text
stringlengths 45
2.98k
| __index_level_0__
float64 0
11.7k
β |
|---|---|
Question: in a recent election , james received 1.5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?
A.901.
B.989.
C.990.
D.971.
e ) 1,001D.
"james = ( 1.5 / 100 ) * 2000 = 30 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 30 = 971 answer : option d" | null |
Question: jolene entered an 18 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 10 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
A.$ 506.00.
B.$ 726.24.
C.$ 900.00.
D.$ 920.24.
e ) $ 926.24B.
if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 726.24 . answer : b . | null |
Question: walking 4 / 3 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
A.22.
B.16.
C.27.
D.28.
e ) 20B.
"speed ratio = 1 : 4 / 3 = 3 : 4 time ratio = 4 : 3 1 - - - - - - - - 4 4 - - - - - - - - - ? 16 m . answer : b" | null |
Question: which is the least number that must be subtracted from 1256 so that the remainder when divided by 7 , 12 , 16 is 4 ?
A.242.
B.232.
C.236.
D.240.
e ) 244E.
"first we need to figure out what numbers are exactly divisible by 7 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,16 ) = 48 * 7 = 336 the numbers which will leave remainder 4 will be { 336 + 4 , 336 x 2 + 4 , 336 x 3 + 4 , . . . } the largest such number less than or equal to 1256 is 336 x 3 + 4 or 1012 to obtain this you need to subtract 244 . e" | null |
Question: if n is the smallest integer such that 108 times n is the square of an integer , what is the value of n ?
A.2.
B.3.
C.6.
D.12.
e ) 24A.
"108 can written as = 2 * 2 * 3 * 3 * 3 - - > 2 ^ 2 * 3 ^ 3 - - - ( 1 ) so for 108 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 2 to make the power of 2 in ( 1 ) even option a is correct" | null |
Question: of the 500 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 40 percent of the employees prefer city y and 60 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ?
A.65.
B.100.
C.115.
D.130.
e ) 325E.
"300 prefer x ( group 1 ) ; 200 prefer y ( group 2 ) . city y needs 375 people : letall 200 who prefer y ( entire group 2 ) be relocated there , the rest 175 will be those who prefer x from group 1 ; city x needs 125 people : 300 - 175 = 125 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 200 + 125 = 325 . answer : e ." | null |
Question: the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 11 . what is the last numbers ?
A.4.
B.5.
C.6.
D.7.
e ) 8A.
"a + b + c = 18 b + c + d = 15 a + d = 11 a β d = 3 a + d = 11 2 d = 8 d = 4 answer : a" | null |
Question: if the cost price of 50 articles is equal to the selling price of 35 articles , then the gain or loss percent is ?
A.16.
B.127.
C.12.
D.18.
e ) 43E.
"percentage of profit = 15 / 35 * 100 = 43 % answer : e" | null |
Question: a batch of cookies was divided amomg 3 tins : 3 / 4 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
A.15 / 2.
B.9 / 4.
C.5 / 9.
D.3 / 5.
e ) 9 / 7D.
"this will help reduce the number of variables you have to deal with : g + b = 3 / 4 r = 1 / 3 b = 1 / 4 we can solve for g which is 1 / 2 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 1 / 2 + 1 / 3 ) = 1 / 2 x = 3 / 5 answer : d" | null |
Question: 10 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?
A.80.
B.160.
C.720.
D.1100.
e ) 1260E.
"no . of ways of picking 2 biology books ( from 10 books ) = 10 c 2 = ( 10 * 9 ) / 2 = 45 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 45 * 28 = 1260 ( option e )" | null |
Question: a grocer has a sale of rs . 6400 , rs . 7000 , rs . 6800 , rs . 7200 and rs . 6500 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
A.rs . 4500.
B.rs . 4700.
C.rs . 4800.
D.rs . 5000.
e ) rs . 5100E.
"total sale for 5 months = rs . ( 6400 + 7000 + 6800 + 7200 + 6500 ) = rs . 33900 required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 33900 ) = rs . 5100 answer : e" | null |
Question: given that a is the average ( arithmetic mean ) of the first 5 positive multiples of 6 and b is the median of the first 12 positive multiples of 6 , what is the ratio of a to b ?
A.3 : 4.
B.6 : 13.
C.5 : 6.
D.13 : 10.
e ) 4 : 3B.
the first nine positive multiples of six are { 6 , 12 , 18 , 24,30 } the first twelve positive multiples of six are { 6 , 12 , 18 , 24 , 30 , 36,42 , 48 , 54 , 60 , 66 , 72 } both sets are evenly spaced , thus their median = mean : a = 18 and b = ( 36 + 42 ) / 2 = 39 - - > a / b = 18 / 39 = 6 / 13 . answer : b . | null |
Question: find the compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually .
A.rs . 610.
B.rs . 612.
C.rs . 614.
D.rs . 616.
e ) none of theseB.
"explanation : amount = [ 7500 Γ ( 1 + 4100 ) 2 ] = ( 7500 Γ 2625 Γ 2625 ) = 8112 so compound interest = ( 8112 - 7500 ) = 612 answer : b" | null |
Question: how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 13 inches than that of a rectangular sheet of paper measuring 6.5 inches by 11 inches ?
['A.50 %', 'B.87 %', 'C.100 %', 'D.187 %', 'e ) 200 %']C.
let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 13 is twice 6.5 then the area will be double which means 100 % greater . the answer is c . | null |
Question: in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,9 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
A.1 / 5.
B.1 / 3.
C.1 / 2.
D.2 / 9.
e ) 4 / 5D.
"the area of the right triangle is ( 1 / 2 ) * 4 * 9 = 18 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 18 = 2 / 9 the answer is d ." | null |
Question: if a sum of money doubles itself in 5 years at simple interest , the ratepercent per annum is
A.12.
B.12.5.
C.20.
D.13.5.
e ) 14C.
"explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 5 ) = 20 option c" | null |
Question: elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 52 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
A.$ 5.
B.$ 10.
C.$ 14.
D.$ 28.
e ) $ 29D.
"bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 52 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 52 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 52 i . e . x = 24 i . e . fixed monthly charge , y = 28 answer : option d" | null |
Question: a started a business with an investment of rs . 70000 and after 9 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 76000 , then the share of b is ?
A.33008.
B.24000.
C.28000.
D.48000.
e ) 81122D.
"ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 3 ) = 7 : 12 total profit = rs . 76000 share of b = 12 / 19 ( 76000 ) = rs . 48000 answer : d" | null |
Question: how many 7 in between 1 to 110 ?
A.18.
B.21.
C.22.
D.23.
e ) 24B.
"7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78 , 79,87 , 97,107 21 7 ' s between 1 to 110 answer : b" | null |
Question: a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3000 , a will get :
A.rs . 1200.
B.rs . 1500.
C.rs . 1800.
D.rs . 2000.
e ) none of theseC.
"explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 120 so , a β s amount = 120 Γ 15 = rs . 1800 . answer : option c" | null |
Question: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 78000 , then the share of b is ?
A.A.34500.
B.B.36099.
C.C.36000.
D.D.38007.
e ) e ) 42000C.
"ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 78000 share of b = 6 / 13 ( 78000 ) = rs . 36000 answer : c" | null |
Question: if an object travels 90 feet in 3 seconds , what is the object β s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
A.17.36.
B.20.45.
C.23.87.
D.26.92.
e ) 29.56B.
"90 feet / 3 seconds = 30 feet / second ( 30 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 20.45 miles / hour ( approximately ) the answer is b ." | null |
Question: if 2 x + y = 7 and x + 2 y = 5 , then xy / 3 =
A.1.
B.4 / 3.
C.17 / 5.
D.18 / 5.
e ) 4A.
"2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 xy / 3 = 3 * 1 / 3 = 1 a" | null |
Question: there are 21 students in a class . in how many different ways can a committee of 3 students be formed ?
A.1180.
B.1330.
C.1540.
D.1760.
e ) 1920B.
"21 c 3 = 21 * 20 * 19 / 6 = 1330 the answer is b ." | null |
Question: the average age of boys in a class is 16 years and that of the girls is 15 years . the average age for the whole class is
A.15 years.
B.15.5 years.
C.16 years.
D.17 years.
e ) can not be computedE.
"clearly , to find the average , we ought to know the numbers of boys , girls or students in the class , neither of which has been given . so the data provided is inadequate . answer : e" | null |
Question: of 800 surveyed students , 20 % of those who read book a also read book b and 25 % of those who read book b also read book a . if each student read at least one of the books , what is the difference between the number of students who read only book a and the number of students who read only book b ?
A.20.
B.25.
C.30.
D.55.
e ) 100E.
"say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 25 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.25 b - - > a = 1.25 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 800 = 1.25 b + b - 0.25 b - - > b = 400 , a = 1.25 b = 500 and { both } = 0.25 b = 100 . the number of students who read only book a is { a } - { both } = 500 - 100 = 400 ; the number of students who read only book b is { b } - { both } = 400 - 100 = 300 ; the difference is 400 - 300 = 100 . answer : e ." | null |
Question: what annual payment will discharge a debt of rs . 1090 due in 2 years at the rate of 5 % compound interest ?
A.993.2.
B.586.21.
C.534.33.
D.543.33.
e ) 646.33B.
explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1090 820 x + 1090 * 441 x = 586.21 so , value of each installment = rs . 586.21 answer : option b | null |
Question: a man sells a car to his friend at 15 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
A.rs . 22941.18.
B.rs . 32941.18.
C.rs . 52941.18.
D.rs . 62941.18.
e ) none of theseC.
"explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 Γ£ β 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 15 % . now s . p = rs . 45000 and loss = 15 % c . p . rs . [ 100 / 85 Γ£ β 45000 ] = rs . 52941.18 correct option : c" | null |
Question: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
A.399.
B.272.
C.666.
D.277.
e ) 311C.
"answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 Γ’ β¬ β 6 = 666 * 1 = 666 answer : c" | null |
Question: how many 0 ' s are there in the binary form of 6 * 1024 + 4 * 64 + 2
A.6.
B.7.
C.8.
D.10.
e ) 9E.
6 * 1024 + 4 * 64 + 2 = 6144 + 256 + 2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2 . so 9 zeros are there . answer : e | null |
Question: what is 7 1 / 4 - 4 2 / 3 divided by 7 / 8 - 3 / 4 ?
A.87 / 36.
B.36 / 17.
C.7 / 6.
D.62 / 3.
e ) 5 / 4D.
"7 1 / 4 - 4 2 / 3 = 29 / 4 - 14 / 3 = ( 87 - 56 ) / 12 = 31 / 12 7 / 8 - 3 / 4 = ( 7 - 6 ) / 8 = 1 / 8 so 31 / 12 / 1 / 8 = 31 / 12 * 8 = 62 / 3 answer - d" | null |
Question: the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 225 , then the mean profit for the last 15 days would be
A.rs . 200.
B.rs . 350.
C.rs . 475.
D.rs . 425.
e ) none of theseC.
"average would be : 350 = ( 225 + x ) / 2 on solving , x = 475 . answer : c" | null |
Question: find out the c . i on rs . 8000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
A.489.66.
B.406.07.
C.406.04.
D.306.03.
e ) 306.01A.
"a = 8000 ( 51 / 50 ) 3 = 8489.66 8000 - - - - - - - - - - - 489.66 answer : a" | null |
Question: jayes can eat 25 marshmallows is 20 minutes . dylan can eat 25 in one hour . in how much time will the two eat 150 marshmallows ?
A.40 minutes ..
B.1 hour and 30 minutes ..
C.1 hour ..
D.1 hour and 40 minutes ..
e ) 2 hours and 15 minutes .C.
rate = output / time jayes rate = 25 / 20 = 5 / 4 dylan rate = 25 / 60 = 5 / 12 combined rate = 5 / 4 + 5 / 12 = 20 / 12 combinedrate * combinedtime = combinedoutput 20 / 12 * t = 150 t = 90 mins = > 1 hr 30 min | null |
Question: how many even number in the range between 10 to 120 inclusive are not divisible by 3
A.15.
B.30.
C.31.
D.37.
e ) 46D.
"we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 120 using ap formula , we can say 120 = 10 + ( n - 1 ) * 2 or n = 56 . for 6 , 12,18 , . . . 120 using ap formula , we can say 120 = 12 + ( n - 1 ) * 6 or n = 19 . hence , only divisible by 2 but not 3 = 56 - 19 = 37 . hence , answer d" | null |
Question: in the biology lab of ` ` jefferson ' ' high school there are 0.037 * 10 ^ 5 germs , equally divided among 74000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
A.10.
B.20.
C.30.
D.40.
e ) 50E.
0.037 * 10 ^ 5 can be written as 3700 74000 * 10 ^ ( - 3 ) can be written as 74 required = 3700 / 74 = 50 answer : e | null |
Question: the largest 4 digit number exactly divisible by 44 is ?
A.9988.
B.9939.
C.9944.
D.9954.
e ) 9960A.
"largest 4 - digit number = 9999 44 ) 9999 ( 227 9988 largest number : 9988 answer : a" | null |
Question: if a certain number is divided by 2 , the quotient , dividend , and divisor , added together , will amount to 62 . what is the number ?
A.18.
B.28.
C.40.
D.38.
e ) 59C.
"let x = the number sought . then x / 2 + x + 2 = 62 . x = 40 . c" | null |
Question: a and b can do a work in 10 days and 15 days respectively . a starts the work and b joins him after 5 days . in how many days can they complete the remaining work ?
A.6 days.
B.2 days.
C.8 days.
D.4 days.
e ) 3 daysE.
"work done by a in 5 days = 5 / 10 = 1 / 2 remaining work = 1 / 2 work done by both a and b in one day = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 remaining work = 1 / 2 * 6 / 1 = 3 days . answer : e" | null |
Question: for the symbol , m β n = n ^ 2 β m for all values of m and n . what is the value of 4 β 2 ?
A.5.
B.3.
C.2.
D.1.
e ) 0E.
"4 β 2 = 4 - 4 = 0 answer : e" | null |
Question: in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1100 employees , then the no . of female employees who are computer literate ?
A.462.
B.674.
C.672.
D.960.
e ) noneA.
"solution : total employees , = 1100 female employees , 60 % of 1100 . = ( 60 * 1100 ) / 100 = 660 . then male employees , = 440 50 % of male are computer literate , = 220 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1100 ) / 100 = 682 computer literate . thus , female computer literate = 682 - 220 = 462 . answer : option a" | null |
Question: total 48 matches are conducted in knockout match type . how many players will be participated in that tournament ?
A.48.
B.47.
C.40.
D.42.
e ) 47E.
"47 players answer : e" | null |
Question: in 130 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
A.20 m.
B.25 m.
C.22.5 m.
D.26 m.
e ) 12 mD.
"distance covered by b in 9 sec . = 130 / 45 x 9 m = 26 m . a beats b by 26 metres . answer : option d" | null |
Question: at a certain university , 69 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?
A.25.
B.37.5.
C.50.
D.52.5.
e ) 75D.
"answer is 75 % total women = 69 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 21 % but question wants to know the percent of men that are tenured 21 % / 40 % = 52.5 % d" | null |
Question: in a dairy farm , 26 cows eat 26 bags of husk in 26 days . in how many days one cow will eat one bag of husk ?
A.1.
B.40.
C.20.
D.26.
e ) 30D.
"explanation : one bag of husk = 26 cows per day β 26 Γ 1 Γ 26 = 1 Γ 26 Γ x for one cow = 26 days answer : d" | null |
Question: the average age of a group of n people is 14 years old . one more person aged 34 joins the group and the new average is 16 years old . what is the value of n ?
A.7.
B.8.
C.9.
D.10.
e ) 11C.
"14 n + 34 = 16 ( n + 1 ) 2 n = 18 n = 9 the answer is c ." | null |
Question: the number 0.650 is how much greater than 1 / 8 ?
A.Β½.
B.21 / 40.
C.1 / 50.
D.1 / 500.
e ) 2 / 500B.
"let x be the difference then . 65 - 1 / 8 = x 65 / 100 - 1 / 8 = x x = 21 / 40 ans b" | null |
Question: if $ 1092 are divided between worker a and worker b in the ratio 5 : 8 , what is the share that worker b will get ?
A.60.32 %.
B.61.54 %.
C.62.21 %.
D.62.76 %.
e ) 63.87 %B.
"worker b will get 8 / 13 = 61.54 % the answer is b ." | null |
Question: a card is drawn from a pack of 52 cards the probability of getting queen of club or aking of a heart ?
A.8 / 58.
B.9 / 25.
C.1 / 26.
D.6 / 25.
e ) 8 / 45C.
"here n ( s ) = 52 let e be the event of getting queen of the club or king of kings n ( e ) = 2 p ( e ) = n ( e ) / n ( s ) = 2 / 52 = 1 / 26 answer ( c )" | null |
Question: 1000 men have provisions for 17 days . if 500 more men join them , for how many days will the provisions last now ?
A.12.9.
B.12.5.
C.11.3.
D.12.2.
e ) 12.1C.
"1000 * 17 = 1500 * x x = 11.3 answer : c" | null |
Question: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 47 minutes . the total distance is ?
A.1 km.
B.2 km.
C.3 km.
D.4 km.
e ) 5 kmC.
"c 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 47 / 60 47 x / 60 = 47 / 60 = > x = 1 . total distance = 3 * 1 = 3 km ." | null |
Question: if x is an integer such that 0 < x < 7 , 0 < x < 15 , 5 > x > β 1 , 3 > x > 0 , and x + 2 < 4 , then x is
A.1.
B.2.
C.3.
D.4.
e ) 5A.
"0 < x < 7 , 0 < x < 15 , 5 > x > β 1 3 > x > 0 x < 2 from above : 0 < x < 2 - - > x = 1 . answer : a ." | null |
Question: an error 5 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is :
A.10.01.
B.9.25.
C.10.25.
D.8.25.
e ) 6.25C.
"explanation : 100 cm is read as 105 cm . a 1 = ( 100 Γ 100 ) cm 2 = 10000 and a 2 = ( 105 Γ 105 ) cm 2 = 10816 ( a 2 - a 1 ) = 11025 - 10000 = 1025 = > 1025 / 10000 * 100 = 10.25 answer : c" | null |
Question: 1 + 1
A.9.
B.8.
C.3.
D.0.
e ) 2E.
e | null |
Question: rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 150 . what is the share of rahul ?
A.$ 50.
B.$ 40.
C.$ 60.
D.$ 100.
e ) $ 90C.
"rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 150 * 2 / 5 = $ 60 answer is c" | null |
Question: a boat m leaves shore a and at the same time boat b leaves shore b . they move across the river . they met at 500 yards away from a and after that they met 300 yards away from shore b without halting at shores . find the distance between the shore a & b
A.1000 yards.
B.1200 yards.
C.1400 yards.
D.1600 yards.
e ) 1800 yardsB.
if x is the distance , a is speed of a and b is speed of b , then ; 500 / a = ( x - 500 ) / b and ( x + 300 ) / a = ( 2 x - 300 ) / b , solving it , we get x = 1200 yards answer : b | null |
Question: a pineapple costs rs 7 each and a watermelon costs rs . 5 each . if i spend rs 38 on total what is the number of pineapple i purchased ?
A.7.
B.6.
C.5.
D.2.
e ) 3D.
explanation : the equation for this problem can be made as : 5 x + 7 y = 38 where x is the number of watermelons and y is the number of pineapples . now test for 2 , 3 and 4 : for y = 2 5 x + 14 = 38 x is not an integer for y = 3 5 x = 17 x not an integer for y = 4 x = 2 so 4 pineapples and 2 watermelons can be bought by 38 rs . answer : d | null |
Question: the sub - duplicate ratio of 25 : 16 is
A.4 : 3.
B.1 : 2.
C.1 : 3.
D.5 : 4.
e ) 2 : 3D.
"root ( 25 ) : root ( 16 ) = 5 : 4 answer : d" | null |
Question: in Ξ΄ pqs above , if pq = 7 and ps = 8 , then
A.9 / 4.
B.12 / 5.
C.56 / 9.
D.15 / 4.
e ) 20 / 3C.
"there are two ways to calculate area of pqs . area remains same , so both are equal . 7 * 8 / 2 = pr * 9 / 2 pr = 56 / 9 c" | null |
Question: ajay can ride 50 km in 1 hour . in how many hours he can ride 1250 km ?
A.10 hrs.
B.15 hrs.
C.20 hrs.
D.25 hrs.
e ) 18 hrsD.
"1 hour he ride 50 km he ride 1250 km in = 1250 / 50 * 1 = 25 hours answer is d" | null |
Question: a boat covers a certain distance downstream in 1 hour , while it comes back in 11 Γ’ Β β 2 hours . if the speed of the stream be 3 kmph , what is the speed of the boat in still water ?
A.31 kmph.
B.16 kmph.
C.19 kmph.
D.15 kmph.
e ) 14 kmphD.
"let the speed of the water in still water = x given that speed of the stream = 3 kmph speed downstream = ( x + 3 ) kmph speed upstream = ( x Γ’ Λ β 3 ) kmph he travels a certain distance downstream in 1 hour and come back in 11 Γ’ Β β 2 hour . i . e . , distance travelled downstream in 1 hour = distance travelled upstream in 11 Γ’ Β β 2 hour since distance = speed Γ£ β time , we have ( x + 3 ) Γ£ β 1 = ( x - 3 ) 3 / 2 2 ( x + 3 ) = 3 ( x - 3 ) 2 x + 6 = 3 x - 9 x = 6 + 9 = 15 kmph answer : d" | null |
Question: in a division , a student took 87 as divisor instead of 36 . his answer was 24 . the correct answer is -
A.42.
B.32.
C.48.
D.28.
e ) 58E.
x / 87 = 24 . x = 24 * 87 . so correct answer would be , ( 24 * 87 ) / 36 = 58 . answer : e | null |
Question: what is the sum of all digits for the number 10 ^ 26 - 51 ?
A.199.
B.209.
C.219.
D.229.
e ) 239D.
"10 ^ 26 is a 27 - digit number : 1 followed by 26 zeros . 10 ^ 26 - 51 is a 26 - digit number : 24 9 ' s and 49 at the end . the sum of the digits is 24 * 9 + 4 + 9 = 229 . the answer is d ." | null |
Question: what is the measure of the angle w made by the diagonals of the any adjacent sides of a cube .
A.30.
B.45.
C.60.
D.75.
e ) 90C.
"c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . c" | null |
Question: what is the compound interest paid on a sum of rs . 6000 for the period of 2 years at 10 % per annum .
A.1260.
B.1320.
C.1200.
D.1250.
e ) none of theseA.
solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 6000 = 6000 * ( 21 / 100 ) = 1260 answer a | null |
Question: a fair 2 sided coin is flipped 8 times . what is the probability that tails will be the result at least twice , but not more than 8 times ?
A.5 / 8.
B.3 / 4.
C.7 / 8.
D.157 / 64.
e ) 143 / 128E.
"at least twice , but not more than 8 timesmeans exactly 2 times , 3 times , 4 times , 5 times , 6 times , 7 times , 8 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 8 c 2 / 2 ^ 8 + 8 c 3 / 2 ^ 8 + 8 c 4 / 2 ^ 8 + 8 c 5 / 2 ^ 8 + 8 c 6 / 2 ^ 8 + 8 c 7 / 2 ^ 8 = 143 / 128 option : e" | null |
Question: the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 54 . what is the rate of interest per annum ?
A.8.
B.2.
C.9.
D.4.
e ) 6E.
"explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 54 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 54 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 54 r 2 = ( 54 * 2 ) / 3 = 36 = > r = 6 rate = 6 % answer : option e" | null |
Question: find the compound ratio of ( 1 : 2 ) , ( 2 : 3 ) and ( 3 : 4 ) is
A.1 : 2.
B.3 : 5.
C.5 : 7.
D.1 : 4.
e ) 2 : 1D.
"required ratio = 1 / 2 * 2 / 3 * 3 / 4 = 1 / 4 = 1 : 4 answer is d" | null |
Question: if 1 is added to the denominator of fraction , the fraction becomes 1 / 2 . if 1 is added to the numerator , the fraction becomes 1 . the fraction is
A.4 / 7.
B.5 / 9.
C.2 / 3.
D.10 / 11.
e ) none of theseC.
explanation : let the required fraction be a / b . then β a / b + 1 = 1 / 2 β 2 a β b = 1 - - - - ( 1 ) β a + 1 / b = 1 β a β b = β 1 β a β b = β 1 - - - - - - - ( 2 ) solving ( 1 ) & ( 2 ) we get a = 2 , b = 3 fraction = a / b = 2 / 3 correct option : c | null |
Question: if the ratio of two number is 2 : 3 and lcm of the number is 120 then what is the number .
A.15.
B.20.
C.25.
D.30.
e ) 35B.
"product of two no = lcm * hcf 2 x * 3 x = 120 * x x = 20 answer : b" | null |
Question: find out the c . i on rs . 4000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
A.244.83.
B.306.07.
C.306.04.
D.306.03.
e ) 306.01A.
"a = 4000 ( 51 / 50 ) 3 = 4244.832 4000 - - - - - - - - - - - 244.83 answer : a" | null |
Question: bert and rebecca were looking at the price of a condominium . the price of the condominium was 40 % more than bert had in savings , and separately , the same price was also 75 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .
A.1 : 4.
B.4 : 1.
C.2 : 3.
D.3 : 2.
e ) 5 : 4E.
suppose bert had 100 so price becomes 140 , this 140 = 1.75 times r ' s saving . . so r ' s saving becomes 80 so required ratio is 100 : 80 = 5 : 4 answer : e | null |
Question: walking at 5 / 6 of her normal speed , a worker is 12 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
A.36.
B.42.
C.48.
D.54.
e ) 60E.
"let v be her normal speed and let t be her normal time . d = ( 5 / 6 ) v * ( t + 12 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 5 / 6 ) v * ( t + 12 ) t / 6 = 10 t = 60 the answer is e ." | null |
Question: if 12 lions can kill 12 deers in 12 minutes how long will it take 100 lions to kill 100 deers ?
A.1 minutes.
B.12 minute.
C.120 minutes.
D.10000 minutes.
e ) 1000 minutesB.
"we can try the logic of time and work , our work is to kill the deers so 12 ( lions ) * 12 ( min ) / 12 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 12 answer : b" | null |
Question: a man cycling along the road noticed that every 18 minutes a bus overtakes him and every 6 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
A.5 minutes.
B.6 minutes.
C.8 minutes.
D.9 minutes.
e ) 10 minutesD.
let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 18 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 18 , d = 18 b - 18 c ; every 6 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 6 , d = 6 b + 6 c ; d = 18 b - 18 c = 6 b + 6 c , - - > b = 2 c , - - > d = 18 b - 9 b = 9 b . interval = \ frac { d } { b } = \ frac { 9 b } { b } = 9 answer : d ( 9 minutes ) . | null |
Question: x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 27000 . what will be the ratio in which they should share the profit at the end of the year ?
A.20 : 9.
B.2 : 1.
C.3 : 2.
D.2 : 3.
e ) 5 : 3A.
"ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 Γ 12 : 27000 Γ 9 = 45 Γ 12 : 27 Γ 9 = 15 Γ 12 : 9 Γ 9 = 20 : 9 answer is a" | null |
Question: the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 15 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait until the hiker catches up ?
A.20.
B.55 / 4.
C.25.
D.14.
e ) 13B.
"after passing the hiker the cyclist travels for 5 minutes at a rate of 15 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 4 miles . in those 5 mins the hiker travels a distance of 1 / 3 miles . so the hiker still has to cover 11 / 12 miles to meet the waiting cyclist . the hiker will need 55 / 4 mins to cover the remaining 11 / 12 miles . so the answer is b ." | null |
Question: if x + y = 10 , x - y = 18 , for integers of x and y , x = ?
A.14.
B.15.
C.25.
D.13.
e ) 42A.
x + y = 10 x - y = 18 2 x = 28 x = 14 answer is a | null |
Question: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 2 / 3 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ?
A.4 / 15.
B.3 / 40.
C.13 / 40.
D.7 / 20.
e ) 13 / 22A.
"p ( 1 and not 2 ) = 2 / 3 * ( 1 - 3 / 5 ) = 4 / 15 . answer : a ." | null |
Question: find the least number must be subtracted from 964807 so that remaining no . is divisible by 8 ?
A.7.
B.6.
C.5.
D.4.
e ) 3A.
"on dividing 964807 by 15 we get the remainder 7 , so 7 should be subtracted a" | null |
Question: if 8 people take an hour to complete a piece of work , then how long should 16 people will take to complete the same piece of work ?
A.15 min.
B.30 min.
C.26 min.
D.28 min.
e ) 18 minB.
if 8 people take an hour to complete a piece of work , then 16 people will take 8 * 60 / 16 = 30 mins to complete the same piece of work . answer : b | null |
Question: find the area of a parallelogram with base 25 cm and height 15 cm ?
A.295 cm 2.
B.385 cm 2.
C.275 cm 2.
D.375 cm 2.
e ) 285 cm 2D.
"area of a parallelogram = base * height = 25 * 15 = 375 cm 2 answer : d" | null |
Question: when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 6 ] * [ 4 ] = ?
A.[ 12 ].
B.[ 44 ].
C.[ 45 ].
D.[ 88 ].
e ) [ 90 ]A.
"[ 6 ] * [ 4 ] = ( 6 / 2 + 1 ) ( 4 / 2 + 1 ) = [ 12 ] . ans - a" | null |
Question: in a certain company , a third of the workers do not have a retirement plan . 60 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
A.80.
B.95.
C.180.
D.120.
e ) 210C.
"set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,4 * 1 / 3 * x 120 = 12 / 30 x x = 300 300 - 120 = 180 answer c" | null |
Question: a bus started its journey from mumbai and reached pune in 65 min with its average speed of 60 km / hr . if the average speed of the bus is increased by 5 km / hr , how much time will it take to cover the same distance ?
A.2 hrs.
B.3 hrs.
C.1 hrs.
D.1 1 / 2 hrs.
e ) 2 1 / 2 hrsC.
sol . distance between ramgarh and devgarh = ( 60 * 65 ) / 60 = 60 average speed of the bus is increased by 5 km / hr then the speed of the bus = 60 km / hr required time = 60 / 60 = 1 hr c | null |
Question: the mean of 50 observations is 200 . but later he found that there is decrements of 47 from each observations . what is the the updated mean is ?
A.165.
B.185.
C.153.
D.198.
e ) 199C.
"153 answer is c" | null |
Question: a bag contains 4 red , 6 blue and 3 green balls . if 3 balls are picked at random , what is the probability that both are blue ?
A.11 / 144.
B.12 / 455.
C.10 / 143.
D.11 / 125.
e ) 14 / 368C.
"p ( both are red ) , = 6 c 3 / 13 c 3 = 10 / 143 c" | null |
Question: what is 120 % of 13 / 24 of 360 ?
A.52.
B.117.
C.234.
D.312.
e ) 576C.
"120 % * 13 / 24 * 360 = 1.2 * 13 * 15 = 234 the answer is c ." | null |
Question: if a farmer sells 10 of his chickens , his stock of feed will last for 4 more days than planned , but if he buys 15 more chickens , he will run out of feed 3 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
A.12.
B.24.
C.48.
D.35.
e ) 60D.
"say farmer has n chicken and he is good for d days . : - we have 3 equations given in question : - ( n - 10 ) * d + 4 = ( n + 15 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 15 d - 3 n = 45 4 n - 10 d = 40 = > n = 35 ans d it is !" | null |
Question: how many 1 / 2 s are there in 37 1 / 2 ?
A.75.
B.150.
C.300.
D.600.
e ) 700A.
"required number = ( 75 / 2 ) / ( 1 / 2 ) = ( 75 / 2 x 2 / 1 ) = 75 answer : a" | null |
Question: a , b , c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 175 , then how much amount should c pay as his share of rent ?
A.23.
B.45.
C.15.
D.28.
e ) 18B.
a : b : c = 10 * 7 : 12 * 5 : 15 * 3 = 2 * 7 : 12 * 1 : 3 * 3 = 14 : 12 : 9 amount that c should pay = 175 * ( 9 / 35 ) = 5 * 9 = 45 answer is b | null |
Question: in a box of 12 pens , a total of 6 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
A.1 / 6.
B.5 / 22.
C.6 / 11.
D.9 / 16.
e ) 3 / 4B.
"method - 1 there are 9 fine pieces of pen and 6 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 6 / 12 ) i . e . probability of second pen not being defective = ( 5 / 11 ) [ 11 pen remaining with 5 defective remaining considering that first was defective ] probability of both pen being non - defective = ( 6 / 12 ) * ( 5 / 11 ) = 5 / 22 answer : option b" | null |
Question: a part of certain sum of money is invested at 6 % per annum and the rest at 15 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
A.4 : 6.
B.4 : 9.
C.4 : 3.
D.5 : 2.
e ) 4 : 2D.
"15 : 6 = 5 : 2 answer : d" | null |
Question: if a randomly selected non - negative single digit integer is added to { 2 , 3 , 5 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ?
A.0.2.
B.0.3.
C.0.4.
D.0.5.
e ) 0.6C.
we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 5 ) / 2 = 4 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c . | null |
Question: on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 630 , the rate of interest being the same in both the cases . the rate of interest is ?
A.8 %.
B.10 %.
C.12 %.
D.14 %.
e ) 16 %B.
"difference in c . i . and s . i for 2 years = $ 630 - $ 600 = $ 30 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 30 rate = ( 100 * 30 ) / ( 300 ) = 10 % the answer is b ." | null |
Question: there are two circles of different radii . the are of a square is 784 sq cm and its side is twice the radius of the larger circle . the radius of the larger circle is seven - third that of the smaller circle . find the circumference of the smaller circle .
A.165 β cm.
B.65 β cm.
C.12 β cm.
D.14 β cm.
e ) 16 β cmC.
"let the radii of the larger and the smaller circles be l cm and s cm respectively . let the side of the square be a cm . a 2 = 784 = ( 4 ) ( 196 ) = ( 22 ) . ( 142 ) a = ( 2 ) ( 14 ) = 28 a = 2 l , l = a / 2 = 14 l = ( 7 / 3 ) s therefore s = ( 3 / 7 ) ( l ) = 6 circumference of the smaller circle = 2 β s = 12 β cm . answer : c" | null |
Question: y and z walk around a circular track . they start at 5 a . m from the same point in the opposite directions . y and z walk at a speed of 3 rounds per hour and 4 rounds per hour respectively . how many times shall they cross each other before 7 a . m
A.14.
B.15.
C.16.
D.17.
e ) 18E.
explanation : relative speed = ( 3 + 4 ) = 9 rounds per hour so , they cross each other 9 times in an hour hence , they cross 18 times before 7 a . m answer : option e | null |
Question: a box contains 10 black , 5 red and 4 green marbles . 3 marbles are drawn from the box at random . what is the probability that all the three marbles are of the same color ?
A.143 / 969.
B.134 / 969.
C.120 / 969.
D.19 / 969.
e ) 120 / 134B.
"explanation : total marbles in a box = 10 black + 5 red + 4 green marbles = 19 marbles 3 marbles are drawn from 19 marbles at random . therefore , n ( s ) = 19 c 3 = 969 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 10 c 3 + 5 c 3 + 4 c 3 = 120 + 10 + 4 = 134 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 134 / 969 answer : b" | null |
Question: a towel , when bleached , lost 20 % of its length and 10 % of its breadth . what is the percentage decrease in area ?
A.26.
B.28.
C.24.
D.20.
e ) 22B.
"formula for percentage change in area is : = ( β x β y + ( xy ) / 100 ) % = ( β 20 β 10 + ( 20 Γ 10 ) / 100 ) % = β 28 % i . e . , area is decreased by 28 % answer is b ." | null |
Question: two numbers are respectively 35 % and 50 % more than a third number . the percentage that is first of the second is ?
A.90 %.
B.47 %.
C.38 %.
D.52 %.
e ) 83 %A.
"i ii iii 135 150 100 150 - - - - - - - - - - 135 100 - - - - - - - - - - - ? = > 90 % answer : a" | null |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.