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Question: if y > 0 , ( 6 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
A.40 %.
B.50 %.
C.60 %.
D.70 %.
e ) 80 %C.
"can be reduced to 3 y / 10 + 3 y / 10 = 3 y / 5 = 60 % c" | null |
Question: if the number is divided by 3 , it reduced by 36 . the number is
A.A.51.
B.B.50.
C.C.45.
D.D.54.
e ) e ) 36D.
"explanation : let the number be x . then , x - ( x / 3 ) = 36 = > 2 x / 3 = 36 = > x = 54 answer : option d" | null |
Question: 8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 10 men , 4 women and 30 children together complete the piece of work ?
A.5 days.
B.15 days.
C.28 days.
D.4 days.
e ) 7 daysD.
"explanation : 1 man β s 1 day β s work = 1 / 8 Γ 12 = 1 / 96 10 men β s 1 day β s work = 1 Γ 10 / 96 = 5 / 48 1 woman β s 1 day β s work = 1 / 192 4 women β s 1 day β s work = 1 / 192 Γ 4 = 1 / 48 1 child β s 1 day β s work = 1 / 240 30 children β s 1 day β s work = 1 / 8 therefore , ( 10 men + 4 women + 30 children ) β s 1 day β s work = 5 / 48 + 1 / 48 + 1 / 8 = 1 / 4 the required no . of days = 4 days answer : option d" | null |
Question: in a group of 150 readers who read science fiction or literacy works or both , 120 read science fiction and 90 read literacy works . how many read both science fiction and literacy works ?
A.70.
B.60.
C.90.
D.100.
e ) 110B.
consider total number of reader n ( s u l ) = 150 people who read science fiction n ( s ) = 120 people who read literacy works n ( l ) = 90 both science fiction and literacy n ( s Γ’ Λ Β© l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s Γ’ Λ Β© l ) 150 = 120 + 90 - n ( s Γ’ Λ Β© l ) n ( s Γ’ Λ Β© l ) = 210 - 150 n ( s Γ’ Λ Β© l ) = 60 so people read both science fiction and literacy works are 160 answer : b | null |
Question: the speed of a boat in still water in 30 km / hr and the rate of current is 7 km / hr . the distance travelled downstream in 36 minutes is :
A.18.4 km.
B.20.6 km.
C.21.4 km.
D.1111 km.
e ) 22.2 kmE.
"explanation : speed downstream = ( 30 + 7 ) = 37 kmph time = 36 minutes = 36 / 60 hour = 3 / 5 hour distance travelled = time Γ speed = ( 3 / 5 ) Γ 37 = 22.2 km answer : option e" | null |
Question: 39 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 3 hours a day , complete the work ?
A.10.
B.26.
C.14.
D.15.
e ) 16B.
"let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 39 : : 12 : x working hours / day 3 : 5 30 x 3 x x = 39 x 5 x 12 x = ( 39 x 5 x 12 ) / ( 30 x 3 ) x = 26 . answer : b" | null |
Question: in what time will two trains cross each other completely , which are running on the same parallel lines in opposite directions , each train running with a speed of 90 kmph being 160 m and 140 m in length respectively ?
A.5.6 sec.
B.6.2 sec.
C.6.0 sec.
D.7.2 sec.
e ) 6.8 secC.
"d = 160 m + 140 m = 300 m * 1 / 1000 = 0.3 kms rs = 90 + 90 = 180 kmph t = ( 0.3 / 180 ) * 3600 = 6.0 sec answer : c" | null |
Question: cole drove from home to work at an average speed of 80 kmh . he then returned home at an average speed of 120 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
A.66.
B.70.
C.72.
D.75.
e ) 78C.
"first round distance travelled ( say ) = d speed = 80 k / h time taken , t 2 = d / 80 hr second round distance traveled = d ( same distance ) speed = 120 k / h time taken , t 2 = d / 120 hr total time taken = 2 hrs therefore , 2 = d / 80 + d / 120 lcm of 80 and 120 = 240 2 = d / 80 + d / 120 = > 2 = 3 d / 240 + 2 d / 240 = > d = 240 * 2 / 5 km therefore , t 1 = d / 80 = > t 1 = ( 240 * 2 ) / ( 5 x 80 ) = > t 1 = ( 6 x 60 ) / 5 - - in minutes = > t 1 = 72 minutes . c" | null |
Question: the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 2 nd year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ?
A.36.
B.38.
C.40.
D.42.
e ) 48A.
"1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 thus for the 2 nd year = 50 , 3 rd year = 50 - 2 = 48 4 th year = 48 - 3 = 45 5 th year = 45 - 4 = 41 . 6 th year = 41 - 5 = 36 the correct answer is a ." | null |
Question: a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 25 % , what should be the sale price of the mixed tea ?
A.23.75.
B.22.
C.20.
D.19.20.
e ) none of theseC.
"c . p . of mixture = 80 Γ 15 + 20 Γ 20 / 80 + 20 = 16 β΄ s . p . = ( 100 + 25 ) / 100 Γ 16 = 20 answer c" | null |
Question: pipe a fills a tank of capacity 800 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?
A.48 minutes.
B.14 minutes.
C.39 minutes.
D.40 minutes 20 seconds.
e ) none of theseA.
"in one cycle they fill 40 + 30 - 20 = 50 liters 800 = 50 * n = > n = 16 here n = number of cycles . total time = 16 * 3 = 48 as in one cycle there are 3 minutes . thus 48 minutes answer : a" | null |
Question: in a dairy farm , 20 cows eat 10 bags of husk in 40 days . in how many days one cow will eat one bag of husk ?
A.20.
B.40.
C.80.
D.30.
e ) 60C.
"one cow eats 10 / 20 = 0.5 bags of husk in 40 days . then , it eats 1 bag in 40 / 0.5 = 80 days answer : c" | null |
Question: if w / x = 1 / 3 and w / y = 3 / 4 , then ( x + y ) / y =
A.13 / 4.
B.6 / 5.
C.7 / 5.
D.8 / 5.
e ) 9 / 5A.
"w / x = 1 / 3 = > x = 3 w and w / y = 3 / 4 = > y = ( 4 / 3 ) w ( x + y ) / y = ( 3 w + 4 / 3 w ) / ( 4 / 3 w ) = ( 13 / 3 w ) / ( 4 / 3 w ) = 13 / 4 correct option : a" | null |
Question: the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 24 minutes is
A.17.2 km.
B.7.2 km.
C.7.6 km.
D.17.6 km.
e ) 27.2 kmB.
"speed of a boat in still water = 15 km / hr speed of the current = 3 km / hr speed downstream = ( 15 + 3 ) = 18 km / hr distance travelled downstream in 24 minutes = ( 24 / 60 ) Γ 18 = ( 2 Γ 18 ) / 5 = 7.2 km answer is b" | null |
Question: a man is 20 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
A.11.
B.25.
C.27.
D.18.
e ) 91D.
"let the son ' s present age be x years . then , man ' s present age = ( x + 20 ) years . ( x + 20 ) + 2 = 2 ( x + 2 ) x + 22 = 2 x + 4 = > x = 18 . answer : d" | null |
Question: a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 193 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
A.8,208.
B.9,409.
C.11,424.
D.12,586.
e ) can not be determinedB.
"let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 193 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 193 ( x + y ) ( x - y ) = 193 193 is a prime number and thus it will be ( 97 + 96 ) * ( 97 - 96 ) . thus x = 97 and y = 96 x ^ 2 = 97 ^ 2 = 9409 the answer is b ." | null |
Question: a shopkeeper sold an article for rs 2564.36 . approximately what was his profit percent if the cost price of the article was rs 2400
A.4 %.
B.5 %.
C.6 %.
D.7 %.
e ) 8 %D.
"explanation : gain % = ( 164.36 * 100 / 2400 ) = 6.84 % = 7 % approx option d" | null |
Question: if d is the smallest positive integer such that 3150 multiplied by d is the square of an integer , then d must be
A.2.
B.5.
C.6.
D.7.
e ) 14E.
solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let β s start by prime factorizing 3150 . 3150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3150 itself is not a perfect square . ) we also are given that 3150 multiplied by d is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x d = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , d = 7 x 2 = 14 answer is e . | null |
Question: at garage sale , all of the prices of the items sold were different . if the price of a radio sold at the garage sale was both the 9 th highest price and the 35 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?
A.43.
B.28.
C.44.
D.49.
e ) 46A.
8 + 34 + 1 = 43 answer : a | null |
Question: excluding the stoppages , the speed of a bus is 12 km / hr and including the stoppages the speed of the bus is 6 km / hr . for how many minutes does the bus stop per hour ?
A.15 min.
B.30 min.
C.12 min.
D.20 min.
e ) 18 minB.
"speed of the bus without stoppage = 12 km / hr speed of the bus with stoppage = 6 km / hr difference in speed = 6 km / hr so , the time taken in the stoppages = time taken to cover 6 km = ( 6 / 12 ) hr = 1 / 2 hr = 30 min answer : b" | null |
Question: the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 14 kmph ?
A.53.03.
B.50.01.
C.23.23.
D.24.23.
e ) 41.23A.
"distance covered in 1 min = ( 14 * 1000 ) / 60 = 233.33 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 233.33 / 4.4 = 53.03 answer : a" | null |
Question: in a park there are two ponds with both brown ducks and green ducks . in the smaller pond there are 45 ducks and in the larger pond there are 55 ducks . if 20 % of the ducks in the smaller pond are green and 40 % of the ducks in the larger pond are green , then what percentage of ducks are green ?
A.25 %.
B.27 %.
C.29 %.
D.31 %.
e ) 33 %D.
"number of ducks in small pond = 45 green ducks in small pond = 20 % of 45 = 9 ducks number of ducks in large pond = 55 green ducks in large pond = 40 % of 55 = 22 ducks total number of ducks = 45 + 55 = 100 total number of green ducks = 9 + 22 = 31 ducks percentage of green ducks = 31 / 100 * 100 = 31 % answer : d" | null |
Question: rice weighing 35 / 2 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )
A.40.
B.50.
C.60.
D.70.
e ) 80D.
35 / 2 Γ· 4 = 35 / 8 pounds in each container 35 / 8 pounds * 16 ounces / pound = 70 ounces in each container the answer is d . | null |
Question: what is the sum of the greatest common factor and the lowest common multiple of 12 and 48 ?
A.20.
B.60.
C.40.
D.56.
e ) 20B.
"prime factorization of 12 = 2 x 2 x 3 prime factorization of 48 = 2 x 2 x 2 x 2 x 3 gcf = 12 lcm = 48 sum = 60 ans : b" | null |
Question: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 10 . if the company β s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
A.$ 3000.
B.$ 1,350.
C.$ 1,725.
D.$ 2,050.
e ) $ 2,250A.
"total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 10 $ then total value is 300 * 10 = 3000 . imo option a is correct answer . ." | null |
Question: ashok secured average of 74 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
A.66.
B.74.
C.78.
D.80.
e ) none of theseB.
"explanation : number of subjects = 6 average of marks in 6 subjects = 74 therefore total marks in 6 subjects = 74 * 6 = 444 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 444 β 370 = 74 answer b" | null |
Question: susan made a block with small cubes of 5 cubic cm volume to make a block 7 small cubes long , 7 small cubes wide and 6 small cubes deep . she realise that she has used more small cubes than she really needed . she realised that she could have glued a fewer number of cubes together ot look like a block with same dimensions , if it were made
['A.194', 'B.195', 'C.196', 'D.197', 'e ) 198']A.
volume of cube of dimensions 7 7 6 is 7 * 7 * 6 = 294 if it were to look hollow the imaginary inside cube volume is to be deducted which is ( 7 - 2 ) * ( 7 - 2 ) * ( 6 - 2 ) = 100 ( here 2 is deducted because the inside cube which has to be hollow is 2 cubes more on every dimension ) so minimum number of cubes required to make hollow cube is 294 - 100 = 194 cubes answer : a | null |
Question: in a dairy farm , 55 cows eat 55 bags of husk in 55 days . in how many days one cow will eat one bag of husk ?
A.34 days.
B.40 days.
C.46 days.
D.50 days.
e ) 55 daysE.
"explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 55 bags 55 1 ] : : 55 : x = > x β 55 β 1 = 55 β 1 β 55 = > x = 55 option e" | null |
Question: today joelle opened an interest - bearing savings account and deposited $ 10,000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?
A.$ 12025.
B.$ 11075.
C.$ 11025.
D.$ 11095.
e ) $ 11015C.
"interest for 1 st year = 10000 * 5 / 100 = 500 interest for 2 nd year = 10500 * 5 / 100 = 525 total = 10000 + 500 + 525 = 11025 answer : c" | null |
Question: what is the prime factors β number of 18 ?
A.2.
B.3.
C.4.
D.5.
e ) 6B.
"prime factors β number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 24 = 2 ^ 1 * 3 ^ 2 prime factors β number will be 1 + 2 = 3 . hence , answer is b ." | null |
Question: a sum of money at simple interest amounts to $ 645 in 3 years and to $ 690 in 4 years . the sum is :
A.$ 153.
B.$ 510.
C.$ 598.
D.$ 549.
e ) $ 675B.
"b $ 510 s . i . for 1 year = $ ( 690 - 645 ) = $ 45 . s . i . for 3 years = $ ( 45 x 3 ) = $ 135 . principal = $ ( 645 - 135 ) = $ 510 ." | null |
Question: john and david can finish a job together in 4 hours . if john can do the job by himself in 5 hours , what percent of the job does david do ?
A.20 %.
B.25 %.
C.24 %.
D.23 %.
e ) 22 %A.
"you can also plug in numbers . for example , bob and alice work at a donut factory and make 20 donuts which is the job ( i picked this as a smart number ) . john on his own works 20 / 5 = 4 donuts per hour . john and david work 20 / 4 = 5 donuts per hour so david works 1 donuts / hour to find out the percentage , david works 1 donuts / hr x 4 hours = 4 donuts per hour . therefore 4 donuts / 20 donuts = 1 / 5 = 20 % answer : a" | null |
Question: a tank is filled in 10 hours by 3 pipes a , b and c . the pipe c is twice as fast as b and b is twice as fast as a . how much time will pipe a alone take to fill the tank ?
A.70 hours.
B.30 hours.
C.35 hours.
D.50 hours.
e ) 60 hoursA.
1 / a + 1 / b + 1 / c = 1 / 10 ( a , b and c 1 hour work ) given . . 1 / b = 2 / a and 1 / c = 2 / b = 4 / a hence 1 / a + 2 / a + 4 / a = 1 / 10 on solving . . . . we get 1 / a = 1 / 70 ( work done by a in 1 hour ) therefore time taken by a is 70 hours to finish the whole work answer : a | null |
Question: in a certain production lot , 40 percent of the toys are red and the remaining toys are green . half of toys are small and half are large . if 10 percent of the toys are red and small , and 40 toys are green and large . how many of the toys are red and large ?
A.40.
B.60.
C.70.
D.80.
e ) 90B.
40 % toys are red . 50 % toys are small - 50 % are large red and small - 10 % red and large must be 30 % ( since there are total 40 % red toys ) but 50 % toys are large . if 30 % are red and large , the rest 20 % large toys must be green . so large and green toys are 20 % . these 20 % large and green toys are actually 40 so total number of toys must be 200 . since red and large toys are 30 % , they must be 60 . answer : b | null |
Question: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4030 , r will receive
A.600.
B.780.
C.800.
D.900.
e ) none of theseB.
"explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4030 * ( 6 / 31 ) = 130 * 6 = 780 . answer : option b" | null |
Question: a train 150 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
A.5 seconds.
B.6 seconds.
C.9 seconds.
D.8 seconds.
e ) 7 secondsC.
"relative speed of train and man = 60 kmph or 300 / 18 m / s time taken by the train to pass the man : length of the train / relative speed 150 / 300 / 18 = 9 seconds . answer : c" | null |
Question: mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 11 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
A.10.
B.11.
C.12.
D.13.
e ) 14C.
if n = 12 mark sold 1 box and ann sold 10 boxes total 11 < 12 answer : c | null |
Question: in a forest 10 rabbits were caught , tagged with electronic markers , then released . a month later , 10 rabbits were captured in the same forest . of these 10 rabbits , it was found that 2 had been tagged with the electronic markers . if the percentage of tagged rabbits in the second sample approximates the percentage of tagged rabbits in the forest , and if no rabbits had either left or entered the forest over the preceding month , what is the approximate number of rabbits in the forest ?
A.150.
B.70.
C.50.
D.1500.
e ) 500C.
given that 10 rabbits were caught and tagged in the first sample , and 10 were caught in the second sample of which 2 had tags , then 2 / 10 approximates the fraction of the population of tagged rabbits in the forest . proportion : a / x = c / d a = rabbits tagged first sample c / d = the fraction of the population of tagged rabbits in the forest x = the population of rabbits in the forest proportion : 10 / x = 1 / 5 x = ( 1 ) ( 10 ) ( 5 ) = 50 . there are approximately 50 rabbits in the forest . answer is c | null |
Question: a man ' s speed with the current is 18 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is ?
A.10.
B.18.
C.50.
D.30.
e ) 40B.
"man ' s speed with the current = 18 km / hr = > speed of the man + speed of the current = 18 km / hr speed of the current is 2.5 km / hr hence , speed of the man = 18 - 2.5 = 20.5 km / hr man ' s speed against the current = speed of the man - speed of the current = 20.5 - 2.5 = 18 km / hr answer is b ." | null |
Question: train a leaves the station traveling at 30 miles per hour . two hours later train Π² leaves the same station traveling in the same direction at 45 miles per hour . how many miles from the station was train a overtaken by train b ?
A.100.
B.120.
C.140.
D.160.
e ) 180E.
"after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 15 miles per hour . the time to catch up is 60 / 15 = 4 hours . in 4 hours , train a travels another 30 * 4 = 120 miles for a total of 180 miles . the answer is e ." | null |
Question: if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units g digit of ( a + 2 ) ^ 2 ?
A.1.
B.3.
C.5.
D.6.
e ) c . 14A.
"i also got a . by punching in numers : g . . . 7 ^ 2 = . . . 9 . . . 8 ^ 2 = . . . 4 . . . 9 ^ 2 = . . . 1 . a" | null |
Question: a distributor sells a product through an on - line store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 30 % profit on the cost of the item ?
A.18.
B.21.6.
C.22.
D.25.7.
e ) 27D.
"producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 30 % of the final price - - > ( final price ) * 0.7 = $ 18 - - > ( final price ) = $ 25.7 . answer : d ." | null |
Question: micheal and adam can do together a piece of work in 20 days . after they have worked together for 15 days micheal stops and adam completes the remaining work in 10 days . in how many days micheal complete the work separately .
A.40 days.
B.100 days.
C.120 days.
D.110 days.
e ) 90 daysA.
"rate of both = 1 / 20 together they do = 1 / 20 * 15 = 3 / 4 left work = 1 - 3 / 4 = 1 / 4 adam completes 1 / 4 work in 10 day so he took 10 * 4 = 40 days to complete the left work alone . thus the rate of adam is 40 / 1 rate of micheal = 1 / 20 - 1 / 40 = 1 / 40 thus micheal takes 40 days to complete the whole work . ans . a ." | null |
Question: pipe a can fill a tank in 6 hours . due to a leak at the bottom , it takes 10 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
A.13.
B.17.
C.15.
D.19.
e ) 12C.
"let the leak can empty the full tank in x hours 1 / 6 - 1 / x = 1 / 10 = > 1 / x = 1 / 6 - 1 / 10 = ( 5 - 3 ) / 30 = 2 / 30 = 1 / 15 = > x = 15 . answer : c" | null |
Question: rs . 1581 is divided among a , b and c in the ratio 10 : 15 : 6 . what is the share of b ?
A.306.
B.765.
C.700.
D.510.
e ) 520A.
"10 + 15 + 6 = 31 1581 / 31 = 51 so b ' s share = 15 * 51 = 765 a ' s share = 10 * 51 = 510 c ' s share = 6 * 51 = 306 answer : a" | null |
Question: employees of a certain company are each to receive a unique 10 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 9 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
A.145,660.
B.149,720.
C.155,420.
D.161,280.
e ) 167,480D.
"there are 8 ! ways to make codes starting with 12 . there are 8 ! ways to make codes starting with 24 . there are 8 ! ways to make codes starting with 36 . there are 8 ! ways to make codes starting with 48 . the number of codes is 4 * 8 ! = 161,280 . the answer is d ." | null |
Question: how many terminating zeroes w 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: two trains 500 m and 750 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
A.10.6.
B.45.
C.10.4.
D.10.8.
e ) 10.1B.
"relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 500 + 750 = 1250 m . required time = 1250 * 9 / 250 = 45 sec . answer : b" | null |
Question: a train 110 m long is running with a speed of 36 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
A.5.
B.6.
C.7.
D.9.
e ) 5D.
"speed of train relative to man = 36 + 6 = 42 km / hr . = 42 * 5 / 18 = 35 / 3 m / sec . time taken to pass the men = 110 * 3 / 35 = 9 sec . answer : d" | null |
Question: if x + y = 3 and y / x = 2 then y = ?
A.0.
B.1 / 2.
C.1.
D.3 / 2.
e ) 2E.
"from the given data : y / ( 3 - y ) = 2 = > y = 6 - 2 y = > y = 2 answer : e" | null |
Question: tough and tricky questions : remainders . 1 ^ 1 + 2 ^ 2 + 3 ^ 3 + . . . + 7 ^ 7 is divided by 7 . what is the remainder ?
A.0.
B.1.
C.2.
D.3.
e ) 4E.
a number is divisible by 5 , if its last digit is divisible by 5 let ' s look into the sum of last digits of each term of the given expression 1 ^ 1 = 1 2 ^ 2 = 4 3 ^ 3 = 7 4 ^ 4 = 6 5 ^ 5 = 5 6 ^ 6 = 6 7 ^ 7 = 3 adding all these numbers we get 32 which gives a remainder of 4 when divided by 7 . so answer must be 4 . bunuel , can you please confirm the answer of this question . yes , the oa is c . clicked the wrong button when posting . edited . thank you . e | null |
Question: a sells a bicycle to b and makes a profit of 50 % . b sells the same bicycle to c at a profit of 25 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .
A.237.
B.126.
C.971.
D.611.
e ) 120E.
"explanation : let cp be 100 a sells at 50 % profit so sp = 150 b sells at 25 % profit = 150 x ( 1 + 25 / 100 ) = 187.50 cp - - - sp 100 - - - 187.50 x - - - 225 cp = 225 x 100 / 187.50 = 120 answer : e" | null |
Question: what is the units digit of ( 147 ^ 17 ) ^ 47 ?
A.1.
B.3.
C.5.
D.7.
e ) 9B.
the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 17 has the form 4 n + 1 so the units digit is 7 inside the bracket . the exponent 47 has the form 4 n + 3 , so the units digit is 3 . the answer is b . | null |
Question: how many times digit 5 is used while writing numbers from 100 to 1000 ?
A.648.
B.300.
C.252.
D.225.
e ) 290E.
"there are 100 numbers which begin with 600 next , in every 10 numbers such as 100 to 110 , 110 to 120 , 120 to 130 5 comes at least once . number of such intervals = end limit - first no . / interval . our range of numbers is 100 - 1000 1000 - 100 = 900 / 10 = 90 number of 10 s interval in this is 90 . so 90 ' 6 s ' so far we have calculated 190 . the total now comes to 280 . the nearest to which is 290 . hence e ." | null |
Question: one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 90,000 as total savings , how much has he saved in public provident fund ?
A.80000.
B.60000.
C.50000.
D.76000.
e ) 90000D.
"let savings in n . s . c and p . p . f . be rs . x and rs . ( 190000 - x ) respectively . then , = 1 / 3 x = 1 / 2 ( 190000 - x ) = x / 3 + x / 2 = 95000 = 5 x / 6 = 95000 = x = 95000 x 6 / 5 = 114000 savings in public provident fund = rs . ( 190000 - 114000 ) = rs . 76000 answer is d" | null |
Question: average marks of a , b , c is 48 . when d joins average becomes 47 . e has 3 more marks than d . average marks of b , c , d , e is 48 . what is the marks of a ?
A.43.
B.44.
C.45.
D.46.
e ) 47A.
a + b + c = 144 a + b + c + d = 188 d = 44 e = 47 b + c + d + e = 192 b + c = 101 a = 43 answer : a | null |
Question: a sum of money at simple interest amounts to rs . 720 after 2 years and to rs . 1020 after a further period of 5 years . the sum is :
A.400.
B.500.
C.600.
D.700.
e ) 800C.
"si of 5 year = ( 1020 - 720 ) = 300 so , si of 1 year = 300 / 5 = 60 so , si of 2 year = 60 * 2 = 120 so , sum is = ( 720 - 120 ) = 600 answer : c" | null |
Question: 3 candidates in an election and received 3136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate got in that election ?
A.45 %.
B.49 %.
C.52 %.
D.59 %.
e ) 61 %C.
"total number of votes polled = ( 3136 + 7636 + 11628 ) = 22400 so , required percentage = 11628 / 22400 * 100 = 52 % c" | null |
Question: two pipes p and q can fill a cistern in 12 and 15 minutes respectively . both are opened together , but at the end of 2 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
A.8.5.
B.9.5.
C.10.5.
D.11.5.
e ) 12.5C.
"let x be the total time it takes for the cistern to fill . 2 / 12 + x / 15 = 1 x / 15 = 5 / 6 x = 12.5 after the first pipe is turned off , it takes 10.5 more minutes to fill the cistern . the answer is c ." | null |
Question: 864.942 - ? + 45.76 = 547.905
A.A.899.015.
B.B.752.804.
C.C.714.642.
D.D.362.797.
e ) of theseD.
"explanation : 362.797 answer : option d" | null |
Question: the l . c . m . of 2 numbers is 66 . the numbers are in the ratio 2 : 3 . find their sum ?
A.36.
B.40.
C.48.
D.32.
e ) 55E.
"let the numbers be 2 x and 3 x l . c . m . = 6 x 6 x = 66 x = 11 the numbers are = 22 and 33 required sum = 22 + 33 = 55 answer is e" | null |
Question: a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x β 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number g of people surveyed by the company ?
A.46.
B.g = 80.
C.g = 90.
D.g = 100.
e ) 200D.
"100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ." | null |
Question: the product x of two prime numbers is between 17 and 55 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 11 but less than 25 , then x =
A.18.
B.29.
C.37.
D.44.
e ) 65E.
"option bc can be ruled out as they themselves are prime numbers 18 = 2 * 9 = 3 * 6 > > ignore 44 = 2 * 22 = 4 * 11 > > ignore 65 = 5 * 13 > > answer answer = e" | null |
Question: a train traveling at 72 kmph crosses a platform in 33 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?
A.240 meters.
B.360 meters.
C.420 meters.
D.300 meters.
e ) can not be determinedD.
"speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 33 = 660 m . so , length of platform = 660 - 360 = 300 m imo , answer d" | null |
Question: lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 84,000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
A.0.20833.
B.0.14544.
C.0.25632.
D.0.35466.
e ) 0.63435A.
"total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 384000 x \ therefore required percentage = \ inline \ frac { 800 x } { 384000 } \ times 100 = 0.20833 a" | null |
Question: the weights of one liter vegetable ghee packet of two brands β a β and β b β are 800 gm and 850 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 3 liters , what is the weight ( in kg ) of the mixture ?
A.3.84.
B.1.75.
C.3.52.
D.2.46.
e ) none of theseD.
"here ' s how i did it . my notes from reading the problem were : 1 l a = 800 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 3 l , so 5 x = 3 - - - > x = 3 / 5 . each part is 3 / 5 of a liter . so if we have 3 parts a , we have 800 * 3 * ( 3 / 5 ) = 1440 if we have 2 parts b , we have 850 * 2 * ( 3 / 5 ) = 1020 1440 + 1020 = 2460 solving for units gives us 2.46 so the answer is d" | null |
Question: if 4 xz + yw = 10 and xw + yz = 20 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
A.9 ..
B.12 ..
C.15 ..
D.50 ..
e ) 18 .D.
"( 2 x + y ) * ( 2 z + w ) = 10 + 2 ( 20 ) = 50 answer : d" | null |
Question: $ 9,000 is deposited in a savings account that pays 14 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ?
A.$ 11304.12.
B.$ 12304.54.
C.$ 11604.14.
D.$ 10304.10.
e ) $ 9304.41D.
this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 14 / 2 = 7 % now , ca = 9000 ( 1 + 7 / 100 ) ^ 2 = $ 10304.10 hence answer is d | null |
Question: a certain bacteria colony doubles in size every day for 25 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat β s limit ?
A.6.33.
B.7.5.
C.10.
D.15.
e ) 24E.
"if there is one bacteria colony , then it will reach the limit of its habitat in 25 days . if there are two bacteria colonies , then in order to reach the limit of habitat they would need to double one time less than in case with one colony . thus colonies need to double 24 times . answer : e . similar questions to practice : hope it helps ." | null |
Question: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 10 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
A.10 %.
B.20 %.
C.21 %.
D.23 %.
e ) can not be determinedA.
answer : a . | null |
Question: if daily wages of a man is 4 times to that of a woman , how many men should work for 25 days to earn rs . 14400 ? given that wages for 40 women for 30 days are rs . 21600 .
A.12.
B.4.
C.6.
D.8.
e ) 20D.
explanation : wages of 1 woman for 1 day = 21600 / 40 Γ£ β 30 wages of 1 man for 1 day = 21600 Γ£ β 4 / 40 Γ£ β 30 wages of 1 man for 25 days = 21600 Γ£ β 4 Γ£ β 25 / 40 Γ£ β 30 number of men = 14400 / ( 21600 Γ£ β 4 Γ£ β 25 / 40 Γ£ β 30 ) = 144 / ( 216 Γ£ β 100 / 40 Γ£ β 30 ) = 8 answer : option d | null |
Question: jerry went to a shop and bought things worth rs . 20 , out of which 30 % went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?
A.14.
B.14.7.
C.21.3.
D.21.5.
e ) 21.7B.
total cost of the items he purchased = rs . 20 given that out of this rs . 20 , 30 % is given as tax = > total tax incurred = 30 % = rs . 30 / 100 let the cost of the tax free items = x given that tax rate = 6 % β΄ ( 20 β 30 / 100 β x ) 6 / 100 = 30 / 100 β 6 ( 20 β 0.3 β x ) = 30 β ( 20 β 0.3 β x ) = 5 β x = 20 β 0.3 β 5 = 14.7 b ) | null |
Question: 5005 - 5000 Γ· 10.00 = ?
A.0.5.
B.50.
C.5000.
D.4505.
e ) noneD.
"answer given expression = 5005 - 5000 Γ· 10.00 = 5005 - 500 = 4505 correct option : d" | null |
Question: machine a takes 50 hours to complete a certain job and starts that job at 6 am . after four hour of working alone , machine a is joined by machine b and together they complete the job at 1 pm . how long would it have taken machine b to complete the job if it had worked alone for the entire job ?
A.9.
B.88.88.
C.4.88.
D.2.88.
e ) 3.88E.
"let us assume total job = 100 units a finishes 100 units in 50 hrs ( given ) hence a ( working rate ) = 2 units / hr now given that a works for 4 hr ( so 8 units done ) then a and b finish total work in 7 hours . hence a and b finish 92 units in 3 hours . of these 3 x 2 = 6 units were done by a . hence b did 86 units in 3 hours . hence b ( working rate ) = 86 / 3 units / hr hence b takes 100 x 3 / 86 = 3.88 hours to complete the job . answer e ." | null |
Question: a random 10 - letter code is to be formed using the letters a , b , c , d , e , f , g , h , i and i ( only the β i β will be used twice ) . what is the probability that a code that has the two i β s adjacent to one another will be formed ?
A.1 / 10.
B.1 / 8.
C.1 / 5.
D.1 / 4.
e ) 1 / 2C.
total number of combinations possible = 10 ! / 2 ! 10 ! / 2 ! total favorable combinations = 9 ! 9 ! - we have considered the two is as one element . since we have two is , they can interchange their positions , without affecting the code . probability = 9 ! / ( 10 ! / 2 ! ) = 9 ! β 2 ! / 10 ! = 1 / 59 ! / ( 10 ! / 2 ! ) = 9 ! β 2 ! / 10 ! = 1 / 5 ans : c | null |
Question: at the end of the day , february 14 th , a florist had 90 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 15 of which were white and 10 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?
A.20 %.
B.75 %.
C.50 %.
D.33.3 %.
e ) 80 %D.
r + w + p = 90 s + l = 90 1 / 3 * 90 = 30 short - stemmed white = 15 short - stemmed pink = 10 = > short - stemmed red = 5 10 / p = 5 / r = > r = p / 2 , p = 2 r so total long stemmed = 60 and long stemmed red + long stemmed pink = 60 so long stemmed red / long stemmed = ? total white = 15 ( as no long stemmed white ) = > r + 2 r + 15 = 90 = > 3 r = 75 and r = 25 long stemmed r = 25 - 5 = 20 so long stemmed red / r = 20 / 60 = 33.3 % answer - d | null |
Question: the average salary / head of allthe workers in a workshop is rs . 1200 , if the average salary / head of 10 technician is rs . 1400 and the average salary / head of the rest is rs . 900 , the total no . of workers in the work - shop is ?
A.18.
B.17.
C.15.
D.19.
e ) 21B.
let the total number of workers be y . so sum of salary for all workers = sum of salary of 10 technician + sum of salary for other y - 10 workers . 10 x 1400 + 900 ( y - 10 ) = 1200 y β 14000 + 900 y - 9000 = 1200 y β 300 y = 5000 β΄ y = 17 so total number of workers = 17 b | null |
Question: two cubes have their volumes are in the ratio 1 : 27 . find the ratio of their surface area ?
['A.1 : 2', 'B.2 : 3', 'C.1 : 9', 'D.2 : 7', 'e ) 3 : 11']C.
let their edges be a and b then , a ^ 3 / b ^ 3 = 1 / 27 ( a / b ) ^ 3 = ( 1 / 3 ) ^ 3 a / b = 1 / 3 ratio of their surface areas = 6 a ^ 2 / 6 b ^ 2 = ( a / b ) ^ 2 = 1 / 9 = 1 : 9 answer is c | null |
Question: if the integer n has exactly 4 positive divisors , including 1 and n , how many positive divisors does n ^ 3 have ?
A.16.
B.11.
C.10.
D.20.
e ) 9A.
take the example of 6 . . . it has 4 positive divisors ( 1,2 , 3,4 ) now , take the example of 216 . . . it has 16 divisors . . so a is the ans | null |
Question: the number 181 can be written as sum of the squares of 2 different positive integers . what is the difference of these 2 different integers ?
A.3.
B.2.
C.1.
D.4.
e ) 5C.
"sum of the squares of 2 different positive integers = 181 10 ^ 2 + 9 ^ 2 = 181 now , differene of these 2 different integers = 10 - 9 = 1 ans - c" | null |
Question: if you roll a fair - sided die twice , what is the probability of getting a double ( 5,5 ) ?
A.1 / 24.
B.1 / 36.
C.1 / 12.
D.1 / 18.
e ) 1 / 3 !E.
"total no . in two dice ( 1,1 ) , ( 2,2 ) . . . . . ( 6 , ) total number of events = 6 * 6 total events of getting same pair ( 5,5 ) = 6 probability = 6 / 6 * 6 = 1 / 6 = 1 / 3 ! e" | null |
Question: a father and his son are waiting at a bus stop in the evening . there is a lamp post behind them . the lamp post , the father and his son stand on the same straight line . the father observes that the shadows of his head and his son β s head are incident at the same point on the ground . if the heights of the lamp post , the father and his son are 6 metres , 1.8 metres and 0.9 metres respectively , and the father is standing 2.1 metres away from the post , then how far ( in metres ) is the son standing from his father ?
A.0.9.
B.0.75.
C.0.6.
D.0.45.
e ) none of theseD.
explanation : l is the lamp post position , f is father and s is son β s position . x is the point where the shadow falls . ld = 0.9 = son β s height , lb = 1.8 = father β s height . so ab = 6 β 1.8 = 4.2 also bc = lf = 2.1 we observe that β abc ~ β ade ( two triangles are similar ) . hence , the corresponding sides are proportional . so , ab / ad = dc / de . 4.2 / 5.1 = 2.1 / de . de = 5.1 * 2.1 / 4.2 = 5.1 / 2 = 2.55 . ls = de = 2.55 fs = ls β lf = 2.55 β 2.1 = 0.45 . answer : d | null |
Question: a collection of books went on sale , and 2 / 3 of them were sold for $ 2.25 each . if none of the 40 remaining books were sold , what was the total amount received for the books that were sold ?
A.$ 160.
B.$ 150.
C.$ 280.
D.$ 200.
e ) $ 180E.
"if 40 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 80 books amount received for sold books = 80 * 2.25 = $ 180 answer : e" | null |
Question: a rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 5 per sq m ?
A.6500.
B.2779.
C.2779.
D.3900.
e ) 2781A.
"area = ( l + b Γ’ β¬ β d ) d ( 80 + 60 Γ’ β¬ β 10 ) 10 = > 1300 m 2 1300 * 5 = rs . 6500 answer : a" | null |
Question: at their respective rates , pump a , b , and c can fulfill an empty tank , or pump - out the full tank in 2 , 3 , and 6 hours . if a and b are used to pump - out water from the half - full tank , while c is used to fill water into the tank , in how many hours , the tank will be empty ?
A.2 / 3.
B.1.
C.3 / 4.
D.3 / 2.
e ) 2C.
rate of a = 1 / 2 tank / hour ; rate of b = 1 / 3 tank / hour ; rate of c = 1 / 6 tank / hour . combined rate when a and b are used to pump - out water , while c is used to fill water into the tank is 1 / 2 + 1 / 3 - 1 / 6 = 2 / 3 tank hour . so , to empty the full tank 3 / 2 hours ( reciprocal of rate ) are needed . to empty the half - full tank half of that time would be needed : 1 / 2 * 3 / 2 = 3 / 4 hours . answer : c . | null |
Question: a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 108 km downstream
A.5 hours.
B.4 hours.
C.3 hours.
D.2 hours.
e ) none of theseB.
"explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 108 km time taken = distance / speed = 108 / 27 = 4 hours . answer : option b" | null |
Question: company c sells a line of 25 products with an average retail price of $ 1,200 . if none of these products sells for less than $ 400 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?
A.12000.
B.13000.
C.14000.
D.15000.
e ) 16000A.
"the average price of 25 products is $ 1,200 means that the total price of 25 products is 25 * 1,200 = $ 30,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 400 each ( min possible ) . now , the remaining 14 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 14 items is $ 1,000 . thus the minimum possible value of 24 products is 10 * 400 + 14 * 1,000 = $ 18,000 . therefore , the greatest possible selling price of the most expensive product is $ 30,000 - $ 18,000 = $ 12,000 . answer : a ." | null |
Question: a man purchased earphone on friday . but he forgot how much it cost . the data he have are mean expenditure of all 7 days is 500 . expenditure on mon , tue , wed , thurs , sat , sun are 450600 , 400500 , 550300 . on friday he purchased 3 things one earphone , one pen and one notebook . pen cost 30 and notebook cost 50 . then what is cost of earphone ?
A.620.
B.530.
C.450.
D.470.
e ) 500A.
solution let expenditure on friday be x ( 450 + 600 + 400 + 500 + x + 550 + 300 ) / 7 = 500 2800 + x = 3500 x = 700 pen + notebook + earphone = 700 earphone = 700 - 80 = 620 answer a | null |
Question: what percent is 6 gm of 1 kg ?
A.1.5 %.
B.0.5 %.
C.0.6 %.
D.3.5 %.
e ) 4 %C.
"1 kg = 1000 gm 6 / 1000 Γ 100 = 600 / 1000 = 3 / 5 = 0.6 % c )" | null |
Question: a train 300 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
A.6 sec ..
B.7 sec ..
C.9 sec ..
D.18 sec ..
e ) noneD.
"solution speed of the train relative to man = ( 68 - 8 ) = 60 kmph = 60 x 5 / 18 = 50 / 3 m / sec . time taken by it to cover 300 m at ( 50 / 3 ) m / sec = ( 300 x 3 / 50 ) sec = 18 sec . answer d" | null |
Question: how many prime numbers are between 51 / 13 and 89 / 9 ?
A.0.
B.1.
C.2.
D.3.
e ) 4C.
"51 / 13 = 4 - 89 / 9 = 10 - prime numbers between 4 and 10 are 5 and 7 - sign signifies that the number is marginally less . answer c" | null |
Question: company c sells a line of 25 products with an average retail price of $ 1,400 . if none of these products sells for less than $ 420 , and exactly 10 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?
A.16000.
B.11400.
C.13200.
D.15400.
e ) 16800E.
"the average price of 25 products is $ 1,400 means that the total price of 25 products is 25 * 1,200 = $ 35,000 . next , since exactly 10 of the products sell for less than $ 1,000 , then let ' s make these 10 items to be at $ 420 each ( min possible ) . now , the remaining 14 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 14 items is $ 1,000 . thus the minimum possible value of 24 products is 10 * 420 + 14 * 1,000 = $ 18,200 . therefore , the greatest possible selling price of the most expensive product is $ 35,000 - $ 18,200 = $ 16,800 . answer : e" | null |
Question: a soccer team played 130 games and won 60 percent of them . how many games did it win ?
A.84.
B.94.
C.100.
D.125.
e ) 78E.
"60 % of 130 = x 0.60 * 130 = x 78 = x answer : e" | null |
Question: what least no . must be subtracted from 5026 so that remaining no . is divisible by 5 ?
A.3.
B.4.
C.5.
D.6.
e ) 1E.
explanation : on dividing 5026 by 5 we get the remainder 1 , so 1 should be subtracted option e | null |
Question: a gambler has won 40 % of his 40 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 70 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?
A.50.
B.60.
C.70.
D.80.
e ) 90D.
"let x be the number of additional games the gambler needs to play . 0.4 ( 40 ) + 0.7 x = 0.6 ( x + 40 ) 0.1 x = 8 x = 80 the answer is d ." | null |
Question: 50 % of a number is added to 200 , the result is the same number . find the number ?
A.300.
B.288.
C.400.
D.129.
e ) 281C.
"( 50 / 100 ) * x + 200 = x x / 2 + 200 = x x + 400 = 2 x x = 400 answer : c" | null |
Question: there is a square with side β a β and one octagon is inscribed in it . what will be perimeter of octagon .
['A.8 a / 3', 'B.7 a / 3', 'C.5 a / 3', 'D.a / 3', 'e ) 11 a / 3']A.
well if it ' s a regular octagon then it actually trisects each side of the square in which 1 / 3 of the lenght of the side of the square is the length of one side of the octagon . if any one has a doubt he can draw the figure and see it going this way lenght of a side of a octagon is a / 3 and thus perimeter would be 8 a / 3 . answer : a | null |
Question: when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction x of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution ?
A.11 / 14.
B.13 / 18.
C.4 / 7.
D.3 / 7.
e ) 3 / 14A.
"if we use variable for total votes there will be too many fractions to manipulate with , so pick some smart # : let set total # of votes is 18 . 2 / 9 of the votes on a certain resolution have been counted - - > 4 counted and 18 - 4 = 14 votes left to be counted ; 3 / 4 of those counted are in favor of the resolution - - > 3 in favor and 1 against ; ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18 * 2 / 3 = 12 people who voted against , so in the remaining 14 votes there should be 12 - 1 = 11 people who voted against . thus x = 11 / 14 of the remaining votes must be against . answer : a ." | null |
Question: the speed of the boat in still water in 12 kmph . it can travel downstream through 54 kms in 3 hrs . in what time would it cover the same distance upstream ?
A.8 hours.
B.6 hours.
C.4 hours.
D.5 hours.
e ) 9 hoursE.
"still water = 12 km / hr downstream = 54 / 3 = 18 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 18 / 2 = 6 km / hr so time taken in upstream = 545 / 6 = 9 hrs answer : e" | null |
Question: if shares of two persons in profits are rs . 400 and rs . 600 then ratio of their capitals is
A.3 : 4.
B.2 : 3.
C.4 : 3.
D.1 : 3.
e ) 1 : 2B.
"profit = time * capital so 400 : 600 = 2 : 3 answer : b" | null |
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