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Question: a can complete the job in 5 hours and b can complete the same job in 3 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete
A.1 / 8.
B.3 / 10.
C.1 / 2.
D.5 / 6.
e ) 8 / 9A.
a = 1 / 8 | null |
Question: in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 35 and 200 , then the least and greatest integer on the card would be
A.3 and 15.
B.3 and 20.
C.4 and 13.
D.4 and 14.
e ) 5 and 14E.
"given : 35 < x ( x + 1 ) < 200 . now , it ' s better to test the answer choices here rather than to solve : if x = 5 then x ( x + 1 ) = 30 > 35 - - > so , the least value is 5 . test for the largest value : if x = 14 then x ( x + 1 ) = 14 * 15 = 210 > 200 answer : e ." | null |
Question: 25 * 25 * 25 * 25 * 25 = 5 ^ ?
A.4.
B.6.
C.5.
D.3.
e ) 10E.
"solution : 5 ^ 2 * 5 ^ 2 * 5 ^ 2 * 5 ^ 2 * 5 ^ 2 = 5 ^ ( 2 + 2 + 2 + 2 + 2 ) = 5 ^ 10 answer : e" | null |
Question: what quantity of water should taken out to concentrate 21 liters of 40 % acidic liquid to 60 % acidic liquid ?
A.5 liters.
B.10 liters.
C.7 liters.
D.8 liters.
e ) 6 litersC.
"required answer is = 21 ( 60 - 40 ) / 60 = 7 liters answer is c" | null |
Question: a and b together can do a work in 6 days . if a alone can do it in 10 days . in how many days can b alone do it ?
A.10.
B.15.
C.77.
D.55.
e ) 21B.
"1 / 6 β 1 / 10 = 1 / 15 = > 15 answer : b" | null |
Question: sam and nik start from a and b respectively at the same time and travel towards each other at constant speeds along the same route . sam meets nik at point c on the road which is 600 m away from starting point a and 400 m away from point b . the speed of sam is 50 m / m ( meter / minute ) . how much time did sam take to cover the distance between a and b ?
A.10 minutes.
B.15 minutes.
C.20 minutes.
D.22 minutes.
e ) 17 minutesC.
total distance from a to b - a - c = 600 m , b - c = 400 m ; therefore a - b = 1000 m ; vs = 50 m / m ; therefore , t = 1000 / 50 = 20 minutes . option c | null |
Question: subtract . simplify your answer and write it as a proper fraction or as a whole or mixed number . 4 / 5 - 1 / 5 =
A.1 / 5.
B.2 / 5.
C.3 / 5.
D.4 / 5.
e ) 5 / 5C.
here ' s how to subtract 1 / 5 from 4 / 5 : 4 / 5 β 1 / 5 since our denominators match , we can subtract the numerators . 4 β 1 = 3 so the answer is : 3 / 5 answer : c | null |
Question: ratio between two numbers is 3 : 4 and their sum is 420 . find the smaller number ?
A.378.
B.180.
C.820.
D.734.
e ) 840B.
explanation : 3 x + 4 x = 420 x = 60 = > 3 x = 180 answer : option b | null |
Question: q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 30 , what is the greatest possible value of q minus r ?
A.23.
B.24.
C.25.
D.26.
e ) 27E.
a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 30 . the greatest multiple of 9 which is less than 30 is 27 . the answer is e . | null |
Question: what is the square root of 121 ?
A.11.
B.12.
C.16.
D.18.
e ) 25A.
"11 x 11 = 121 answer a" | null |
Question: if equation | x / 5 | + | y / 5 | = 2 encloses a certain region on the coordinate plane , what is the area of this region ?
A.20.
B.50.
C.200.
D.100.
e ) 400C.
the equation can be reduced to intercept form as | x / 10 | + | y / 10 | = 1 , so these are lines in four quadrants with x and y intercept as 10 , so it is a rhombus with diagonals of 20 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 20 * 20 = 200 . answer c . | null |
Question: in a vehicle ' s repair shed , 3 men and 8 boys can do a piece of work in 15 days ; 4 men and 9 boys can do the same work in 12 days . then , 5 men and 5 boys can do double the amount of this work in :
A.20 days.
B.33 days.
C.24 days.
D.28 days.
e ) none of theseC.
explanation : solution : ( 3 * 15 ) men + ( 8 * 15 ) boys = ( 4 * 12 ) men + ( 9 * 12 ) boys 45 m + 120 b = 48 m + 108 b < = > 3 m = 12 b = > 1 m = 4 b . . ' . 3 m + 8 b = ( 3 * 4 ) b + 8 b = 20 b . 5 m + 5 b = ( 5 * 4 ) b + 5 b = 25 b . let the required number of days be x . now , more boys , less days ( ip ) more work , more days ( dp ) boys 25 : 20 } : : 15 : x work 1 : 2 . ' . ( 25 * 1 * x ) = ( 20 * 2 * 15 ) = > x = 40 * 15 / 25 = 24 . answer : c | null |
Question: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 50 hours . if harry and james were paid the same amount last week , how many hours did harry work last week ?
A.35.
B.36.
C.37.
D.38.
e ) 50E.
"amount earned by james = 40 * x + 10 * 2 x = 60 x therefore , amount earned by james = 60 x but we know the amount harry earned assuming working y hours ( y > 30 ) is 30 * x + ( y - 30 ) * 1.5 x [ [ we know y > 30 because in 30 h the most harry could earn is 30 x , but he has earned 60 x ] ] so x * ( 1.5 y - 45 + 30 ) = 60 x or x * ( 1.5 y - 15 ) = 60 x so 1.5 y - 15 = 60 so 1.5 y = 75 so y = 50 answer is e" | null |
Question: increasing the original price of an article by 8 percent and then increasing the new price by 8 percent is equivalent to increasing the original price by
A.16.16 %.
B.16.32 %.
C.16.64 %.
D.17.26 %.
e ) 18.56 %C.
"1.08 * 1.08 * x = 1.1664 * x the answer is c ." | null |
Question: if 6 women can color 180 m long cloth in 3 days , then 5 women can color 200 m long cloth in ?
A.6 days.
B.5 days.
C.4 days.
D.2 days.
e ) 3 daysC.
the length of cloth painted by one woman in one day = 180 / 6 Γ 3 = 10 m no . of days required to paint 200 m cloth by 5 women = 200 / 5 Γ 10 = 4 days answer : c | null |
Question: sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 210 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 3 of the days were hot , then what was the price of 1 cup on a hot day ?
A.$ 1.50.
B.$ 1.64.
C.$ 2.25.
D.$ 2.50.
e ) $ 3.25B.
"7 regular days - - > sales = 7 * 32 * x = 224 x ; 3 hot days - - > sales = 3 * 32 * ( 1.25 x ) = 120 x ; total sales = 224 x + 120 x = 344 x . total cost = 10 * 32 * 0.75 = 240 . profit = 344 x - 240 = 210 - - > x = 1.308 . 1.25 x = ~ 1.64 . answer : b ." | null |
Question: if x β 2 + 9 β 4 = 5 β 4 , what is the value of x ?
A.β 2.
B.β 1.
C.0.
D.1.
e ) 2A.
"x β 2 + 9 β 4 = 5 β 4 let ' s multiply both sides by 4 . 2 x + 9 = 5 2 x = - 4 x = - 2 the answer is a ." | null |
Question: how many zeros does 65 ! end with ?
A.20.
B.15.
C.25.
D.30.
e ) 32B.
"according to above 65 ! has 65 / 5 + 65 / 25 = 13 + 2 = 15 trailing zeros . answer : b ." | null |
Question: the price of a certain painting increased by 30 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
A.102 %.
B.105 %.
C.110.5 %.
D.112.5 %.
e ) 100 %C.
easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 30 = 130 price at the end of year 2 = 130 - 130 * 0.15 = 130 * 0.85 = 110.5 hence required answer = ( 110.5 / 100 ) * 100 % = 110.5 % answer is c . | null |
Question: a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 27 more than the correct answer . find the number .
A.40.
B.50.
C.60.
D.70.
e ) 80C.
let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 27 25 x = 16 x + 540 9 x = 540 x = 60 the answer is c . | null |
Question: in a forest 150 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 20 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
A.150.
B.6,000.
C.1,250.
D.1,500.
e ) 2,500B.
"the percentage of tagged deer in the second sample = 20 / 50 * 100 = 40 % . so , 150 tagged deers comprise 10 % of total # of deers - - > total # of deers = 150 * 40 = 6,000 . answer : b" | null |
Question: the water level in a reservoir has been dropping at the rate of 14 inches per day . exactly 5 days ago , the water level was at w inches . what will be the water level exactly 3 days from now if the rate at which the level is dropping remains the same ?
A.w β 126.
B.w β 56.
C.w β 112.
D.w + 14.
e ) w + 126C.
"drop = 14 inches / day 5 days ago = w , means now it ' s equal w - 70 and in 3 days = w - 70 - 42 = w - 112 answer c" | null |
Question: what is 15 % of 2 / 3 of 0.6 ?
A.0.06.
B.0.9.
C.9.
D.90.
e ) none of the aboveA.
"the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 6 / 10 ) = 180 / 3000 = 0.06 option a" | null |
Question: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 150 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
A.110.
B.146.
C.152.
D.162.
e ) 170A.
"the probability of survival for each of the first 3 months of life is 1 - 1 / 10 = 9 / 10 , so of 150 newborn 150 * 9 / 10 * 9 / 10 * 9 / 10 = ~ 110 is expected to survive . answer : a ." | null |
Question: the units digit of ( 35 ) ^ ( 7 ) + ( 93 ) ^ ( 45 ) is :
A.2.
B.4.
C.6.
D.8.
e ) 0D.
"any power of anything ending in 5 always has a units digit of 5 . so the first term has a units digit of 5 . done . the second term takes a little more work . we can ignore the tens digit , and just treat this base as 3 . here is the units digit patter for the powers of 3 . 3 ^ 45 has a units digit of 3 of course 5 + 3 = 8 , d" | null |
Question: uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought less of toyota than honda at the ratio of 7 : 3 . if 70 % of the toyota bought and 30 % of the honda bought were suv Γ£ Β’ Γ’ β Β¬ Γ’ β Β’ s . how many suv Γ£ Β’ Γ’ β Β¬ Γ’ β Β’ s did uba capital buy in the aforementioned purchase ?
A.76 %.
B.58 %.
C.68 %.
D.89 %.
e ) 49 %B.
let total no of vehicles bought be 100 , toyota 70 and honda 30 , so total number of suv ' s bought for toyota and honda respectively 70 * 70 / 100 = 49 and 30 * 30 / 100 = 9 so total 58 suv ' s were bought out of 100 vehicles bought . . so required % is 58 % answer : b | null |
Question: how many 4 - digit numbers are completely divisible by 7 ?
A.1354.
B.1286.
C.1178.
D.1224.
e ) noneB.
"solution : 4 - digit numbers divisible by 7 are : 1001 , 1008 , 1015 β¦ . . 9996 . this is an a . p . in which a = 1001 , d = 7 , l = 9996 . let the number of terms be n . then tn = 9996 . . ' . a + ( n - 1 ) d = 9996 = > 1001 + ( n - 1 ) 7 = 9996 = > ( n - 1 ) 7 = 8995 = > ( n - 1 ) = 8995 / 7 = 1285 = > n = 1286 . . ' . number of terms = 1286 . answer b" | null |
Question: what is the units digit of ( 3 ^ 16 ) ( 4 ^ 13 ) ?
A.2.
B.4.
C.6.
D.7.
e ) 8B.
"- > the ones place of ( ~ 3 ) ^ n repeats after 4 times like 3 ο 9 ο 7 ο 1 ο 3 . the ones place of ( ~ 4 ) ^ n repeats after 2 times like 4 ο 6 ο 4 . then , 3 ^ 16 = 3 ^ 4 * 4 = ο 3 ^ 0 = 1 . , 4 ^ 13 = 4 ^ 2 * 6 + 1 = 4 ^ 1 = ~ 4 which is ( 3 ^ 16 ) ( 4 ^ 13 ) ο ( 3 ^ 0 ) ( ~ 4 ) = ( ~ 1 ) ( ~ 4 ) = ~ 4 . therefore , the answer is b ." | null |
Question: a can do a piece of work in 10 days , b in 15 days . they work for 5 days . the rest of work finished by c in 2 days . if they get rs 1500 for the whole work , the daily wages of b and c are ?
A.225.
B.276.
C.126.
D.187.
e ) 1267A.
explanation : let the total work = 30 units . then capacity of a = 3 units , b = 2 units . now they worked for 5 days . so they must have completed 25 units . rest of the work 5 units done by c in 2 days . so c capacity = 5 / 2 = 2.5 units . given that toatal wages are rs . 1500 for 30 units . so for 1 unit of work they get rs . 50 . now b and c per day work = ( 2 + 2.5 ) = 4.5 units . so their daily wages = 4.5 Γ 50 = rs . 225 answer : a | null |
Question: crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 20 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?
A.$ 20.
B.$ 40.
C.$ 50.
D.$ 80.
e ) $ 100D.
cost + profit = income ( selling price ) profit now = 0.5 x or x - 50 0.5 x = x - 50 50 = 0.5 x x = 100 $ is selling price so , profit before was 0.2 * 100 = 20 $ cost = 100 - 20 = 80 $ answer : d | null |
Question: if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 900 responses are needed , what is the minimum number of questionnaires that should be mailed ?
A.1300.
B.1350.
C.1400.
D.1450.
e ) 1500E.
"let x be the minimum number of questionnaires to be mailed . 0.6 x = 900 x = 1500 the answer is e ." | null |
Question: salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 18 % vinegar , dressing p comprises what percentage of the new dressing ?
A.20 %.
B.30 %.
C.40 %.
D.50 %.
e ) 60 %C.
"let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.18 0.2 x = 0.08 x = 0.4 = 40 % the answer is c ." | null |
Question: find the value o f 72519 x 9999 = m ?
A.434539873.
B.355797990.
C.435453490.
D.m = 725117481.
e ) 873430134D.
"72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d" | null |
Question: ( 4 ! ) ^ n is a factor of 12 ! , but ( 4 ! ) ^ ( n + 1 ) is not factor of 12 ! . what is the value of n ?
A.1.
B.2.
C.3.
D.4.
e ) 5C.
12 ! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 4 ! = 24 question can be rephrased as how many 24 ' s are there in 12 ! 12 * 2 = 24 4 * 6 = 24 3 * 8 = 24 value of n = 3 answer : c | null |
Question: a motorcyclist goes from bombay to pune , a distance of 256 kms at an average of 32 kmph speed . another man starts from bombay by car 2 Β½ hours after the first , and reaches pune Β½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
A.1 : 2.
B.1 : 5.
C.1 : 4.
D.1 : 1.
e ) 5 : 8E.
"t = 256 / 32 = 8 h t = 8 - 3 = 5 time ratio = 8 : 5 speed ratio = 5 : 8 answer : e" | null |
Question: the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years x in which the population would be doubled assuming there is no emigration or immigration is
A.20.
B.x = 25.
C.x = 30.
D.x = 35.
e ) 40D.
"suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ." | null |
Question: when the positive integer y is divided by 9 , the remainder is 5 . what is the remainder when 3 y is divided by 9 ?
A.0.
B.1.
C.3.
D.4.
e ) 6E.
lets take the number as y when y is divided by 9 the remainder is 5 hence y can be written as y = 9 k + 5 multiplying by 3 will give 3 y = 27 k + 15 we can also write 3 y = 27 k + 9 + 6 now 27 k and 9 are divisible by 9 leaving the remainder as 6 hence e is the answer . | null |
Question: let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 70 th number in this set ?
A.557.
B.608.
C.613.
D.616.
e ) 621A.
"the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 70 th number = 8 * ( 70 - 1 ) + 5 = 557 answer = a" | null |
Question: find the minimum value of 5 cosa + 12 sina + 12
A.- 1.
B.1.
C.2.
D.3.
e ) none of theseA.
"solution : 5 cosa + 12 sina + 12 = 13 ( 5 / 13 cosa + 12 / 13 sina ) + 12 now , for any values of b we can get sinb = 5 / 13 and we can replace cosb = 12 / 13 . we see that our assumption is right because we satisfy the condition sin ^ 2 b + cos ^ 2 b = 1 so we get 13 ( sinbcosa + cosbsina ) + 12 = 13 ( sin ( a + b ) ) + 12 . therefore we know that minimum value of sinx = - 1 and greatest is 1 so the least value of the expression becomes when sin ( a + b ) = - 1 then the value of the whole term becomes 13 . ( - 1 ) + 12 = - 13 + 12 = - 1 answer a" | null |
Question: julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 120 and $ 122 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?
A.600.
B.720.
C.1080.
D.2200.
e ) 3600E.
"$ 120 for 2 years = $ 60 per year . extra $ 2 yearned with the compound interest is the percent yearned on percent . so , $ 2 is yearned on $ 60 , which means that the interest = 30 % . this on the other hand means that half of the savings = 60 * 30 = $ 1800 . twice of that = $ 3,600 . answer : e ." | null |
Question: when positive integer n is divided by 7 , the remainder is 1 . when n is divided by 11 , the remainder is 5 . what is the smallest positive integer k such that k + n is a multiple of 77 ?
A.2.
B.4.
C.6.
D.8.
e ) 10C.
"n = 7 p + 1 = 11 q + 5 n + 6 = 7 p + 7 = 11 q + 11 n + 6 is a multiple of 7 and 11 , so it is a multiple of 77 . the answer is c ." | null |
Question: a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 29 m * 2 m * 0.75 m ?
A.29000.
B.27908.
C.78902.
D.25000.
e ) 27991A.
"29 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 29 = 1 / 100 * x = > x = 29000 answer : a" | null |
Question: on a map , 1 inch represents 28 miles . how many b inches would be necessary to represent a distance of 383.6 miles ?
A.5.2.
B.7.4.
C.13.7.
D.21.2.
e ) 28.7C.
b inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c | null |
Question: a worker is paid a regular rate of rs . 30 for completing a survey . the worker completes 100 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 20 % higher than her regular rate . if she completed 50 surveys involving the use of her cellphone , how much did she get that week ?
A.2200.
B.1100.
C.2500.
D.2800.
e ) 3300E.
"amount earned using her cell phone = 50 * 36 = 1800 earned for remaining surveys = 50 * 30 = 1500 total earning = 3300 answer : e" | null |
Question: a man goes from a to b at a speed of 20 kmph and comes back to a at a speed of 30 kmph . find his average speed for the entire journey ?
A.11.
B.24.
C.55.
D.66.
e ) 71B.
"distance from a and b be ' d ' average speed = total distance / total time average speed = ( 2 d ) / [ ( d / 20 ) + ( d / 30 ) ] = ( 2 d ) / [ 5 d / 60 ) = > 24 kmph . answer : b" | null |
Question: find the maximum value of the function f ( x ) = x β 5 if x is a number between - 5 and 13 .
A.6.
B.7.
C.8.
D.9.
e ) noneC.
solution : since f ( x ) is a linear function whose slope is 1 , a positive number , it is strictly increasing for all x . therefore its maximal value is reached for the largest value of x , x = 13 and f ( x ) = 13 - 5 = 8 . answer c | null |
Question: a shopkeeper sold 30 articles at the cost price of 35 articles . then find the profit % or lost %
A.12 %.
B.15 %.
C.16.67 %.
D.18 %.
e ) 22 %C.
"here 30 articles selling price = 35 articles cost price so the difference = 35 - 30 = 5 % of profit = 5 * 100 / 30 = 16.67 % correct option is c" | null |
Question: a cycle is bought for rs . 900 and sold for rs . 1140 , find the gain percent ?
A.11.
B.27.
C.99.
D.77.
e ) 18B.
"900 - - - - 240 100 - - - - ? = > 27 % answer : b" | null |
Question: the average of 5 quantities is 12 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
A.24.
B.10.
C.8.
D.9.5.
e ) none of theseA.
"answer : a ( 5 x 12 - 3 x 4 ) / 2 = 24" | null |
Question: a trained covered x km at 30 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
A.22.5.
B.99.
C.24.
D.66.
e ) 887A.
"total time taken = x / 30 + 2 x / 20 hours = 2 x / 15 hours average speed = 3 x / ( 2 x / 15 ) = 22.5 kmph answer : a" | null |
Question: the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 28,000 is made ?
A.328897.
B.120000.
C.877888.
D.124000.
e ) 188871D.
"the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 28,000 is made = 96,000 + 28,000 = rs . 1 , 24,000 answer : d" | null |
Question: if | 20 x - 10 | = 130 , then find the product of the values of x ?
A.- 45.
B.50.
C.- 42.
D.35.
e ) - 30C.
"| 20 x - 10 | = 130 20 x - 10 = 130 or 20 x - 10 = - 130 20 x = 140 or 20 x = - 120 x = 7 or x = - 6 product = - 6 * 7 = - 42 answer is c" | null |
Question: gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 60 and the turban . find the price of the turban .
A.27.
B.30.
C.29.
D.10.
e ) 11B.
"let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 60 . thus , 3434 ( 90 + x ) = 60 + x or 270 + 3 x = 240 + 4 x or x = 30 answer : b" | null |
Question: find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 1450 ?
A.rs . 1000.
B.rs . 1250.
C.rs . 1010.
D.rs . 10000.
e ) none of theseB.
"explanation : 1450 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1250 answer : option b" | null |
Question: how many seconds will a 600 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
A.25.
B.36.
C.40.
D.45.
e ) 50B.
"relative speed of the train = 63 - 3 = 60 kmph = 60 * 5 / 18 = 50 / 3 m / sec t = 600 * 3 / 50 = 36 sec answer : b" | null |
Question: a ship 450 m long is running at a speed of 24 km / hr . in what time will it pass a bridge 900 m long ?
A.202.5 sec.
B.205.5 sec.
C.200 sec.
D.1350 sec.
e ) 900 secA.
total length = 450 + 900 = 1350 speed = 24 km / h = ( 24 * 5 ) / 18 = 20 / 3 m / s time = ( 1350 * 3 ) / 20 = 202.5 sec . answer : a | null |
Question: at company x , senior sales representatives visit the home office once every 12 days , and junior sales representatives visit the home office once every 8 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?
A.10 %.
B.25 %.
C.33 %.
D.50 %.
e ) 67 %D.
"each 24 - day period , senior representatives visit the home office 2 times while junior representatives visit 3 times , thus 50 % more . the answer is d ." | null |
Question: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 40 is a prime number , when each of the given numbers is equally likely to be selected ?
A.10 / 40.
B.12 / 40.
C.8 / 40.
D.3 / 40.
e ) 7 / 40B.
"let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23,29 , 31,37 } n ( x ) = 12 , n ( s ) = 40 hence , the required probability is 12 / 40 . answer : b" | null |
Question: john can complete a given task in 10 days . jane will take only 20 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 4 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
A.8.
B.9.
C.8.5.
D.9.5.
e ) 10.5C.
"in such questions , you need to start from the end . last 4 days john works alone and completes 4 * ( 1 / 10 ) = 2 / 5 of the work . so 3 / 5 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 20 + 1 / 12 = 8 / 60 time taken to complete 4 / 5 of the work = ( 3 / 5 ) / ( 8 / 60 ) = 9 / 2 days . so total number of days taken to complete the work = 9 / 2 + 4 = 8.5 days . c" | null |
Question: find the sum the difference between the compound and s . i . on a certain sum of money for 5 years at 20 % per annum is rs . 75 of money ?
A.1489.
B.6845.
C.2598.
D.1875.
e ) 2600D.
"p = 75 ( 100 / 20 ) 5 = > p = 1875 answer : d" | null |
Question: p has $ 32 more than what q and r together would have had if both b and c had 1 / 6 of what p has . how much does p have ?
A.$ 44.
B.$ 48.
C.$ 52.
D.$ 56.
e ) $ 60B.
"p = ( 2 / 6 ) * p + 32 ( 4 / 6 ) * p = 32 p = 48 the answer is b ." | null |
Question: a salt manufacturing company produced a total of 2000 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 ?
A.80.
B.85.
C.83.
D.95.
e ) 00C.
"total production of salt by the company in that year = 2000 + 2100 + 2200 + . . . . + 3100 = 30600 . average monthly production of salt for that year = 30600 / 365 Γ’ β° Λ 84 answer : c" | null |
Question: how many terminating zeroes e does 200 ! have ?
A.40.
B.48.
C.49.
D.55.
e ) 64C.
you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c | null |
Question: the average age of a group of n people is 14 years old . one more person aged 32 joins the group and the new average is 16 years old . what is the value of n ?
A.5.
B.6.
C.7.
D.8.
e ) 9D.
"14 n + 32 = 16 ( n + 1 ) 2 n = 16 n = 8 the answer is d ." | null |
Question: a 75 - liter solution of cool - drink is made from 8 % jasmine water . if 3 liters of jasmine and 12 liters of water were added to the solution , what percent of the solution is jasmine ?
A.10.3 %.
B.11.5 % ..
C.10 % ..
D.12.2 %.
e ) 12 % .C.
"denominator 75 + 3 + 12 90 numerator 75 * 0.08 = 6 - - - > jasmine water 6 + 3 = 9 - - - > new content of jasmine water in new solution ratio 9 / 90 answer : c" | null |
Question: the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 216 . find the principal ?
A.2277.
B.2667.
C.5400.
D.2766.
e ) 1811C.
"p = 216 ( 100 / 5 ) ^ 2 = > p = 5400 answer : c" | null |
Question: a train running at the speed of 60 km / hr crosses a pole in 15 sec . what is the length of the train ?
A.287.
B.699.
C.250.
D.168.
e ) 150C.
"speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 12 = 250 m answer : c" | null |
Question: rewrite ( 10 ^ 38 ) β 85 as a base 10 integer , what is the sum of the digits in that integer ?
A.354.
B.357.
C.330.
D.370.
e ) 360C.
we know that ( 10 ^ 38 ) is ending 00 , so ( 10 ^ 38 ) β 85 = 9 . . . . 9915 total number of digits in ( 10 ^ 38 ) β 85 is 38 , or 36 digits of 9 and two digits 1 and 5 . answer choice is 36 * 9 + 6 = 330 answer is c 330 | null |
Question: he average of 10 numbers is 23 . if each number is increased by 4 , what will the new average be ?
A.26.
B.27.
C.88.
D.99.
e ) 12B.
sum of the 10 numbers = 230 if each number is increased by 4 , the total increase = 4 * 10 = 40 the new sum = 230 + 40 = 270 the new average = 270 / 10 = 27 . answer : b | null |
Question: a man buy a book in rs 50 & sale it rs 70 . what is the rate of profit ? ? ?
A.10 %.
B.40 %.
C.30 %.
D.25 %.
e ) 28 %B.
"cp = 50 sp = 70 profit = 70 - 50 = 20 % = 20 / 50 * 100 = 40 % answer : b" | null |
Question: a tank is filled by 3 pipes a , b , c in 6 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
A.25 hr.
B.42 hr.
C.40 hr.
D.20 hr.
e ) 50 hrB.
suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 6 7 / x = 1 / 6 x = 42 hours answer is b | null |
Question: first column specifies the no of days prior to departure information . second column specifies the percentage discount offered . 0 - 6 days = = > 0 % 7 - 13 days = = > 10 % 14 - 29 days = = > 25 % 30 days or more = = > 40 % the table above shows the discount structure for advanced purchase of tickets at a particular airline . a passenger bought a ticket at this airline for $ 1050 . the ticket agent informed her that , had she purchased the ticket one day later , she would have paid $ 210 more . how many days before her departure did she purchase her ticket .
A.6.
B.7.
C.13.
D.14.
e ) 29D.
first i figured out the percentage change from the immediate previous amount for each of the period . thus it comes - 0 - 6 days = = > 0 % 7 - 13 days = = > 10 % ( 90 % of the price ) 14 - 29 days = = > 17 % ( approx ) ( went from 90 % to 75 % ) 30 days or more = = > 20 % ( went from 75 % to 60 % ) if the passenger had to pay the extra amount , she had to pay = ( 210 + 1050 ) = 1260 now 210 is somehow between 10 % and 20 % of 1260 . so 17 % is the choice here . correct ans : 14 days answer : d | null |
Question: a no . when divided by 158 gives a remainder 50 , what remainder will be obtainedby dividingthe same no . 16 ?
A.10.
B.11.
C.12.
D.13.
e ) 14D.
"158 + 50 = 208 / 16 = 13 ( remainder ) d" | null |
Question: a man can row a distance of 6 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 20 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?
A.2.
B.8.
C.1.
D.6 : 41.
e ) 5D.
"explanation : he covered 6 km in 1 hour , so he might cover 20 km in 3 hours 19 minutes . but he took 10 hours . he would have saved 10 Γ’ β¬ β 3 hours 19 minutes = 6 hours 41 minutes . answer : d" | null |
Question: 1395 x 1395
A.1946025.
B.1981709.
C.18362619.
D.2031719.
e ) none of theseA.
"1395 x 1395 = ( 1398 ) 2 = ( 1400 - 2 ) 2 = ( 1400 ) 2 + ( 5 ) 2 - ( 5 x 1400 x 5 ) = 1946025 . answer : option a" | null |
Question: the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n ^ 3 / 3 + c * n ^ 2 + n / 6 , where c is a constant . what is the sum of the first 20 positive perfect squares ?
A.1,010.
B.1,164.
C.1,240.
D.2,316.
e ) 2,870E.
"first we need to find the constant ' c ' . the easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively . hence lhs = 1 + 4 and plug n = 2 for rhs and simplify to get c = 1 / 2 . plug values of n = 20 and c = 1 / 2 into the equation and simplify to get the answer 2870 . option e ." | null |
Question: a mixture of 70 litres of milk and water contains 10 % water . how many litres of water should be added to the mixture so that the mixture contains 12 1 / 2 % water ?
A.2.
B.8.
C.6.
D.3.
e ) 4A.
"a 2 quantity of milk in the mixture = 90 / 100 ( 70 ) = 63 litres . after adding water , milk would form 87 1 / 2 % of the mixture . hence , if quantity of mixture after adding x liters of water , ( 87 1 / 2 ) / 100 x = 63 = > x = 72 hence 72 - 70 = 2 litres of water must be added ." | null |
Question: if a = 2 , what is the value of β ( a ^ 2 + a ^ 3 + a ^ 4 + a ^ 5 ) ?
A.- 14.
B.- 60.
C.0.
D.4.
e ) 14B.
"if a = - 1 , then putting values in equation = - [ ( 2 ) ^ 2 + ( 2 ) ^ 3 + ( 2 ^ 4 ) + ( 2 ^ 5 ) ] = - [ 4 + 8 + 16 + 32 ] = - 60 answer = b = - 60" | null |
Question: how many even number in the range between 20 to 100 inclusive are not divisible by 3
A.28.
B.30.
C.31.
D.33.
e ) 46A.
"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 , 20 , 22,24 . . . 100 using ap formula , we can say 100 = 20 + ( n - 1 ) * 2 or n = 41 . for 6 , 24,36 . . . 96 using ap formu 24 la , we can say 96 = 24 + ( n - 1 ) * 6 or n = 13 . hence , only divisible by 2 but not 3 = 41 - 13 = 28 . hence , answer a" | null |
Question: a clock shows the time as 9 a . m . if the minute hand gains 7 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
A.30 min.
B.35 min.
C.63 min.
D.50 min.
e ) 55 minC.
"there are 9 hours in between 9 a . m . to 6 p . m . 9 * 7 = 63 minutes . answer : c" | null |
Question: how much interest will $ 10,000 earn in 9 months at an annual rate of 4 % ?
A.$ 300.
B.$ 350.
C.$ 450.
D.$ 550.
e ) $ 650A.
soln : - 9 months = 3 / 4 of year ; 4 % = 4 / 100 = 1 / 25 ; $ 10,000 ( principal ) * 1 / 25 ( interest rate ) * 3 / 4 ( time ) = $ 300 . answer : a | null |
Question: if the perimeter of a rectangular garden is 700 m , its length when its breadth is 100 m is ?
A.299 m.
B.777 m.
C.200 m.
D.250 m.
e ) 128 mD.
"2 ( l + 100 ) = 700 = > l = 250 m answer : d" | null |
Question: you have been given a physical balance and 7 weights of 40 , 42 , 36 , 33 , 47 , 52 and 67 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 169 kgs .
A.163.
B.166.
C.162.
D.164.
e ) 165E.
"67 + 52 + 47 = 166 answer : e" | null |
Question: the average of first five multiples of 7 is
A.21.
B.6.
C.9.
D.12.
e ) 15A.
"solution average = 7 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 105 / 5 . = 21 answer a" | null |
Question: a shopkeeper loses 15 % , if an article is sold for rs . 102 . what should be the selling price of the article to gain 20 % ?
A.rs . 146.
B.rs . 144.
C.rs . 129.
D.rs . 123.
e ) rs . 128B.
"given that sp = rs . 102 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 102 ) / 85 = 20 * 6 = rs . 120 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 120 * 120 ) / 100 = rs . 144 answer : b" | null |
Question: sum of the squares of 3 no . ' s is 62 and the sum of their products taken two at a time is 131 . find the sum ?
A.20.
B.24.
C.26.
D.18.
e ) 30D.
"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 62 + 2 * 131 a + b + c = β 324 = 18 d" | null |
Question: some persons can do a piece of work in 12 days . two times the number of these people will do half of that work in ?
A.3.
B.4.
C.5.
D.6.
e ) 8A.
"12 / ( 2 * 2 ) = 3 days answer : a" | null |
Question: how many multiples of 4 are there between 12 and 92 , inclusive ?
A.21.
B.22.
C.23.
D.24.
e ) 25A.
"the multiples of 4 are from 4 * 3 up to 4 * 23 . 23 - 3 + 1 = 21 . the answer is a ." | null |
Question: a metered rikshaw charges rs 13.50 for the first 1 km and 2.50 per 1 / 3 km there after . what would the charge if this rikshaw is hired for 13 kms ? in approx ? ?
A.103.5 rs.
B.104.5 rs.
C.105.5 rs.
D.106.5 rs.
e ) 107.5 rsA.
for 1 st km : rs . 13.50 ramaining distance : 13 - 1 = 12 km 1 / 3 km costs 2.5 rs 1 km costs ( 2.5 * 3 ) remaining 12 km costs ( 2.5 * 3 ) * 12 = 90 rs total cost = 90 + 13.5 = 103.5 rs answer : a | null |
Question: two pipes a and b separately fill in 15 / 2 min and 5 min respactively and third pipe c can empty of 14 l / m if all the pipes are open when the cistern is full , it is emptied in 1 hr . how many litres does the cistern hold ?
A.40.
B.30.
C.50.
D.80.
e ) 54A.
let total water in cistern = x liter speed of a = 2 x / 15 l / m ( speed = liter / time ) speed of b = x / 5 l / m speed of c = 14 l / m according to question x + ( x / 5 + 2 x / 15 ) * 60 = 60 * 14 x + = 60 * 14 x = 40 liter answer : a | null |
Question: if 4 men can colour 48 m long cloth in 2 days , then 6 women can colour 36 m long cloth in ?
A.day.
B.day.
C.days.
D.days.
e ) daysB.
"the length of cloth painted by one man in one day = 48 / 4 Γ 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 Γ 6 = 1 day . b )" | null |
Question: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a black card and the second card is a king ?
A.1 / 26.
B.1 / 13.
C.3 / 52.
D.3 / 26.
e ) 15 / 26A.
"p ( black card ) = 1 / 2 p ( king ) = 1 / 13 p ( black card then a king ) = 1 / 2 * 1 / 13 = 1 / 26 the answer is a ." | null |
Question: a fruit seller sells mangoes at the rate of rs . 12 per kg and thereby loses 10 % . at what price per kg , he should have sold them to make a profit of 15 % ?
A.rs . 11.81.
B.rs . 12.
C.rs . 15.33.
D.rs . 12.31.
e ) noneC.
"solution 90 : 12 = 115 : x x = ( 12 Γ£ β 115 / 90 ) = rs . 15.33 hence , s . p per kg = rs . 15.33 answer c" | null |
Question: working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 12 , 20 , and 20 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
A.4 / 11.
B.1 / 2.
C.15 / 22.
D.10 / 1.
e ) 11 / 4D.
"p 1 takes 12 hrs rate for p 2 p 3 together = 1 / 20 + 1 / 20 = 1 / 10 therefore they take 10 ratio = 10 / 1 = d" | null |
Question: two numbers have a h . c . f of 20 and a product of two numbers is 2560 . find the l . c . m of the two numbers ?
A.140.
B.150.
C.160.
D.128.
e ) 180D.
l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2560 / 20 = 128 . answer : d | null |
Question: a cylindrical bucket of height 36 cm and radius 21 cm is filled with sand . the bucket is emptied on the ground and a conical heap of sand is formed , the height of the heap being 12 cm . the radius of the heap at the base is :
['A.63 cm', 'B.53 cm', 'C.56 cm', 'D.66 cm', 'e ) none of these']A.
volume of the bucket = volume of the sand emptied volume of sand = Ο ( 21 ) 2 Γ 36 let r be the radius of the conical heap . then , 1 β 3 Ο r 2 Γ 12 = Ο ( 21 ) 2 Γ 36 or r 2 = ( 21 ) 2 Γ 9 or r = 21 Γ 3 = 63 answer a | null |
Question: a man opens a shop . he buys water bottles for 50 cents each , fruit for 25 cents each , and snacks for a dollar each . he wants to start a bundle of selling a bottle a water , 3 snacks and 2 fruits for d dollars . every 5 th bundle sold will be sold for 2 dollars and a complimentary snack at the owner ' s expense . what should he charge at least to not lose any money ?
A.4.6.
B.3.0.
C.4.1.
D.3.2.
e ) 2.9A.
w = 0.50 f = 0.25 s = 1.00 b = w + 2 f + 3 s = 4.00 they pay , he pays 4 , net loss 0 fifth bundle = 2 they pay , he pays 5 , net loss 3 dollars 3 / 5 = 60 cents . charging 60 more cents on each bundle will be safe . answer : a | null |
Question: there is 60 % increase in an amount in 6 years at simple interest . what will be the compound interest of $ 12,000 after 3 years at the same rate ?
A.$ 2160.
B.# 3120.
C.$ 3972.
D.$ 6240.
e ) none of theseC.
"let p = $ 100 . then , s . i . $ . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = $ 12000 . t = 3 years and r = 10 % p . a . c . i . = $ 12000 x 1 + 10 3 - 1 100 = $ 12000 x 331 1000 = 3972 answewr : c 3972" | null |
Question: a person is traveling at 75 km / hr and reached his destiny in 4 hr then find the distance ?
A.300 km.
B.200 km.
C.250 km.
D.400 km.
e ) 220 kmA.
"t = 4 hrs d = t * s = 75 * 4 = 300 km answer is a" | null |
Question: a can do a piece of work in 80 days . he works at it for 10 days & then b alone finishes the remaining work in 42 days . in how much time will a and b , working together , finish the work ?
A.30 days.
B.20 days.
C.25 days.
D.35 days.
e ) 45 daysA.
"work done by a in 10 days = 10 / 80 = 1 / 8 remaining work = ( 1 - ( 1 / 8 ) ) = 7 / 8 now , work will be done by b in 42 days . whole work will be done by b in ( 42 x 8 / 7 ) = 48 days therefore , a β s one day β s work = 1 / 80 b β s one day β s work = 1 / 48 ( a + b ) β s one day β s work = 1 / 80 + 1 / 48 = 8 / 240 = 1 / 30 hence , both will finish the work in 30 days . answer : a" | null |
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