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Question: a box contains 11 apples , 10 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
A.3.
B.4.
C.5.
D.6.
e ) 7D.
p ( choosing a red apple 6 times in a row ) = 10 / 11 * 9 / 10 * 8 / 9 * 7 / 8 * 6 / 7 * 5 / 6 = 5 / 11 < 0.5 the answer is d . | null |
Question: bob wants to run a mile in the same time as his sister . if bob ’ s time for a mile is currently 11 minutes 20 seconds and his sister ’ s time is currently 9 minutes 36 seconds , by what percent does bob need to improve his time in order run a mile in the same time as his sister ?
A.3 %.
B.5 %.
C.8 %.
D.10 %.
e ) 15 %E.
"bob ' s time = 680 secs . his sis ' time = 576 secs . percent increase needed = ( 680 - 576 / 680 ) * 100 = 104 / 640 * 100 = 15 % . ans ( e ) ." | null |
Question: if the price of a certain computer increased 30 percent from x dollars to 351 dollars , then 2 x =
A.540.
B.570.
C.619.
D.649.
e ) 700A.
"before price increase price = x after 30 % price increase price = x + ( 30 / 100 ) * x = 1.3 x = 351 ( given ) i . e . x = 351 / 1.3 = $ 270 i . e . 2 x = 2 * 270 = 540 answer : option a" | null |
Question: in the mundane goblet competition , 6 teams compete in a “ round robin ” format : that is , each team plays every other team exactly once . a team gets 3 points for a win , 1 point for a tie ( a draw ) , and 0 points for a loss . what is the difference between the maximum total points and the minimum total points that can be gained by all teams ( added together ) in the mundane goblet competition ?
A.15.
B.30.
C.45.
D.60.
e ) 75A.
no oa yet : my method : max points : a b c d e f 15 12 9 6 3 0 = 45 points min points a b c d e f 5 5 5 5 5 5 = 30 45 - 30 = 15 points = = = = > ( a ) ans | null |
Question: how many integers between 324,805 and 458,705 have tens digit 2 and units digit 3 ?
A.1,352.
B.1,359.
C.1,329.
D.1,349.
e ) 1,348D.
"there is one number in hundred with 2 in the tens digit and 3 in the units digit : 23 , 123 , 223 , 323 , . . . the difference between 324,700 and 458,600 is 458,600 - 324,700 = 134,900 - one number per each hundred gives 133,900 / 100 = 1,349 numbers . answer : d ." | null |
Question: a can do a job in 15 days and b in 20 days . if they work on it together for 4 days , then the fraction of the work that is left is ?
A.2 / 15.
B.8 / 15.
C.3 / 11.
D.1 / 12.
e ) 6 / 13B.
"a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 15 + 1 / 20 = 7 / 60 a + b 4 days work = 7 / 60 * 4 = 7 / 15 remaining work = 1 - 7 / 15 = 8 / 15 answer is b" | null |
Question: diana is painting statues . she has 3 / 6 of a gallon of paint remaining . each statue requires 1 / 6 gallon of paint . how many statues can she paint ?
A.3.
B.20.
C.28.
D.14.
e ) 19A.
"number of statues = all the paint ÷ amount used per statue = 3 / 6 ÷ 1 / 6 = 3 / 6 * 6 / 1 = 3 / 1 = 3 answer is a ." | null |
Question: what is the units digit of ( 6 ! * 4 ! + 6 ! * 5 ! ) / 12 ?
A.0.
B.3.
C.2.
D.1.
e ) 4A.
"( 6 ! * 4 ! + 6 ! * 5 ! ) / 12 = 6 ! ( 4 ! + 5 ! ) / 12 = 720 ( 24 + 120 ) / 12 = ( 720 * 144 ) / 12 = 720 * 12 units digit of the above product will be equal to 0 answer a" | null |
Question: jack and christina are standing 240 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 5 feet per second and christina walks in a straight line toward jack at a constant speed of 3 feet per second . lindy runs at a constant speed of 9 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
A.180.
B.210.
C.240.
D.270.
e ) 300D.
the relative speed of jack and christina is 5 + 3 = 8 feet per second . the distance between them is 240 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 240 / 8 = 30 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 9 * 30 = 270 feet . answer : d . | null |
Question: a slot machine in a las vegas casino has an average profit of $ 600 for each 8 - hour shift for the 5 days sunday through thursday , inclusive . if the average per - shift profit on friday and saturday is 25 % greater than on the other days of the week and the slot machine is in operation every hour of every day , what is the total weekly profit that the casino makes from the slot machine ?
A.a - 4500.
B.b - 9000.
C.c - 13500.
D.d - 15500.
e ) e - 27000C.
correct answer is c - 13500 . total profit per weekday = $ 600 x 3 ( shifts ) = $ 1800 total profit per week ( apart from saturdaysunday ) = $ 1800 x 5 = $ 9000 total profit per shift on weekends = $ 600 x 125 / 100 = $ 750 total profit on weekends = $ 750 x 3 ( shifts ) x 2 ( saturday , sunday ) = $ 4500 . hence the answer is - $ 4500 + $ 9000 = $ 13500 . ( c ) | null |
Question: if the price of a certain bond on may 1 st was 3 / 4 the price of the bond on june 1 st and the price of the bond on july 1 st was 25 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
A.50 %.
B.75 %.
C.118.5 %.
D.133 1 / 3 %.
e ) 150 %C.
"the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 3 / 4 * 12 = 9 ; the price on july 1 st = 9 * 1.25 = 11.25 . the average price of the bond on may 1 st and july 1 st = ( 9 + 11.25 ) / 2 = 10.125 . the price of the bond on june 1 st ( 12 ) is 32 / 27 times ( 118.5 % ) the average price of the bond on may 1 st and july 1 st . answer : c ." | null |
Question: the average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .
A.47.55 kg.
B.48 kg.
C.48.55 kg.
D.49.25 kg.
e ) 59.25 kgC.
"16 * 50.25 + 8 * 45.15 / 24 = 48.55 answer : c" | null |
Question: how much water should be added to 13 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
A.25 liters.
B.27 liters.
C.30 liters.
D.32 liters.
e ) 35 litersB.
"let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 13 + x ) ) ) 2 = 5 % * ( 13 + x ) - - - - - - - - > x = 27 ans b" | null |
Question: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 40 .
A.3.
B.4.
C.7.
D.32.
e ) 35C.
"first , let us say i have a number n which is divisible by 5 and by 7 . we all agree that it will be divisible by 35 , the lcm of 5 and 7 . now , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1 , we can say the number is of the form n = 5 a + 1 e . g . 5 + 1 , 10 + 1 , 15 + 1 , 20 + 1 , 25 + 1 , 30 + 1 , 35 + 1 etc and n = 7 b + 1 e . g . 7 + 1 , 14 + 1 , 21 + 1 , 28 + 1 , 35 + 1 etc so when it is divided by the lcm , 35 , it will give 1 as remainder ( as is apparent above ) next , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3 , we can say the number is of the form n = 5 a + 1 and n = 7 b + 3 now , the only thing you should try to understand here is that when n is divided by 5 and if i say the remainder is 1 , it is the same as saying the remainder is - 4 . e . g . when 6 is divided by 5 , remainder is 1 because it is 1 more than a multiple of 5 . i can also say it is 4 less than the next multiple of 5 , ca n ' t i ? 6 is one more than 5 , but 4 less than 10 . therefore , we can say n = 5 x - 4 and n = 7 y - 4 ( a remainder of 3 when divided by 7 is the same as getting a remainder of - 4 ) now this question is exactly like the question above . so when you divide n by 40 , remainder will be - 4 i . e . n will be 4 less than a multiple of 40 . so you must add 7 to n to make it a multiple of 40 c" | null |
Question: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.7 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :
A.2 : 5.
B.2 : 3.
C.2 : 4.
D.2 : 1.
e ) 4 : 9E.
"let the ratio be k : 1 . then , k * 16.7 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.7 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.9 = 4 / 9 required ratio = 4 / 9 : 1 = 4 : 9 . answer : e" | null |
Question: what is the hcf of 2 / 3 , 4 / 10 and 6 / 5
A.7 / 45.
B.1 / 15.
C.4 / 15.
D.8 / 45.
e ) 9 / 45B.
"explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 10 , 5 ) = 2 / 30 = 1 / 15 answer : option b" | null |
Question: at veridux corporation , there are 215 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ?
A.50.
B.20.
C.25.
D.30.
e ) 35A.
"well , first let â € ™ s take care of the â € œ totals â € . the numbers in the â € œ totals â € row must add up . if 90 are females , the other 215 â € “ 90 = 125 must be males . similarly , the numbers in the â € œ totals â € column must add up . if 40 are managers , then the other 215 â € “ 40 = 175 must be associates . now , in the â € œ associate â € row , 135 + e = 175 , which means e = 40 â € ” the other 40 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the â € œ female â € column : b + 40 = 90 , which means b = 50 . there are fifteen female managers in this company . thus , the answer = 50 ( a ) ." | null |
Question: a number when divided by a divisor leaves a remainder of 30 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
A.12.
B.13.
C.35.
D.43.
e ) 59D.
let the number is n , the divisor = d , i will make the two equations - n = xd + 30 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 43 as d is also integer and 43 is a prime number , the d should be 43 to satisfy the above equation . hence answer is ' d ' | null |
Question: a student got twice as many sums wrong as he got right . if he attempted 36 sums in all , how many did he solve correctly ?
A.12.
B.16.
C.18.
D.24.
e ) 26A.
"explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 36 3 x = 36 x = 12 . answer : a" | null |
Question: if 6 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ?
A.- 7.
B.- 4.
C.- 3.
D.- 9.
e ) 6D.
the phrase “ 6 is one solution of the equation ” means that one value of x is 6 . thus , we first must plug 6 for x into the given equation to determine the value of k . so we have 6 ^ 2 + ( 3 ) ( 6 ) + k = 10 36 + 18 + k = 10 54 + k = 10 k = - 44 next we plug - 44 into the given equation for k and then solve for x . x ^ 2 + 3 x – 44 = 10 x ^ 2 + 3 x – 54 = 0 ( x + 9 ) ( x - 6 ) = 0 x = - 9 or x = 6 thus , - 9 is the other solution . answer d . | null |
Question: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 8 ounces of corn syrup , how many ounces of water does it contain ?
A.45.
B.50.
C.55.
D.60.
e ) 120E.
"f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 8 * 180 / 12 = 120 ounces of water e" | null |
Question: in a certain large company , the ratio of college graduates with a graduate degree to non - college graduates is 1 : 8 , and ratio of college graduates without a graduate degree to non - college graduates is 2 : 3 . if one picks a random college graduate at this large company , what is the probability q this college graduate has a graduate degree ?
A.1 / 11.
B.1 / 12.
C.1 / 13.
D.3 / 19.
e ) 3 / 43D.
"in believe the answer is d . please see below for explanation . 0 ) we are told the following ratios cgd - college graduate with degree ncg - non college graduate cgn - college graduate no degree cgd ncg cgn 1 8 3 2 in order to make cgd and cgn comparable we need to find the least common multiple of 8 and 3 and that is 24 multiplying the first ratio by 3 and the second ratio by 8 we get cgd ncg cgn 3 24 16 if one picks a random college graduate at this large company , what is the probability this college graduate has a graduate degree ? nr of cgd = 3 nr of cg = 3 + 16 = 19 probability of cgd / ( cg ) q - > 3 / 19 answer d" | null |
Question: in the youth summer village there are 125 people , 50 of them are not working , 25 of them have families and 75 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?
A.75.
B.80.
C.85.
D.100.
e ) 90A.
"total = 125 not working = 50 having family = 25 like to sing in shower = 75 working = 125 - 50 = 75 not having family = 125 - 25 = 100 like to sing in shower = 100 largest possible number is the lowest possible among the above thus 75 a" | null |
Question: solution y is 20 percent liquid x and 80 percent water . if 2 kilograms of water evaporate from 8 kilograms of solution y and 2 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
A.20 %.
B.21 1 / 2 %.
C.22 %.
D.24 %.
e ) 25 %E.
"in 8 kilograms of solution y there are 0.2 * 8 = 1.6 kilograms of solution x ; after 2 kilograms of water are replaced by 2 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.2 * 2 = 0.4 kilograms of solution x are added , so in the new solution of 8 kilograms there are 1.6 + 0.4 = 2 kilograms of solution x , which is 2 / 8 * 100 = 25 % of this new solution . answer : e ." | null |
Question: 20.036 divided by 0.04 gives :
A.50.09.
B.5.06.
C.50.06.
D.100.9.
e ) 500.9E.
"= 20.036 / 0.04 = 2003.6 / 4 = 500.9 answer is e ." | null |
Question: the ratio between the sale price and the cost price of an article is 12 : 7 . what is the ratio between the profit and the cost price of that article ?
A.2 : 9.
B.2 : 5.
C.3 : 6.
D.5 : 7.
e ) 2 : 1D.
"let c . p . = rs . 7 x and s . p . = rs . 12 x . then , gain = rs . 5 x required ratio = 5 x : 7 x = 5 : 7 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 . 6800 ?
A.s . 4991.
B.s . 5991.
C.s . 6001.
D.s . 6791.
e ) s . 7991D.
"total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6800 * 6 ) - 34009 ] = rs . ( 40800 - 34009 ) = rs . 6791 . answer : d" | null |
Question: when 17 is divided by positive integer x , the remainder is 1 . for how many values of x is this true ?
A.1.
B.2.
C.3.
D.4.
e ) 5D.
when 17 is divided by x , the remainder is 1 i . e . 1 orange left over after grouping , so x must be greater than 1 . it also means that 16 is completely divisible by x . factors of 16 are 1 , 2 , 4 , 8 , 16 . out of these , x can be 2 , 4 , 8 , and 16 . answer ( d ) . | null |
Question: sakshi can do a piece of work in 12 days . tanya is 20 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work is ?
A.10.
B.12.
C.14.
D.16.
e ) 18A.
"ratio of times taken by sakshi and tanys = 120 : 100 = 6 : 5 suppose tanya takes x days to do the work . 6 : 5 : : 12 : x = > x = 10 days . hence , tanya takes 10 days to complete the work . answer : a" | null |
Question: a river 4 m deep and 40 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is ?
A.10666.
B.11678.
C.12345.
D.10678.
e ) 19099A.
"( 4000 * 4 * 40 ) / 60 = 10666 m 3 answer : a" | null |
Question: in one hour , a boat goes 11 km along the stream and 5 km against the stream . the speed of the boat in still water is :
A.3.
B.5.
C.8.
D.9.
e ) 10C.
"solution speed in still water = 1 / 2 ( 11 + 5 ) kmph = 8 kmph . answer c" | null |
Question: what least number should be subtracted from 1398 so that the remainder when divided by 7 , 9 , and 11 will leave in each case the same remainder 5 ?
A.6.
B.7.
C.8.
D.10.
e ) 11B.
"the lcm of 7 , 9 , and 11 is 693 . the next multiple is 2 * 693 = 1386 . 1386 + { remainder } = 1386 + 5 = 1391 , which is 7 less than 1398 . answer : b ." | null |
Question: if the sides of a triangle are 32 cm , 27 cm and 12 cm , what is its area ?
A.120 cm 2.
B.112 cm 2.
C.162 cm 2.
D.666 cm 2.
e ) 886 cm 2C.
"the triangle with sides 32 cm , 27 cm and 12 cm is right angled , where the hypotenuse is 32 cm . area of the triangle = 1 / 2 * 27 * 12 = 162 cm 2 answer : c" | null |
Question: 9.99 x 9.9 x 9 ÷ 9.9 ÷ 0.3 = ?
A.276.
B.299.
C.310.
D.3.33.
e ) 365D.
"explanation : ? = ( 9.99 x 9.9 x 9 ) / ( 9.9 x 0.9 x 0.3 ) = 3.33 answer : option d" | null |
Question: a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1233 . find the number to be multiplied .
A.130.
B.132.
C.134.
D.137.
e ) 138D.
"let the required number be x . then , 43 x – 34 x = 1233 or 9 x = 1233 or x = 137 . required number = 137 . answer : d" | null |
Question: two letters from the word barkhint are selected at random . what is the probability that at least one of the selected letters is a consonant ?
A.30 / 28.
B.40 / 28.
C.25 / 28.
D.27 / 28.
e ) 32 / 28D.
there are 6 consonants and 2 vowels in barkhint . probability that at least one of the selected letters is a consonant = 1 - ( probability of both vowels ) probability of both vowels = 2 c 2 / 8 c 2 = 1 / 28 so , answer is 1 - 1 / 28 = 27 / 28 answer : d | null |
Question: if ( a + b ) = 4 , ( b + c ) = 8 and ( c + d ) = 3 , what is the value of ( a + d ) ?
A.16 ..
B.8 ..
C.7 ..
D.2 ..
e ) - 1 .E.
"given a + b = 4 b + c = 8 c + d = 3 then ( a + b ) - ( b + c ) + ( c + d ) = 4 - 8 + 3 = - 1 option e . . ." | null |
Question: ( 69842 x 69842 - 30158 x 30158 ) / ( 69842 - 30158 ) = ?
A.100000.
B.69842.
C.39684.
D.30158.
e ) noneA.
answer given expression = [ ( 69842 ) 2 - ( 30158 ) 2 ] / [ ( 69842 - 30158 ) ] = [ ( 69842 - 30158 ) ( 69842 + 30158 ) ] / ( 60842 - 30158 ) = 100000 correct option : a | null |
Question: two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 6 seconds . the length of the faster train is
A.80 m.
B.100 m.
C.120 m.
D.135 m.
e ) noneD.
"solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 6 ) m = 135 m . answer d" | null |
Question: a train running at the speed of 20 km / hr crosses a post in 10 seconds . what is the length of the train ?
A.150.
B.250.
C.415.
D.200.
e ) 312D.
"speed = ( 20 x 5 / 18 ) = 50 / 9 m / sec . length of the train = ( speed x time ) . length of the train = 50 / 9 x 10 m = 200 m . answer : d" | null |
Question: 8 percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?
A.15 %.
B.20 %.
C.25 %.
D.69 %.
e ) 75 %D.
initially 92 % and 8 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) ∗ 92 so , the required % is [ ( 3 / 4 ) ∗ 92 / 100 ] ∗ 100 = 69 % answer : d | null |
Question: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 20 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
A.80 %.
B.160 %.
C.120 %.
D.124.2 %.
e ) 138 %B.
"0,16 r = x / 100 * 0.1 r answer b" | null |
Question: suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 750 ( before payroll deductions ) ?
A.1600.
B.1625.
C.1650.
D.1655.
e ) 1675B.
"total pay = 40 * $ 12.50 + $ 0.16 * x = 760 x = 260 / 0.16 = 1625 the answer is b ." | null |
Question: 2 pipes can separately fill a tank in 20 hrs and 30 hrs respectively . both the pipes are opened to fillthe tank , a leak develops in the tank through which one - third of water supplied by both the pipes goes out . what is the total time taken to fill the tank ?
A.10 hrs.
B.12 hrs.
C.16 hrs.
D.18 hrs.
e ) 20 hrsC.
1 / 20 + 1 / 30 = 1 / 12 1 + 1 / 3 = 4 / 3 1 - - - 12 4 / 3 - - - ? 4 / 3 * 12 = 16 hrs c | null |
Question: the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 15 . the larger of the two numbers is :
A.276.
B.299.
C.322.
D.345.
e ) 354D.
"clearly , the numbers are ( 23 x 13 ) and ( 23 x 15 ) . larger number = ( 23 x 15 ) = 345 . answer : option d" | null |
Question: an assembly line produces 15 cogs per hour until an initial order of 60 cogs is completed . the speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced . what is the overall average output , in cogs per hour , for the assembly line during this whole time ?
A.20.
B.22.
C.24.
D.26.
e ) 28C.
"the time to produce the first 60 cogs is 60 / 15 = 4 hours . the time to produce the next 60 cogs is 60 / 60 = 1 hour . the average output is 120 cogs / 5 hours = 24 cogs per hour . the answer is c ." | null |
Question: 210 students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
A.25.
B.40.
C.50.
D.60.
e ) 75B.
we are told that 60 students claimed that they preferred mac to windows , which means that 60 preferred mac but not windows , so # of students who preferred mac ( p ( a ) as you wrote ) , does not equal to 60 , it equals to 60 + 20 ( 20 is # of students who equally preferred both brands ) . also we are asked to find # of the students who preferred windows to mac , so if you denote x as those who prefer windows then you should calculate x - 20 . so , if we use your formula it should be : 210 = { mac } + { windows } - { both } + { neither } = ( 60 + 20 ) + x - 20 + 90 - - > x = 60 ( # of student who prefer windows ) - - > # of the students who preferred windows to mac is x - 20 = 40 . | null |
Question: the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 19 - inch screen would be how many square inches greater than the area of a square 17 - inch screen ?
A.36.
B.4.
C.16.
D.38.
e ) 40A.
"pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 19 ^ 2 / 2 - 17 ^ 2 / 2 = 72 / 2 = 36 ans a ." | null |
Question: increasing the original price of a certain item by 20 percent and then increasing the new price by 20 percent is equivalent to increasing the original price by what percent ?
A.31.25.
B.37.5.
C.50.0.
D.52.5.
e ) 44.0E.
"we ' re told that the original price of an item is increased by 20 % and then that price is increased by 20 % . . . . if . . . . starting value = $ 100 + 20 % = 100 + . 20 ( 100 ) = 120 + 20 % = 120 + . 20 ( 120 ) = 120 + 24 = 144 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 44 / 100 = 44 % final answer : e" | null |
Question: the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 63 ounces of this substance ?
A.27.
B.36.
C.42.
D.64.
e ) 147A.
"112 ounces of a substance has a volume of 48 cubic inches 63 ounces of a substance has a volume of ( 48 / 112 ) * 63 = 27 cubic inches answer a alternatively , we can use estimation 112 ounces of a substance has a volume of 48 cubic inches 56 ounces of a substance has a volume of 24 cubic inches therefore , 63 will have a volume a little more than 24 , that is 27 answer : a" | null |
Question: if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 266 m , what is its area ?
A.4290.
B.2535.
C.2530.
D.2515.
e ) 2520A.
"length = breadth + 23 . therefore , 4 × breadth + 2 × 23 = 266 m ⇒ breadth = 55 m length = 55 + 23 = 78 m area = 78 × 55 = 4290 m 2 answer is a ." | null |
Question: the chance of rain on any given day in tel - aviv is 50 % . what is the probability z that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?
A.15 / 64.
B.30 / 64.
C.1 / 2.
D.1 / 4.
e ) 52 / 64A.
"chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days z = 15 / 64 ans a it is ." | null |
Question: if a ^ 2 is divisible by 240 what is the least possible value of integer a ?
A.120.
B.30.
C.90.
D.60.
e ) 12D.
"240 can be written as ( 2 ^ 4 ) * 3 * 5 . for a ^ 2 to be divisible by 240 it should contain at least 2 ^ 4 and 3 and 5 in its factors . we can leave out option e because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 2 will have 2 as the maximum power of 2 , so we can leave out this option too . option d is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 2 = ( 2 ^ 4 ) * ( 3 ^ 2 ) * ( 5 ^ 2 ) . so it shows that 60 ^ 2 is divisible by 240 and hence the answer . answer : d" | null |
Question: little john had $ 7.10 . he spent $ 1.05 on sweets and gave to his two friends $ 1.00 each . how much money was left ?
A.$ 4.85.
B.$ 4.15.
C.$ 4.65.
D.$ 4.55.
e ) $ 4.05E.
"john spent and gave to his two friends a total of 1.05 + 1.00 + 1.00 = $ 3.05 money left 7.10 - 3.05 = $ 4.05 answer : e" | null |
Question: in a class of 32 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
A.3.
B.5.
C.8.
D.11.
e ) 15D.
"total # of students = 32 avg # of books per student = 2 total # of books = 32 * 2 = 64 # of student borrowed at least 3 books = 32 - 2 - 12 - 10 = 8 # of books borrowed by above 8 students = 60 - ( 12 * 1 ) + ( 10 * 2 ) = 32 considering that 7 out of above 8 students borrowed only 3 books , # of books borrowed = 7 * 3 = 21 so maximum # of books borrowed by any single student = 32 - 21 = 11 option d" | null |
Question: the average of 10 numbers is calculated as 21 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
A.A.16.
B.B.18.
C.C.19.
D.D.22.
e ) e ) 24D.
"explanation : 10 * 21 + 36 – 26 = 220 = > 220 / 10 = 22 d )" | null |
Question: - 45 * 29 + 108 = ?
A.1197.
B.1897.
C.- 1197.
D.- 1900.
e ) none of theseC.
"= > - 45 * ( 30 - 1 ) + 108 ; = > - ( 45 * 30 ) + 45 + 108 ; = > - 1350 + 153 = - 1197 . correct option : c" | null |
Question: in a family gathering , there is a basket in which there are oranges , bananas and apples . half of the people in the family eat oranges , half of the other half eat bananas and the rest eat apples . if the number of people who eat oranges are 10 less than the total number of people , find the number of people in the gathering .
A.5.
B.10.
C.15.
D.20.
e ) 25D.
let the number of people who eat oranges be x . then , total number of people = x + ( x / 2 ) + ( x / 2 ) = 2 x = > 2 x - 10 = x = > x = 10 = > total number of people were 2 x = 20 option d | null |
Question: excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 15 km / hr . for how many minutes does the bus stop per hour ?
A.22.
B.88.
C.77.
D.20.
e ) 45E.
"in 1 hr , the bus covers 60 km without stoppages and 15 km with stoppages . stoppage time = time take to travel ( 60 - 15 ) km i . e 45 km at 60 km / hr . stoppage time = 45 / 60 hrs = 45 min . answer : e" | null |
Question: in a garment industry , 12 men working 9 hours per day complete a piece of work in 10 days . to complete the same work in 12 days , working 15 hours a day , the number of men required is :
A.4.
B.5.
C.6.
D.7.
e ) 9D.
"explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 15 : 9 : : 12 : x = > 12 x 15 x x = 10 x 8 x 12 = > x = 10 x 9 x 12 / ( 12 x 15 ) = > x = 7 answer : d" | null |
Question: laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 20 kmph and prasanna moves southward at a speed of 30 kmph . how far will be prasanna from laxmi after 60 minutes ?
A.11.
B.50.
C.28.
D.27.
e ) 18B.
explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 20 kmph x 1 hr = 20 km total southward prasanna ' s distance = 30 kmph x 1 hr = 30 km total distance between prasanna and laxmi is = 20 + 30 = 50 km . answer : b | null |
Question: there is a train and car . the ratio between the speed of a train & a car is 16 : 15 respectively . also , a bus covered a distance of 320 km in 5 hours . the speed of the bus is 4 / 5 th of the speed of the train . how many kilometers will the car cover in 7 hours ?
A.375.
B.425.
C.475.
D.525.
e ) 575D.
the speed of the bus is 320 / 5 = 64 km / hr the speed of the train is ( 64 * 5 ) / 4 = 80 km / hr the speed of the car is 80 / 16 * 15 = 75 km / hr the distance covered by the car in 7 hours is 75 × 7 = 525 km the answer is d . | null |
Question: ( ( ( 13 ! ) ^ 16 ) - ( ( 13 ! ) ^ 8 ) ) / ( ( ( 13 ! ) ^ 8 ) + ( ( 13 ! ) ^ 4 ) ) = a then what is the units digit for a / ( ( 13 ! ) ^ 4 ) =
A.7.
B.8.
C.9.
D.6.
e ) 5C.
( ( ( 13 ! ) ^ 16 ) - ( ( 13 ! ) ^ 8 ) ) / ( ( ( 13 ! ) ^ 8 ) + ( ( 13 ! ) ^ 4 ) ) = a solving it , we get a / ( ( 13 ! ) ^ 4 ) = ( ( 13 ! ) ^ 4 - 1 ) last digit of ( 13 ! ) ^ 4 will be 0 . so last digit of ( ( 13 ! ) ^ 4 - 1 ) will be 9 . answer : c | null |
Question: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6358 , how much amount did raghu invest ?
A.1287.
B.2200.
C.2000.
D.1129.
e ) 1192B.
"let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6358 = x = 6358 / 2.89 = 2200 therefore , amount invested by raghu is rs . 2200 . answer : b" | null |
Question: jacob is 16 years old . he is 2 times as old as his brother . how old will jacob be when he is twice as old ?
A.13.
B.14.
C.15.
D.16.
e ) 24E.
"j = 16 ; j = 2 b ; b = 16 / 2 = 8 ; twice as old so b = 8 ( now ) + ( 8 ) = 16 ; jacob is 16 + 8 = 24 answer : e" | null |
Question: a bag of potatoes weighs 50 lbs divided by half of its weight . how much does the bag of potatoes weigh ?
A.10 lb.
B.20 lb.
C.30 lb.
D.40 lb.
e ) 50 lbA.
"a 10 lb 50 ÷ 5 = 10 ." | null |
Question: in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors a ?
A.2.
B.3.
C.5.
D.6.
e ) 8B.
"i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have a = 2 * 3 * 5 * 7 = 840 thus , answer b" | null |
Question: the payment per hour for a daily - wages employee is increased by 33.33 and the working time is reduced by 33.33 % . what is the percentage change in the employee ' s income ?
A.rs . 0.7889.
B.rs . 0.8889.
C.rs . 0.9889.
D.rs . 1.8889.
e ) rs . 2.8889B.
if payment per hr is increased by 33.33 % , then 11.11 % decrease in income if earlier he is getting rs 1 hr per hr and working for 1 hr , income = rs 1 now he is getting rs 1.3333 per hr and working for 0.66667 hrs , income = rs . 0.8889 answer : b | null |
Question: the sub - duplicate ratio of 16 : 64 is
A.4 : 3.
B.1 : 2.
C.1 : 3.
D.1 : 4.
e ) 2 : 4E.
"root ( 16 ) : root ( 64 ) = 4 : 8 = 2 : 4 answer : e" | null |
Question: there are 38 students in a certain geometry class . if two thirds of the students are boys and 3 fourths of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ?
A.6.
B.12.
C.19.
D.24.
e ) 27C.
38 * 2 / 3 * 3 / 4 = 19 answer : c | null |
Question: a boat crossed a lake from north to east at the speed of 7 km / h , entered a river and covered twice as much distance going upstream at 6 km / h . it then turned around and stopped at the south shore of the lake . if it averaged 3.8 km / h that day , what was its approximate downstream speed ?
A.4.
B.5.
C.6.
D.7.
e ) 8E.
"one way of solving this is : speed of boat on still water ( lake ) = 7 kmph speed upstream = 6 kmph = speed in still water - speed of river = > speed of river = 1 kmph = > speed downstream = speed in still water + speed of river = 7 + 1 = 8 kmph ans is e" | null |
Question: a bullet train 120 m long is running with a speed of 50 kmph . in what time will it pass a man who is running at 4 kmph in the direction opposite to that in which the bullet train is going ?
A.23 sec.
B.15 sec.
C.12 sec.
D.8 sec.
e ) 16 secD.
"d 8 sec speed of the bullet train relative to man = ( 50 + 4 ) kmph = 54 * 5 / 18 m / sec = 45 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 120 m at ( 45 / 3 ) m / sec = ( 120 * 3 / 45 ) sec = 8 sec" | null |
Question: a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 8 is
A.189.
B.197.
C.221.
D.227.
e ) 230A.
"in that case , the sophie prime numbers greater than 8 are 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be a ." | null |
Question: how many digits will be there to the right of the decimal point in the product of 89.635 and . 02218 ?
A.5.
B.6.
C.7.
D.8.
e ) 9C.
"explanation : sum of decimal places = 3 + 5 = 8 the last digit to the extreme right is zero ( since 5 x 8 = 40 ) hence , there will be 7 significant digits to the right of the decimal point . answer : option c" | null |
Question: 70,76 , 74,85 , 90,105 , 105,130 , 130,130 the list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . if the standard deviation of the 10 running times is 22.4 , rounded to the nearest tenth of a second , how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times .
A.1.
B.2.
C.3.
D.4.
e ) 5C.
how many of the 10 running times are more than one sd below the meanmeans how many data points from given 10 are less thanmean - 1 sd . we are given that sd = 22.4 , so we should find mean - - > mean = 100 - - > there are only 3 data points below 100 - 22.4 = 77.6 , namely 70 75 , and 74 . answer : c . | null |
Question: if the cost price of 60 articles is equal to the selling price of 40 articles , then what is the percent profit ?
A.30 %.
B.40 %.
C.50 %.
D.60 %.
e ) 70 %C.
"let x be the cost price of one article . let y be the selling price of one article . 40 y = 60 x y = 1.5 x the answer is c ." | null |
Question: john is the owner of a company and for thanksgiving he wants to give a turkey to each employee to celebrate the holiday . each turkey cost him $ 25 . if he has 85 employees , how much would john need to spend ?
A.$ 2125.
B.$ 1320.
C.$ 2000.
D.$ 1580.
e ) $ 2000.75A.
answer is ( a ) . if john wants to give each of his employees a turkey to help celebrate the thanksgiving holiday and each one costs him $ 25 multiplied by the number of employees ( 85 ) , he would have to pay a total of $ 2125 . | null |
Question: set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 5 ?
A.A.1.
B.B.2.
C.C.4.
D.D.8.
e ) e ) 5E.
"points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is e" | null |
Question: there are 28 balls which are red , blue or green . if 12 balls are green and the sum of red balls and green balls is less than 24 , at most how many red balls are there ?
A.10.
B.12.
C.11.
D.13.
e ) 14C.
r + g + b = 28 g = 12 r + g < 24 = > r + 12 < 24 = > r < 12 = > at most 11 red balls answer : c | null |
Question: a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 480 . find the sum ?
A.7000.
B.7029.
C.4000.
D.2800.
e ) 2791C.
"let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 480 = > 36 x / 100 - 24 x / 100 = 480 = > 12 x / 100 = 480 = > x = 4000 . answer : c" | null |
Question: what is 66.67 % of 804 ?
A.587.69.
B.536.
C.627.
D.300.87.
e ) 567.67B.
"66.67 % = 2 / 3 2 / 3 of 804 = 2 / 3 * 804 = 536 . . . . ans - b" | null |
Question: a 7 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point ?
A.4 / 5.
B.6 / 7.
C.5 / 8.
D.7 / 9.
e ) 9 / 10B.
"the longer wire will form a square with an area more than 1 if the wire is cut at a point within three meters of either end . the probability of this is 6 / 7 . the answer is b ." | null |
Question: a train 200 m long can cross an electric pole in 20 sec and then find the speed of the train ?
A.987.
B.271.
C.72.
D.27.
e ) 36E.
"length = speed * time speed = l / t s = 200 / 20 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph answer : e" | null |
Question: a fair coin is tossed 5 times . what is the probability that it lands heads up at least twice ?
A.1 / 16.
B.5 / 16.
C.2 / 5.
D.13 / 16.
e ) 27 / 32D.
fair coin is tossed 5 times . hence total number of outcomes = 2 ^ 5 = 32 . problem asks for probability of getting atleast heads twice . hence if we calculate probability of getting heads exactly once and probability of not getting heads at all and subract it from the total probability of the event which is 1 ( as total probability of certain event will be always 1 ) we can get the probability of getting atleast heads twice . probability of getting exactly one head and no heads = ( number of possible outcomes [ htttt , thttt , tthtt , tttht , tttth , ttttt ] = 6 ) / ( total possible outcomes = 32 ) = > 6 / 32 = 3 / 16 hence probability of getting atleast heads twice = 1 - ( 3 / 16 ) = 13 / 16 = > choice [ d ] | null |
Question: there are 50 students in a class . if 6 % are absent on a particular day , find the number of students present in the class .
A.47.
B.36.
C.28.
D.12.
e ) 11A.
"number of students absent on a particular day = 6 % of 50 i . e . , 6 / 100 × 50 = 3 therefore , the number of students present = 50 - 3 = 47 students . answer : a" | null |
Question: what is 3 / 4 of 4 / 5 of 2 / 3 ?
A.1 / 4.
B.2 / 5.
C.9 / 16.
D.5 / 8.
e ) 16 / 9B.
"3 / 4 * 4 / 5 * 2 / 3 = 2 / 5 answer : b" | null |
Question: if the numerator of a fraction is increased by 20 % and its denominator is diminished by 25 % value of the fraction is 2 / 15 . find the original fraction ?
A.1 / 12.
B.1 / 16.
C.1 / 19.
D.1 / 14.
e ) 1 / 13A.
"x * ( 120 / 100 ) - - - - - - - - - - - - - - - - = 2 / 15 y * ( 75 / 100 ) x / y = 1 / 12 answer : a" | null |
Question: when w is divided by 13 , the reminder is 0 . if w is 3 more than it value and when divided by 11 its remainder is 0 . what is the value of w ?
A.13.
B.52.
C.39.
D.26.
e ) 35B.
w is divided by 13 so that is multiple of 14 as 13 , 26,39 . . . w + 3 is divided by 11 the remainder is 0 so it is divisible by 11 . consider from option let us take the number is 13 it is divisible by 14 but 13 + 3 is not divisible by 11 so it is not answers so let us take 2 nd option 52 which is divisible by 13 and 52 + 3 = 55 is divisible by 11 so ans is b | null |
Question: which is the least number that must be subtracted from 1828 so that the remainder when divided by 8 , 12 , 16 is 4 ?
A.0.
B.4.
C.8.
D.6.
e ) 2A.
"first we need to figure out what numbers are exactly divisible by 8 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 8 , 12,16 ) = 48 = 48 number is to be subtracted is 0 the largest such number less than or equal to 1828 is 48 * 38 + 4 a" | null |
Question: a high school has 400 students 1 / 2 attend the airthmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 1 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .
A.300.
B.200.
C.250.
D.150.
e ) 160C.
basically , this question is asking you to figure out how many students are being double - counted . a - club has 200 members ( 1 / 2 of 400 ) b - club has 250 members ( 5 / 8 of 400 ) c - club has 300 members ( 3 / 4 of 400 ) we can create an equation to solve this : 200 + 250 + 300 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 50 ) . 750 = 400 + x + 100 x = 250 c | null |
Question: the difference between the place values of two eights in the numerical 38140482 is
A.7999920.
B.799920.
C.7920.
D.79920.
e ) none of themA.
"required difference = ( 8000000 - 80 ) = 7999920 . answer is a" | null |
Question: a is two years older than b who is twice as old as c . if the total of the ages of a , b nd c be 27 , then how old is b ?
A.7.
B.8.
C.9.
D.10.
e ) 11D.
"solution let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ∴ ( 2 x + 2 ) + 2 x + x = 27 ⇔ 5 x = 25 ⇔ x = 5 . hence , b ' s age = 2 x = 10 years . answer d" | null |
Question: last year elaine spent 20 % of her annual earnings on rent . this year she earned 35 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?
A.202.5.
B.194.5.
C.197.5.
D.182.5.
e ) 177.5A.
"for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 15 % more , or $ 135 . she would ' ve spent 30 % of this on rent , or $ 40.5 do $ 40.5 / $ 20 this will give you 202.5 % a is the correct answer ." | null |
Question: i chose a number and divide it by 4 . then i subtracted 24 from the result and got 10 . what was the number i chose ?
A.170.
B.700.
C.800.
D.900.
e ) noneA.
"solution : let x be the number i chose , then x / 4 â ˆ ’ 24 = 10 x / 5 = 34 x = 170 answer : a" | null |
Question: an agent , gets a commission of 2.5 % on the sales of cloth . if on a certain day , he gets rs . 21 as commission , the cloth sold through him on that day is worth
A.333.
B.500.
C.840.
D.299.
e ) 132C.
"explanation : let the total sale be rs . x . then , 2.5 % . of x = 21 < = > ( 25 / 10 * 1 / 100 * x ) = 21 < = > x = 840 . answer : c" | null |
Question: the average temperature for tuesday , wednesday and thursday was 32 ° c . the average temperature for wednesday , thursday and friday was 34 ° c . if the temperature on friday be 44 ° c , what was the temperature on tuesday ?
A.39 ° c.
B.44 ° c.
C.38 ° c.
D.42 ° c.
e ) none of theseC.
"explanation : t + w + t = 32 × 3 = 96 ° c w + t + f = 34 × 3 = 102 ° c also , temperature on friday = 44 ° c temperature on tuesday = 96 + 44 - 102 = 38 ° c answer : option c" | null |
Question: a cyclist bikes x distance at 10 miles per hour and returns over the same path at 9 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?
A.8.1.
B.8.3.
C.8.6.
D.8.9.
e ) 9.5E.
"distance = d 1 = x miles speed = s 1 = 10 miles per hour time = t 1 = distance / speed = x / 10 2 . going from b to a distance = d 2 = x miles speed = s 2 = 9 miles per hour time = t 2 = distance / speed = x / 9 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 10 + x / 9 = x ( 1 / 10 + 1 / 9 ) = x ( 4 + 5 ) / 40 = 19 x / 90 speed = 2 x / ( 19 x / 90 ) = ( 2 x * 90 ) / 9 x = 180 x / 19 x = 180 / 19 = 9.5 answer : e" | null |
Question: the diagonal of a cube is 8 √ 3 . find its volume and surface area .
['A.354', 'B.384', 'C.324', 'D.344', 'e ) 364']B.
√ 3 . a = 8 √ 3 = > a = 8 volume = a ( power ) 3 = > ( 8 × 8 × 8 ) cm ( power ) 3 = > 512 cm ( power ) 3 surface area = > 6 a ( power ) 2 = > ( 6 × 8 × 8 ) cm ( power ) 2 = > 384 cm ( power ) 2 answer is b . | null |
Question: a certain rectangular crate measures 8 feet by 14 feet by 16 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?
A.4.
B.5.
C.6.
D.8.
e ) 10C.
"ans is ` ` b ' ' . for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 14 x 20 i . e . of radius 12 / 2 = 6 c" | null |
Question: a group of boy scouts and girls scouts is going on a rafting trip . 70 % of the scouts arrived with signed permission slips . if 60 % of the scouts were boy scouts and 75 % of the boy scouts arrived with signed permission slips , then what percentage of the girl scouts arrived with signed permission slips ? round to the nearest percent .
A.50 %.
B.60 %.
C.63 %.
D.66 %.
e ) 70 %C.
60 % were boy scouts so 40 % ( 100 - 60 = 40 ) were girl scouts . # of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed ( 75 % of 60 % of the total going ) + ( ? % of 40 % of the total going ) = 70 % of the total going we can let the ` ` total going ' ' = 1,000 arbitrarily since we only care about the percent ( of girl scouts w / permission signed ) . 75 * . 60 * 1,000 + x * . 40 * 1,000 = . 70 * 1,000 450 + x * 400 = 700 400 x = 250 x = 250 / 400 x = . 625 converting this to a percent , we have 62.5 % . rounding , we have 63 % . c | null |
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