Answer: c
Problem: a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party e . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: "s = 100 not ( e and b ) = 35 only e = 20 ( e and b ) / b = 1 / 2 let ( e and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans"
Answer: a
Problem: if y ¤ w = y ^ ( 2 w ) for all positive integers , then ( 3 ¤ 4 ) ¤ 2 =
Options: a ) 3 ^ 8 , b ) 3 ^ 12 , c ) 3 ^ 16 , d ) 3 ^ 24 , e ) 3 ^ 32
Rationale: y ¤ w = y ^ ( 2 w ) 3 ¤ 4 = 3 ^ ( 8 ) ( 3 ¤ 4 ) ¤ 2 = ( 3 ^ 8 ) ¤ 2 = ( 3 ^ 8 ) ^ 4 = 3 ^ 32 correct option : e
Answer: e
Problem: a circular rim a having a diameter of 45 inches is rotating at the rate of x inches / min . another circular rim b with a diameter of 30 inches is rotating at the rate of y inches / min . what is the value of y in terms of x , if both the rims reach their starting positions at the same time after every rotation .
Options: a ) 3 x / 2
b ) 4 x / 5
c ) 7 x / 5
d ) 5 x / 7
e ) 3 x / 4
Rationale: t = s 1 / v 1 = s 2 / v 2 or , 45 / x = 30 / y or , y = 45 x / 30 = 3 x / 2 ( answer a )
Answer: a
Problem: a typist uses a sheet measuring 20 cm by 30 cm lengthwise . if a margin of 2 cm is left on each side and a 3 cm margin on top and bottom , then percent of the page used for typing is
Options: a ) 40 , b ) 60 , c ) 64 , d ) 72 , e ) none
Rationale: solution area of the sheet = ( 20 x 30 ) cm ² = 600 cm ² area used for typing = [ ( 20 - 4 ) x ( 30 - 6 ) ] cm ² = 384 cm ² required percentage = ( 384 / 600 x 100 ) % = 64 % . answer c
Answer: c
Problem: the h . c . f . of two numbers is 12 and their difference is 12 . the numbers are :
Options: a ) 66 , 78 , b ) 70 , 82 , c ) 94 , 106 , d ) 84 , 96 , e ) none of these
Rationale: explanation : out of the given numbers , the two with h . c . f . 12 and difference 12 are 84 and 96 . answer is d
Answer: d
Problem: john , james and jim ' investment ratio in a business is 4 : 7 : 9 . if total total investment is 80000 . find jim ' s investment ?
Options: a ) 35000 , b ) 40000 , c ) 16000 , d ) 36000 , e ) 60000
Rationale: let the investment of john james and jim is 4 x 7 x and 9 x 4 x + 7 x + 9 x = 80000 20 x = 80000 x = 4000 jim ' investment = 9 * 4000 = 36000 answer : d
Answer: d
Problem: two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 3 days ?
Options: a ) 1 / 5 , b ) 1 / 1 , c ) 1 / 6 , d ) 1 / 3 , e ) 1 / 7
Rationale: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 3 days = 3 ( 1 / 18 ) = 1 / 6 . answer : c"
Answer: c
Problem: calculate how long it will take a swimmer to swim a distance of 8 km against the current of a river which flows at 1.4 km / hr , given that he can swim in still water at 3 km / h
Options: a ) 20 seconds , b ) 3 , c ) 4 , d ) 1 , e ) 5
Rationale: swim in still water at = 3 speed of river = 1.4 us = 3 - 1.4 = 1.6 distance = 8 t = 8 / 1.6 = 5 answer : e
Answer: e
Problem: if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 39
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "p ã · 44 = 432 = > p = 432 * 44 = 19008 p / 39 = 19008 / 39 = 487 , remainder = 15 c"
Answer: c
Problem: a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 8 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 8 , e ) 1 / 24
Rationale: "let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 8 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 8 ) = 3 x . the fraction of sensors which have been upgraded is x / ( x + 3 x ) = x / 4 x = 1 / 4 the answer is a ."
Answer: a
Problem: if the operation ø is defined for all positive integers x and w by x ø w = ( 2 ^ x ) / ( 2 ^ w ) then ( 4 ø 2 ) ø 1 = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "4 ø 2 = 2 ^ 4 / 2 ^ 2 = 4 4 ø 1 = 2 ^ 4 / 2 = 8 the answer is c ."
Answer: c
Problem: if 3 ^ x * 4 ^ y = 531,441 and x – y = 12 , then x = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "since 531,441 is an odd number , it is not a multiple of 4 . this means that y must equal zero . since x - y = 12 and y = 0 , then x = 12 . the answer is c ."
Answer: c
Problem: a man buys a cycle for rs . 2300 and sells it at a loss of 30 % . what is the selling price of the cycle ?
Options: a ) s . 1690 , b ) s . 1610 , c ) s . 1890 , d ) s . 1602 , e ) s . 1092
Rationale: "s . p . = 70 % of rs . 2300 = rs . 70 x 2300 / 100 = rs . 1610 answer : option b"
Answer: b
Problem: how many hours are there in 660 minutes ?
Options: a ) 60 hours , b ) 6 hours , c ) 30 hours , d ) 11 hours , e ) 10 hours
Rationale: "solution : number of minutes in 1 hour = 60 minutes so just divide 660 by 60 660 ã · 60 = 11 , so there are 11 hours in 660 minutes option d"
Answer: d
Problem: a is twice as good a workman as b and they took 9 days together to do the work b alone can do it in ?
Options: a ) 25 days , b ) 88 days , c ) 21 days , d ) 27 days , e ) 13 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 9 x = 1 / 27 = > 27 days answer : d"
Answer: d
Problem: tom read a book containing 480 pages by reading the same number of pages each day . if he would have finished the book 5 days earlier by reading 16 pages a day more , how many days did tom spend reading the book ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: "say the number of days tom spent reading the book was dd . then : the number of pages he read per day would be 480 / d the number of pages he would read per day with an increased speed would be 480 / d − 5 e are told that the number of pages for the second case was 16 pages per day more , so 480 / d = 480 / d − 5 − 16 at this point it ' s much better to plug answer choices rather than solve for dd . answer choice cc fits : 480 / 15 = 32 = 480 / 15 − 5 − 16 answer : c"
Answer: c
Problem: ajay and vijay have some marbles with them . ajay told vijay ` ` if you give me ' x ' marbles , both of us will have equal number of marbles ' ' . vijay then told ajay ` ` if you give me twice as many marbles , i will have 30 more marbles than you would ' ' . find ' x ' ?
Options: a ) 7 , b ) 5 , c ) 6 , d ) 4 , e ) 3
Rationale: if vijay gives ' x ' marbles to ajay then vijay and ajay would have v - x and a + x marbles . v - x = a + x - - - ( 1 ) if ajay gives 2 x marbles to vijay then ajay and vijay would have a - 2 x and v + 2 x marbles . v + 2 x - ( a - 2 x ) = 30 = > v - a + 4 x = 30 - - - ( 2 ) from ( 1 ) we have v - a = 2 x substituting v - a = 2 x in ( 2 ) 6 x = 30 = > x = 5 . answer : b
Answer: b
Problem: the average of temperatures at noontime from monday to friday is 45 ; the lowest one is 42 , what is the possible maximum range of the temperatures ?
Options: a ) 15 , b ) 25 , c ) 40 , d ) 45 , e ) 75
Rationale: "there are 5 days so the sum of temperature can be 45 * 5 = 225 lowest is 42 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 42 = 168 . on the fifth day it is 225 - 168 = 57 range is therefore 57 - 42 = 15 answer a"
Answer: a
Problem: david is 12 years older than his daughter rosy . in 4 years david will be twice as old as rosy . what is rosy current age .
Options: a ) 9 , b ) 10 , c ) 11 , d ) 8 , e ) 12
Rationale: "now : rosy = x , david = x + 12 in 4 years rosy = x + 4 , david = x + 12 + 4 or 2 ( x + 4 ) x + 16 = 2 x + 8 x = 8 rosy is 8 years old answer : d"
Answer: d
Problem: one - third of 1200 is what percent of 236 ?
Options: a ) 169.49 , b ) 30 , c ) 120.32 , d ) 125.32 , e ) 15.152
Rationale: "answer let one - third of 1200 is n % of 236 . ∵ 1200 / 3 = ( n x 236 ) / 100 ∴ n = ( 400 x 100 ) / 236 = 169.49 correct option : a"
Answer: a
Problem: if 2 is the remainder when m is divided by 5 , what is the remainder when 3 m is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: let ' s find a number which when divided by 5 leaves remainder 2 = 5 + 2 = 7 i . e . one possible value of m = 7 value of 3 m = 3 * 7 = 21 when em is divided by 5 then remainder = rem ( 21 / 5 ) = 1 answer : option b
Answer: b
Problem: the population of a town is 8100 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9000 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8100 × 100 / 90 × 100 / 90 = 10000 e )"
Answer: e
Problem: average age of students of an adult school is 48 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
Options: a ) 1200 , b ) 160 , c ) 360 , d ) 240 , e ) none of these
Rationale: explanation : let the original no . of students be x . according to situation , 48 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 40 so , required no . of students after joining the new students = x + 120 = 160 . answer : b
Answer: b
Problem: if 9 - 4 / x = 7 + 8 / x , then x =
Options: a ) 15 , b ) 6 , c ) 1 , d ) 5 , e ) 12
Rationale: we ' re given the equation 9 - 4 / x = 7 + 8 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we have to multiple 2 of the numbers to give them that denominator . . . 9 x - 4 x / x = 7 x + 8 x / x we can then eliminate that denominator , which gives us . . . . 9 x - 4 = 7 x + 8 12 = 2 x both 2 x and 12 have a common denominator of 2 , so we divide both sides by 2 for our final answer . . . 6 = x b
Answer: b
Problem: calculate the circumference of a circular field whose radius is 4 centimeters .
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "circumference c is given by c = 2 ï € r = 2 ï € * 4 = 8 ï € cm correct answer d"
Answer: d
Problem: it costs $ 4 for the first 1 / 4 hour to use the laundry machine at the laundromat . after the first ¼ hour it costs $ 12 per hour . if a certain customer uses the laundry machine for 3 hours and 25 minutes , how much will it cost him ?
Options: a ) $ 25 , b ) $ 32 , c ) $ 36 , d ) $ 40 . , e ) $ 42 .
Rationale: "3 hrs 25 min = 205 min first 15 min - - - - - - > $ 4 time left is 190 min . . . now , 60 min costs $ 12 1 min costs $ 12 / 60 190 min costs $ 12 / 60 * 190 = > $ 38 so , total cost will be $ 38 + $ 4 = > $ 42 hene answer will be ( e ) $ 42"
Answer: e
Problem: the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 637 , krishan has ?
Options: a ) s . 2890 , b ) s . 2330 , c ) s . 3757 , d ) s . 1620 , e ) s . 2680
Rationale: "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 637 : n & there n = 289 x 637 / 49 = rs . 3757 answer : c"
Answer: c
Problem: last week david spent 40 percent of his wages on recreation . this week , his wages are 5 percent less than last week ʼ s wages and he spent 50 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week
Options: a ) 118.75 % , b ) 128.75 % , c ) 116.75 % , d ) 117.75 % , e ) 114.75 %
Rationale: say david ' s wages last week were $ 100 , so he spent 0.40 * 100 = $ 40 on recreation ; this week ' s wages is 0.95 * 100 = $ 95 , so he spends 0.5 * 95 = $ 47.5 on recreation ; 47.5 / 40 = 1.1875 , hence the amount he spends on recreation this week is 118.75 % of the amount he spent on recreation last week : 40 * 1.1875 = 47.5 answer : a
Answer: a
Problem: the data a and b are equal to the data subtracted c ; the data b is 3 times the data a ; if the data a is equal to 12 what is the sum of the data a , b and c ?
Options: a ) 86 , b ) 92 , c ) 84 , d ) 102 , e ) 96
Rationale: the equations raised . a + b = c b = 3 a a = 12 then b = 36 and c = 48 a + b + c = 96 answer : e
Answer: e
Problem: the population of a town is 30000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 4300 , b ) 19200 , c ) 5120 , d ) 5230 , e ) 5366
Rationale: "30000 × 80 / 100 × 80 / 100 = 19200 answer ; b"
Answer: b
Problem: a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 150 more than a :
Options: a ) 2348 , b ) 7250 , c ) 4350 , d ) 1998 , e ) 2771
Rationale: "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 150 total earning = \ inline \ frac { 58 xy } { 100 } = 4350 answer : c ) rs . 4350"
Answer: c
Problem: a man can row downstream at 18 kmph and upstream at 6 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 9
Rationale: let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 6 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 24 = > x = 12 , y = 6 . answer : c
Answer: c
Problem: the ratio of 3 numbers is 1 : 2 : 4 and the sum of their squares is 1701 . the sum of the numbers is ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9
Rationale: let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 1701 21 x ^ 2 = 1701 x ^ 2 = 81 x = 9 answer is e
Answer: e
Problem: a lady builds 10 cm length , 18 cm width , and 4 cm height box using 12 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 107 , b ) 70 , c ) 78 , d ) 60 , e ) 111
Rationale: "number of cubes required = volume of box / volume of cube = 10 * 18 * 4 / 12 = 60 cubes answer : d"
Answer: d
Problem: the sum of the first 80 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ?
Options: a ) 5,050 , b ) 7,500 , c ) 10,500 , d ) 15,000 , e ) 19,600
Rationale: "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 80 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 80 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 80 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 8000 + 2500 = 10500 c is the answer ."
Answer: c
Problem: a 300 m long train crosses a platform in 45 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 287 , b ) 350 , c ) 828 , d ) 450 , e ) 122
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 45 = 50 / 3 3 x + 900 = 2250 = > x = 450 m . answer : d"
Answer: d
Problem: in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 10 and the other one , that is cheaper , costs $ 3.5 . the factory holds a $ 45 worth stock of 11 modules . how many of the modules in the stock are of the cheaper kind ?
Options: a ) 30 , b ) 28 , c ) 25 , d ) 20 , e ) 10
Rationale: so the number of $ 3.50 modules must be 10 so that the leftover 1 modules are of $ 10 which will give a total value $ 45 . 10 * 3.50 + 1 * 10 = 35 + 10 = 45 answer : e
Answer: e
Problem: the average salary of all the workers in a workshop is rs . 10000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 8000 . the total number of workers in the workshop is :
Options: a ) 14 , b ) 21 , c ) 88 , d ) 37 , e ) 29
Rationale: "explanation : lot the total number of workers be v then , 10000 v = ( 12000 * 7 ) + 8000 ( v - 7 ) < = > 2000 v = 28000 < = > v = 14 answer : a ) 14"
Answer: a
Problem: a salt manufacturing company produced a total of 4000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?
Options: a ) 140 , b ) 149 , c ) 156 , d ) 195 , e ) 100
Rationale: "total production of salt by the company in that year = 4000 + 4100 + 4200 + . . . . + 5100 = 54600 . average monthly production of salt for that year = 54600 / 365 â ‰ ˆ 149 answer : b"
Answer: b
Problem: a little girl is numbering her collection of butterflies by placing single - digit stickers under each specimen . if the girl has 330 butterflies , how many stickers does she need ? ( the numbers are consecutive and the number of the first butterfly is 1 ) .
Options: a ) 882 , b ) 901 , c ) 1001 , d ) 1003 , e ) 1346
Rationale: for the first 9 butterflies we need 9 stickers . for the next 90 we need 2 stickers each or 180 stickers . for the next 900 butterflies we need 3 stickers each . the first 99 butterflies correspond to 189 stickers . subtract 99 from the total number of butterflies ( 330 ) . this leaves 231 butterflies that use 3 stickers each . so , multiply 231 by 3 to get 693 . add 693 to 189 stickers to get 882 stickers . answer : a
Answer: a
Problem: a batsman in his 17 th innings makes a score of 80 , and thereby increases his average by 2 . what is his average after the 17 th innings ? he had never been ’ not out ’ .
Options: a ) 48 , b ) 37 , c ) 39 , d ) 43 , e ) 42
Rationale: "average score before 17 th innings = 80 - 2 × 17 = 46 average score after 17 th innings = > 46 + 2 = 48 answer : a"
Answer: a
Problem: 19 times a number gives 342 . the number is
Options: a ) 18 , b ) 19 , c ) 16 , d ) none , e ) can not be determined
Rationale: "explanation : let the number be ' n ' 19 × n = 342 ⇒ n = 18 correct option : a"
Answer: a
Problem: 1.45 , 2.56 , 4.78 , 8.11 , 12.55 , ( . . . . )
Options: a ) 17.3 , b ) 16.2 , c ) 15.3 , d ) 19.5 , e ) 18.1
Rationale: "explanation : 1.11 , 2.22 , 3.33 , 4.44 , 5.55 , hence 5.55 = 18.1 answer : e"
Answer: e
Problem: how many positive integers less than 1000 are multiples of 5 but not of 4 or 7 ?
Options: a ) 114 , b ) 121 , c ) 122 , d ) 129 , e ) 136
Rationale: "there are 1000 / 5 = 200 multiples of 5 . now we have to find the number of multiples of 5 and 4 that is 20 between 0 to 1000 and 5 and 7 that is 35 between 0 to 1000 . multiples of 20 = 1000 / 20 = 50 multiples . and multiples of 35 = 1000 / 35 = 28.5 so 28 multiples of 35 . so multiples of 5 between o to 1000 not including multiples of 20 and 35 are equal to 200 - 78 = 122 multiples . so the answer is c ."
Answer: c
Problem: a trader bought a car at 20 % discount on its original price . he sold it at a 45 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) a ) 10 % , b ) b ) 12 % , c ) c ) 16 % , d ) d ) 20 % , e ) e ) 22 %
Rationale: "original price = 100 cp = 80 s = 80 * ( 145 / 100 ) = 116 100 - 116 = 16 % c )"
Answer: c
Problem: the diagonal of the floor of a rectangular closet is 7 feet . the shorter side of the closet is 4 feet . what is the area of the closet in square feet ?
Options: a ) 20 sq . ft
b ) 27 sq . ft
c ) 37 sq . ft
d ) 47 sq . ft
e ) 57 sq . ft
Rationale: other side = 15 2 - 9 2 2 2 ft = 225 - 81 4 4 ft = 144 4 ft = 6 ft . area of closet = ( 6 x 4.5 ) sq . ft = 27 sq . ft . b )
Answer: b
Problem: whats the reminder when 445876 , 985420 , 215546 , 656452 is divided by 8
Options: a ) 1 , b ) 7 . , c ) 4 , d ) 3 , e ) 9
Rationale: a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . a number ending in 3 zeroes is divisible by 8 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 445876 , 985420 , 215546 , 656452 = 445876 , 985420 , 215546 , 656000 + 452 the first number is divisible by 8 . you just have to find the remainder when you divide 452 by 8 . that will be the remainder when you divide the original number by 8 . 452 / 8 gives remainder 4 . answer ( c )
Answer: c
Problem: each day a man meets his wife at the train station after work , and then she drives him home . she always arrives exactly on time to pick him up . one day he catches an earlier train and arrives at the station an hour early . he immediately begins walking home along the same route the wife drives . eventually his wife sees him on her way to the station and drives him the rest of the way home . when they arrive home the man notices that they arrived 10 minutes earlier than usual . how much time did the man spend walking ?
Options: a ) 45 minutes , b ) 50 minutes , c ) 55 minutes , d ) 52 minutes , e ) 35 minutes
Rationale: as they arrived 10 minutes earlier than usual , they saved 10 minutes on round trip from home to station ( home - station - home ) - - > 5 minutes in each direction ( home - station ) - - > wife meets husband 5 minutes earlier the usual meeting time - - > husband arrived an hour earlier the usual meeting time , so he must have spent waking the rest of the time before their meeting , which is hour - 5 minutes = 55 minutes . answer : c
Answer: c
Problem: in what time will a railway train 75 m long moving at the rate of 50 kmph pass a telegraph post on its way ?
Options: a ) 3 , b ) 5.4 , c ) 4.3 , d ) 6.5 , e ) 7
Rationale: "t = 75 / 50 * 18 / 5 = 5.4 sec answer : b"
Answer: b
Problem: in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 27 to the thrice of the remainder . the dividend is
Options: a ) 74 , b ) 78 , c ) 186 , d ) 92 , e ) 98
Rationale: "divisor = ( 6 * 3 ) + 27 = 45 5 * quotient = 45 quotient = 9 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 9 ) + 6 = 186 . c )"
Answer: c
Problem: the sum of two numbers is 64 , and one of them is 12 more than the other . what are the two numbers ?
Options: a ) 26 - 38 , b ) 50 - 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 64 : word problem = 64 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 64 â ˆ ’ 12 = 52 . x = 52 / 2 = 26 . this is the first number . therefore the other number is x + 12 = 26 + 12 = 38 . the sum of 26 + 38 is 64 . a"
Answer: a
Problem: two whole numbers whose sum is 36 can not be in the ratio
Options: a ) 2 : 4 , b ) 3 : 4 , c ) 3 : 6 , d ) 1 : 3 , e ) 3 : 36
Rationale: b ) 3 : 4
Answer: b
Problem: if x ⁄ 2 + 3 ⁄ 4 = 9 ⁄ 4 , what is the value of x ?
Options: a ) – 2 , b ) – 1 , c ) 1 , d ) 3 , e ) 5
Rationale: "x ⁄ 2 + 3 ⁄ 4 = 9 ⁄ 4 let ' s multiply both sides by 4 . 2 x + 3 = 9 2 x = 6 x = 3 the answer is d ."
Answer: d
Problem: a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) none
Rationale: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then ‹ = › ( x + 24 ) + 2 = 2 ( x + 2 ) ‹ = › x + 26 = 2 x + 4 x = 22 . answer d"
Answer: d
Problem: two mechanics were working on your car . one can complete the given job in 4 hours , but the new guy takes eight hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ?
Options: a ) 2 , b ) 4 / 3 , c ) 15 / 4 , d ) 10 / 3 , e ) 17 / 5
Rationale: "rate ( 1 ) = 1 / 4 rate ( 2 ) = 1 / 8 combined = 3 / 8 work done in 2 days = 3 / 4 work left = 1 / 4 rate * time = work left 1 / 8 * time = 1 / 4 time = 2 a"
Answer: a
Problem: yearly subscription to professional magazines cost a company $ 940.00 . to make a 30 % cut in the magazine budget , how much less must be spent ?
Options: a ) 654 , b ) 655 , c ) 656 , d ) 657 , e ) 658
Rationale: "total cost 940 940 * 30 / 100 = 282 so the cut in amount is 282 the less amount to be spend is 940 - 282 = 658 answer : e"
Answer: e
Problem: water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 9 meters . what is value of the radius in meters ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1.5 , d ) 3 , e ) 6
Rationale: 10 * 0.31 = 3.1 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 9 ) which is about 1 / 9 r = 1 / 3 the answer is b .
Answer: b
Problem: what is 10 - 8 + 6 - 4 + . . . + ( - 16 ) ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "the expression considers all even numbers between 10 and - 16 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , - 10 , - 12 , - 14 , and - 16 . now , the first term is positive and the next term is subtracted . so , the required expression becomes , 10 - 8 + 6 - 4 + 2 - 0 + ( - 2 ) - ( - 4 ) + ( - 6 ) - ( - 8 ) + ( - 10 ) - ( - 12 ) + ( - 14 ) - ( - 16 ) = 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 = 58 - 44 = 14 hence the correct answer choice is d ."
Answer: d
Problem: how many 7 in between 1 to 90 ?
Options: a ) 19 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78 , 79,87 , 19 7 ' s between 1 to 90 answer : a"
Answer: a
Problem: for a race a distance of 224 meters can be covered by p in 16 seconds and q in 32 seconds . by what distance does p defeat q eventually ?
Options: a ) 232 m , b ) 238 m , c ) 224 m , d ) 331 m , e ) 236 m
Rationale: "explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 16 = 14 m / s = > speed of q = 224 / 32 = 7 m / s = > difference in time taken = 16 seconds therefore , distance covered by p in that time = 14 m / s x 16 seconds = 224 metres answer : c"
Answer: c
Problem: a merchant has selected two items to be placed on sale , one of which currently sells for 25 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ?
Options: a ) 52 % , b ) 40 % , c ) 30 % , d ) 20 % , e ) 10 %
Rationale: "expensive item = $ 100 ; cheap item = $ 75 ; we must increase $ 75 to $ 100 , so by $ 25 , which is approximately 30 % increase : ( 100 - 75 ) / 75 = 1 / 3 = ~ 0.33 answer : c ."
Answer: c
Problem: if the wheel is 15 cm then the number of revolutions to cover a distance of 1540 cm is ?
Options: a ) 11 , b ) 14 , c ) 18 , d ) 12 , e ) 16
Rationale: "2 * 22 / 7 * 15 * x = 1540 = > x = 16 answer : e"
Answer: e
Problem: you enter a weight loss challenge game and manage to lose 14 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
Options: a ) 13 % , b ) 9.22 % , c ) 9 % , d ) 14 % , e ) 12.28 %
Rationale: "( 100 % - 14 % ) * ( 100 % + 2 % ) = 0.86 * 1.02 = 12.28 % the weigh in records your weight loss at 12.28 % ! the answer is e"
Answer: e
Problem: in what proportion must flour at $ 0.8 per pound be mixed with flour at $ 0.9 per pound so that the mixture costs $ 0.865 per pound ?
Options: a ) 1 : 3 , b ) 1 : 2 , c ) 1 : 1 , d ) 2 : 1 , e ) 3 : 1
Rationale: using weighted average method : let x be the proportion in which the $ 0.8 per pound flour is mixed with $ 0.9 per pound flour . thus 0.8 * x + 0.9 * ( 1 - x ) = 0.865 0.9 – 0.1 x = 0.865 x = 0.35 thus ratio of both flours is 1 : 2 b
Answer: b
Problem: a rectangular block 12 cm by 20 cm by 36 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 135 , b ) 10 , c ) 15 , d ) 40 , e ) 22
Rationale: "volume of the block = 12 * 20 * 36 = 8640 cm ^ 3 side of the largest cube = h . c . f of 12 , 20,36 = 4 cm volume of the cube = 4 * 4 * 4 = 64 cm ^ 3 number of cubes = 8640 / 64 = 135 answer is a"
Answer: a
Problem: the average of 45 results is 10 . the average of first 22 of them is 16 and that of last 22 is 20 . find the 23 result ?
Options: a ) 600 , b ) 480 , c ) 538 , d ) 650 , e ) 560
Rationale: "23 th result = sum of 45 results - sum of 44 results 10 * 45 - 16 * 22 + 20 * 22 = 450 - 352 + 440 = 538 answer is c"
Answer: c
Problem: an escalator moves towards the top level at the rate of 15 ft . sec and its length is 200 feet . if a person walks on the moving escalator at the rate of 5 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 5 sec , b ) 10 sec , c ) 20 sec , d ) 15 sec , e ) 25 sec
Rationale: "explanation : time taken to cover the entire length = tot . dist / resultant speed = 200 / ( 15 + 5 ) = 10 sec answer : b"
Answer: b
Problem: 4 barrels of water have an average capacity of 8 gallons . what is the maximum possible capacity of the smallest barrel e if the median is 10 gallons ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: suppose 4 barrels are b 1 , b 2 , b 3 , b 4 in ascending capacity . ( b 1 + b 2 + b 3 + b 4 ) / 4 = 8 b 1 + b 2 + b 3 + b 4 = 32 median is 10 . . . . . . . as the no . of terms are even i . e 4 , median = ( b 2 + b 3 ) / 2 = = > b 2 + b 3 = 20 now we have b 1 + b 4 = 32 - 20 = 12 only the following possible cases can be there : 19 , 1111 110 , 1011 210 , 1010 max value of smallest barrel e = 2 = b
Answer: b
Problem: the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1200 , then what is the income of p 1 ?
Options: a ) s . 800 , b ) s . 2400 , c ) s . 3000 , d ) s . 3200 , e ) s . 4200
Rationale: "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x – 3 y = 1200 … ( i ) and 4 x – 2 y = 1200 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1200 - > x = 600 p 1 ’ s income = rs 5 * 600 = rs . 3000 answer : c"
Answer: c
Problem: in a two - digit number , if it is known that its unit ' s digit exceeds its 10 ' s digit by 2 and that the product of the given number and the sum of its digits is equal to 144 , then the number is :
Options: a ) 24 , b ) 26 , c ) 42 , d ) 46 , e ) 48
Rationale: let the ten ' s digit be x . then , unit ' s digit = x + 2 . number = 10 x + ( x + 2 ) = 11 x + 2 sum of digits = x + ( x + 2 ) = 2 x + 2 ( 11 x + 2 ) ( 2 x + 2 ) = 144 2 x 2 + 26 x - 140 = 0 ( x - 2 ) ( 11 x + 35 ) = 0 x = 2 hence , required number = 11 x + 2 = 24 . answer : a
Answer: a
Problem: what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 70 ?
Options: a ) 120 , b ) 140 , c ) 130 , d ) 150 , e ) 160
Rationale: "put in simple words , we need to find the highest power of 2 in 100 ^ 70 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 70 = ( 2 ^ 2 * 5 ^ 2 ) ^ 70 = 2 ^ 140 * 5 ^ 140 answer : b"
Answer: b
Problem: a certain box has 12 cards and each card has one of the integers from 1 to 12 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 12 cards ?
Options: a ) 1 / 11 , b ) 2 / 23 , c ) 3 / 34 , d ) 4 / 45 , e ) 5 / 56
Rationale: "the average of the numbers is 6.5 the total number of ways to choose 2 cards from 12 cards is 12 c 2 = 66 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } , { 1,4 } , { 1,5 } , { 2,3 } , { 2,4 } the probability is 6 / 66 = 1 / 11 the answer is a ."
Answer: a
Problem: the average of first five multiples of 4 is ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 5 , e ) 12
Rationale: "average = 4 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 60 / 5 = 12 . answer : e"
Answer: e
Problem: priya takes a trip and drives 5 hours from town x to town z at a rate of 50 miles per hour . on her way back , priya drives 60 miles per hour and stops in town y which is midway between town x and town z . how many hours does it take scott to drive from town z to town y ?
Options: a ) 3.0 , b ) 2.25 , c ) 2.08 , d ) 1.75 , e ) 2.0
Rationale: distance from x to z = 5 hr * 50 mph = 250 miles hence distance from y to z = 1 / 2 * 250 = 125 time = 125 / 60 = 2.08 hrs imo : c
Answer: c
Problem: in a ratio which is equal to 4 : 6 , if the antecedent is 50 , then the consequent is ?
Options: a ) 75 , b ) 85 , c ) 64 , d ) 51 , e ) 45
Rationale: we have 4 / 6 = 50 / x 4 x = 50 * 6 x = 75 consequent = 75 answer is a
Answer: a
Problem: shekar scored 76 , 65 , 82 , 67 and 85 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 90
Rationale: "explanation : average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 hence average = 75 answer : c"
Answer: c
Problem: an escalator moves towards the top level at the rate of 12 ft . sec and its length is 210 feet . if a person walks on the moving escalator at the rate of 2 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 15 sec , b ) 10 sec , c ) 12 sec , d ) 8 sec , e ) 9 sec
Rationale: "time taken to cover the entire length = tot . dist / resultant speed = 210 / ( 12 + 2 ) = 15 sec answer : a"
Answer: a
Problem: two employees x and y are paid a total of rs . 800 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 200.63 , b ) s . 250.63 , c ) s . 290.63 , d ) s . 300.63 , e ) s . 363.63
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 800 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 800 ⇒ y [ 12 / 10 + 1 ] = 800 ⇒ 22 y / 10 = 800 ⇒ 22 y = 8000 ⇒ y = 8000 / 22 = rs . 363.63 e )"
Answer: e
Problem: elena ’ s bread recipe calls for 5 ounces of butter for each 7 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 28
Rationale: solving through algebra route : 5 b + 7 f = x amount if we multiply this equation with 4 we get : 20 b + 28 f = 4 x therefore , we got 20 ounces of butter and 4 x amount of quantity when we use 28 ounces of floor . ans : e
Answer: e
Problem: tom left a job paying $ 75000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission . if each of his sales is for $ 750 , what is the least number of sales he must make per year if he is not to lose money because of the change ?
Options: a ) 40 , b ) 200 , c ) 266 , d ) 267 , e ) 600
Rationale: in order not to lose money because of the change tom ' s total commission must beat least $ 75000 - $ 45000 = $ 30000 , so total sales must beat least $ 30000 / 0.15 = $ 200000 . which means that he must makeat least $ 200000 / 750 = 800 / 3 = 266.6 sales , so 267 sales . answer : d .
Answer: d
Problem: there are 192 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ?
Options: a ) 72 , b ) 85 , c ) 107 , d ) 98 , e ) 108
Rationale: "you had the answer almost right . the x = 84 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 84 + set ab = 84 + 23 = 17 c"
Answer: c
Problem: a family travelled for 12 hours . they covered the first half of the distance at 35 kmph and remaining half of the distance at 40 kmph . find the distance travelled by the family ?
Options: a ) 270 km , b ) 890 km , c ) 684 km , d ) 320 km , e ) 560 km
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 35 + ( x / 2 ) / 40 = 12 = > x / 70 + x / 80 = 12 = > ( 8 x + 7 x ) / 560 = 12 = > x = 560 km answer : e
Answer: e
Problem: of the 250 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 100 answer : option e"
Answer: e
Problem: the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 360 . find the principal ?
Options: a ) 2277 , b ) 2667 , c ) 9000 , d ) 2766 , e ) 1811
Rationale: "p = 360 ( 100 / 5 ) ^ 2 = > p = 9000 answer : c"
Answer: c