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Question: each light bulb at a hotel is either incandescent or fluorescent . at a certain moment , thirty percent of the incandescent bulbs are switched on , and eighty percent of the fluorescent bulbs are switched on . if 40 percent of all the bulbs are switched on at this moment , what percent of the bulbs that are switched on are incandescent ?
A.20 %.
B.40 %.
C.50 %.
D.60 %.
e ) 80 %D.
"let i be the number of incandescent bulbs . let f be the number of fluorescent bulbs . 0.3 i + 0.8 f = 0.4 ( i + f ) 0.4 f = 0.1 i f = 0.25 i this means that for every 4 incandescent bulbs , there is 1 fluorescent bulb . the percent of bulbs that are switched on which are incandescent is : 0.3 i / ( 0.3 i + 0.8 f ) = 0.3 i / ( 0.3 i + 0.8 * 0.25 i ) = 0.3 i / 0.5 i = 3 / 5 = 60 % . the answer is d ." | null |
Question: a train 300 m long is running at a speed of 99 km / hr . in what time will it pass a bridge 195 m long ?
A.17.
B.18.
C.19.
D.20.
e ) 21B.
"speed = 99 * 5 / 18 = 55 / 2 m / sec total distance covered = 300 + 195 = 495 m required time = 495 * 2 / 55 = 18 sec answer : b" | null |
Question: f ( x ) is a function such that f ( 2 x + 1 ) = 2 f ( x ) + 1 for all real numbers x and f ( 0 ) = 2 . find the value of f ( 3 ) .
A.10.
B.11.
C.12.
D.13.
e ) 14B.
f ( 2 x + 1 ) = 2 f ( x ) + 1 : given f ( 3 ) = 2 f ( 1 ) + 1 : x = 1 in a f ( 1 ) = 2 f ( 0 ) + 1 : x = 0 in a f ( 3 ) = 11 : substitute correct answer b | null |
Question: evaluate 28 % of 450 + 45 % of 260
A.232.
B.243.
C.252.
D.262.
e ) 282B.
"explanation : = ( 28 / 100 ) * 450 + ( 45 / 100 ) * 260 = 126 + 117 = 243 answer : option b" | null |
Question: what is the units digit of ( 44 ^ 4 ) ( 33 ^ 5 ) ( 21 ^ 6 ) ?
A.0.
B.2.
C.4.
D.6.
e ) 8E.
"the units digit of 44 ^ 4 is the units digit of 4 ^ 4 which is 6 . the units digit of 33 ^ 5 is the units digit of 3 ^ 5 which is 3 . the units digit of 21 ^ 6 is the units digit of 1 ^ 6 which is 1 . the units digit of 6 * 3 * 1 is 8 . the answer is e ." | null |
Question: the largest 4 digit number exactly divisible by 55 is ?
A.9935.
B.9939.
C.9944.
D.9955.
e ) 9960D.
"largest 4 - digit number = 9999 55 ) 9999 ( 181 9955 answer : d" | null |
Question: a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 2662 in 3 years . find the rate percent ?
A.23 %.
B.10 %.
C.32 %.
D.98 %.
e ) 31 %B.
"2420 - - - 242 100 - - - ? = > 10 % answer : b" | null |
Question: a car started running at a speed of 36 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey .
A.45 km.
B.76 km.
C.25 km.
D.15 km.
e ) 30 kmA.
"a 45 km the total distance covered by the car in the first 10 hours = 36 + 38 + 40 + 42 + 44 + 46 + 48 + 50 + 52 + 54 = sum of 10 terms in ap whose first term is 36 and last term is 54 = 10 / 2 [ 36 + 54 ] = 450 km ." | null |
Question: the average age of a class of 20 students is 18 years . the average increased by 2 when the teacher ' s age also included . what is the age of the teacher ?
A.40 years.
B.41 years.
C.42 years.
D.43 years.
e ) 44 yearsA.
"if age of the teacher was 18 , average would not have changed . since average increased by 2 , age of the teacher = 18 + 22 Γ 1 = 40 answer : a" | null |
Question: the profits of qrs company rose 30 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?
A.15 %.
B.32 %.
C.56 %.
D.62 %.
e ) 80 %C.
"assume 100 in march , then 130 in april as 30 % increase , then 104 in may as 20 % decrease from april , and then 156 in june which is 150 % of 104 . so overall increase is from 100 to 156 is 56 % answer c" | null |
Question: if the radius of a circle is increased by 20 % then the area is increased by :
A.44 %.
B.120 %.
C.144 %.
D.40 %.
e ) none of the aboveA.
"initially a = pi * r 2 now r 2 = 120 / 100 r then area = pi * ( 120 r / 100 ) 2 area = 144 r / 100 that is area increases from 100 to 144 = increase in area = 44 % answer : a" | null |
Question: one half of a two digit number exceeds its one third by 7 . what is the sum of the digits of the number ?
A.A.3.
B.B.5.
C.C.7.
D.D.9.
e ) e ) 10E.
"x / 2 β x / 3 = 7 = > x = 46 4 + 6 = 10 answer : e" | null |
Question: the sum of two consecutive numbers is 37 . what are they ?
A.18 and 19.
B.18 and 21.
C.18 and 23.
D.19 and 20.
e ) noneA.
"two consecutive numbers are like 8 and 9 , or 51 and 52 . let x , then , be the first number . then the number after it is x + 1 . the problem states that their sum is 37 : word problem = 37 2 x = 37 β 1 = 36 . x = 36 2 = 18 . the two numbers are 18 and 19 . option is a" | null |
Question: a pupil ' s marks were wrongly entered as 83 instead of 63 . due to that the average marks for the class got increased by half . the number of pupils in the class is :
A.45.
B.40.
C.39.
D.37.
e ) 38B.
"explanation : let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 . answer : b" | null |
Question: if 40 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?
A.2.5 %.
B.10 %.
C.5 %.
D.14 %.
e ) 25 %D.
40 % of ( x - y ) = 30 % of ( x + y ) ( 40 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 4 ( x - y ) = 3 ( x + y ) x = 7 y x = 7 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 7 y ) x 100 ) = 14 % answer is d . | null |
Question: one fast typist type some matter in 4 hrs and another slow typist type the same matter in 6 hrs . if both do combine in how much time they will take to finish .
A.10 hr.
B.1 hr.
C.2 hr 24 mins.
D.3 hr 4 mins.
e ) 4 hr 10 minsC.
"fast ' s 1 hr work = 1 / 4 slow ' s 1 hr work = 1 / 6 1 / 4 + 1 / 6 = 5 / 12 they ll finish in 12 / 5 hrs = 2 2 / 5 = = > 2 hr 24 mins answer : c" | null |
Question: there are 20 players on a rugby team . if the average weight of the players is 180 pounds , what will be the new average height if a 210 pound player will join the team ?
A.185.
B.183.22.
C.184.96.
D.181.43.
e ) 182.78D.
( sum of the 20 weights ) / 20 = 180 sum of the 20 weights = 3600 new sum = 3600 + 210 = 3810 new average = 3810 / 21 = 181.43 ans : d | null |
Question: if in a 20 over cricket match , there were no wide balls , no wides , no extras and no overthrows . what is the maximum number of runs that a batsman can score in an ideal case scenario ?
A.663.
B.720.
C.625.
D.640.
e ) noneA.
solution : 663 explanation : for an ideal case , the batsman will hit a six on each ball . but if he hits six on the last ball of the over , the strike will change in the next over . thus , the best he can do in the last ball is run 3 runs so that he retains the strike even in the next over . thus the total runs that he can score in each over : 6 * 5 + 3 = 33 but this will have to go like it only till the 19 th over . in the last over , he can hit a six in the last ball as well as that will be the last ball of the match . thus runs for the last over will be 6 * 6 = 36 . hence the maximum runs = 33 * 19 + 36 = 663 answer a | null |
Question: what annual payment will discharge a debt of rs . 1025 due in 2 years at the rate of 5 % compound interest ?
A.rs . 550.
B.rs . 551.25.
C.rs . 560.
D.rs . 560.75.
e ) rs . 660.75B.
"let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1025 820 x + 1025 * 441 x = 551.25 so , value of each installment = rs . 551.25 answer : b" | null |
Question: after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 5130 . what was the number of original inhabitants ?
A.7300.
B.7600.
C.7900.
D.8200.
e ) 8500B.
"let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 5130 ( 27 / 40 ) * x = 5130 x = 5130 * 40 / 27 = 7600 the answer is b ." | null |
Question: 40 is subtracted from 70 % of a number , the result is 30 . find the number ?
A.150.
B.997.
C.266.
D.288.
e ) 100E.
"( 70 / 100 ) * x β 40 = 30 7 x = 700 x = 100 answer : e" | null |
Question: find the greatest number that will divide 28 , 128 and 147 leaving 10 , 2 and 3 as remainders respectively
A.19.
B.17.
C.13.
D.9.
e ) 18E.
"explanation : answer will be hcf of ( 28 - 10 , 128 - 2 , 147 - 3 ) hcf of ( 18 , 126 , 144 ) = 18 option e" | null |
Question: if a train , travelling at a speed of 120 kmph , crosses a pole in 6 sec , then the length of train is ?
A.281.
B.125.
C.200.
D.266.
e ) 121C.
"d = 120 * 5 / 18 * 6 = 200 m answer : c" | null |
Question: sakshi can do a piece of work in 5 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
A.4.
B.16.
C.18.
D.25.
e ) 10A.
"solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 5 : x β x = ( 5 x 4 / 5 ) β x = 4 days . hence , tanya takes 16 days is complete the work . answer a" | null |
Question: two pipes a and b can separately fill a cistern in 60 minutes and 80 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 40 minutes . in how much time , the third pipe alone can empty the cistern ?
A.90 min.
B.100 min.
C.240 min.
D.120 min.
e ) 130 minC.
1 / 40 - ( 1 / 60 + 1 / 80 ) = - 1 / 240 third pipe can empty in 240 minutes answer : c | null |
Question: 13 buckets of water fill a tank when the capacity of each bucket is 51 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 17 litres ?
A.39.
B.28.
C.23.
D.12.
e ) 24A.
"capacity of the tank = ( 13 Γ 51 ) litre number of buckets required of capacity of each bucket is 17 litre = 13 Γ 51 / 17 = 13 Γ 3 = 39 answer is a" | null |
Question: a candidate appearing for an examination has to secure 55 % marks to pass paper i . but he secured only 45 marks and failed by 25 marks . what is the maximum mark for paper i ?
A.127.
B.120.
C.130.
D.140.
e ) 150A.
he secured 45 marks nd fail by 25 marks so total marks for pass the examinatn = 70 let toal marks x x * 55 / 100 = 70 x = 127 answer : a | null |
Question: by selling 15 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
A.8.
B.7.
C.6.
D.4.
e ) 10E.
"80 % - - - 15 120 % - - - ? 80 / 120 * 15 = 10 answer : e" | null |
Question: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 10 cm ?
A.827 cm 2.
B.216 cm 2.
C.285 cm 2.
D.178 cm 2.
e ) 190 cm 2E.
"area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 10 ) = 190 cm 2 answer : e" | null |
Question: a sum of money is to be divided among ann , bob and chloe . first , ann receives $ 4 plus one - half of what remains . next , bob receives $ 4 plus one - third of what remains . finally , chloe receives the remaining $ 32 . how much money n did bob receive ?
A.20.
B.22.
C.24.
D.26.
e ) 52B.
"notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ n = 20 answer : b" | null |
Question: two trains leave a station traveling the same direction . train a leaves the station traveling at a constant speed of 60 mph , and train b leaves the station traveling at a constant speed of 80 mph . if both trains maintain constant speeds , in how many minutes will train b overtake train a if train a left 40 minutes prior to train b ?
A.90.
B.100.
C.110.
D.120.
e ) 130D.
we can use d = rt [ distance = rate * time ] train a will have traveled for 40 minutes longer than train b when b overtakes a , so time of train a : t + 40 minutes = t + ( 2 / 3 ) hours ( use hours since the rate is in hours ) time of train b : t rate of train a : 60 mph rate of train b : 80 mph the distances traveled by each will be equal when train b overtakes train a , so we can set the right sides of d = rt equal for the two trains ( rate of train a ) * ( time of train a ) = ( rate of train b ) * ( time of train b ) 60 * ( t + 2 / 3 ) = 80 * t 60 t + 40 = 80 t 40 = 20 t 2 = t 2 hours = 120 minutes d | null |
Question: if the average of 5 positive integers is 50 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
A.50.
B.58.
C.49.
D.48.
e ) 44B.
sum of 5 integer ( a , b , c , d , e ) = 5 * 50 = 250 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 250 i . e . 5 a = 240 i . e . a = 48 i . e . largest e = 48 + 10 = 58 answer : option b | null |
Question: what is the smallest number which , when increased by 7 , is divisible by 8 , 11 , and 24 ?
A.264.
B.257.
C.269.
D.270.
e ) 282B.
"lcm ( 8 , 11,24 ) = 24 x 11 = 264 so the least divisible number is 264 , and the number we are looking for is 264 - 7 = 257 . the answer is b ." | null |
Question: in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 210 girls , the total number of students in the college is ?
A.562.
B.356.
C.452.
D.416.
e ) 546E.
"let the number of boys and girls be 8 x and 5 x then , 5 x = 210 x = 42 total number of students = 13 x = 13 * 42 = 546 answer is e" | null |
Question: the grade point average of one third of the classroom is 15 ; the grade point average of the rest is 18 . what is the grade point average of the whole class ?
A.17.
B.19.
C.21.
D.23.
e ) 25A.
"let n = total students in class total points for 1 / 3 class = 15 n / 3 = 5 n total points for 2 / 3 class = 18 * 2 n / 3 = 12 n total points for whole class = 5 n + 12 n = 17 n 17 n total class points / n total students = 17 grade point average for total class answer : a" | null |
Question: arjun started a business with rs . 10,000 and is joined afterwards by anoop with rs . 40 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
A.3.
B.4.
C.5.
D.6.
e ) 9E.
"suppose anoop joined after 3 months . then , 10000 * 12 = 40000 * ( 12 β x ) = > x = 9 . answer : e" | null |
Question: if the operation @ is defined for all a and b by the equation a @ b = ( a - b ) / 5 , then ( 3 @ - 2 ) @ 6 = ?
A.0.
B.1.
C.2.
D.- 2.
e ) - 1E.
work within the parenthesis first so solve ( 3 @ - 2 ) first ( 3 @ - 2 ) = ( 3 - ( - 2 ) ) / 5 = ( 3 + 2 ) / 5 = 1 now take 1 plug back into equation and solve the rest ( 1 @ 6 ) = ( 1 - 6 ) / 5 = - 5 / 5 = - 1 so - 1 is the answer . . . . this question is merely testing order of operations remember pemdas answer is option : e | null |
Question: what is the ratio of 5 / 7 to the product 3 * ( 7 / 3 ) ?
A.3 : 7.
B.1 : 3.
C.5 : 49.
D.1 : 7.
e ) 3 : 49C.
"3 / 7 / 21 / 3 = 5 / 49 . . . imo option c ." | null |
Question: a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 15 sec . what is the length of the goods train ?
A.299.
B.277.
C.276.
D.270.
e ) 50E.
"speed = 72 * 5 / 18 = 20 m / sec . time = 15 sec . let the length of the train be x meters . then , ( x + 250 ) / 15 = 20 x = 50 m . answer : e" | null |
Question: a goods train runs at the speed of 72 km / hr and crosses a 290 m long platform in 26 sec . what is the length of the goods train ?
A.278.
B.166.
C.151.
D.230.
e ) 109D.
"speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 290 ) / 26 = 20 x = 230 m . answer : d" | null |
Question: the contents of a certain box consist of 24 oranges and 30 kiwis . how many kiwis must be added to the box so that exactly 30 % of the pieces of fruit in the box will be oranges ?
A.24.
B.26.
C.30.
D.46.
e ) 50B.
oranges = ( oranges + kiwi + x ) * 0.3 24 = ( 30 + 24 + x ) * 0.3 x = 26 . answer : b . | null |
Question: if s is the sum of reciprocals of a list of consecutive integers from 55 to 64 , inclusive , s is approximately equal to
A.0.16.
B.0.2.
C.0.3.
D.0.4.
e ) 0.5A.
we need to find the approximate value of 1 / 55 + 1 / 56 + 1 / 57 + 1 / 58 + 1 / 59 + 1 / 60 + 1 / 61 + 1 / 62 + 1 / 63 + 1 / 64 . now , the sum of these 10 terms will be very close to 10 times 1 / 60 , which is 0.016 * 10 = 0.16 . answer : a . | null |
Question: the sector of a circle has radius of 28 cm and central angle 135 o . find its perimeter ?
A.122 cm.
B.92.2 cm.
C.28.9 cm.
D.29.2 cm.
e ) 98.2 cmA.
"perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 28 ) + 2 ( 28 ) = 66 + 56 = 122 cm answer : a" | null |
Question: a swimmer swims downstream 55 km and upstream 10 km taking 5 hours each time ; what is the speed of the current ?
A.4.6.
B.4.5.
C.4.4.
D.4.3.
e ) 4.2B.
55 - - - 5 ds = 11 ? - - - - 1 10 - - - - 5 us = 2 ? - - - - 1 s = ? s = ( 11 - 2 ) / 2 = 4.5 answer : b | null |
Question: what is the sum of the greatest common factor and the lowest common multiple of 16 and 72 ?
A.142.
B.152.
C.124.
D.160.
e ) 184B.
"prime factorization of 16 = 2 x 2 x 2 x 2 . prime factorization of 72 = 2 x 2 x 2 x 3 x 3 gcf = 8 lcm = 144 sum = 152 . answer b ." | null |
Question: a is half good a work man as b and together they finish a job in 13 days . in how many days working alone b finish the job ?
A.23.
B.22.
C.39 / 2.
D.36.
e ) 48C.
c 39 / 2 wc = 1 : 2 2 x + x = 1 / 13 = > x = 1 / 39 2 x = 2 / 39 = > 39 / 2 days | null |
Question: 33 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
A.10.
B.11.
C.13.
D.18.
e ) 19B.
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 : 33 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 33 x 5 x 12 x = ( 33 x 5 x 12 ) / ( 30 x 6 ) x = 11 answer b | null |
Question: the diagonal of a rectangle is β 41 cm and its area is 20 sq . cm . the perimeter of the rectangle must be :
['A.18', 'B.28', 'C.38', 'D.48', 'e ) 58']A.
explanation : l 2 + b 2 = 41 also , lb = 20 ( l + b ) 2 = l 2 + b 2 + 2 lb = 41 + 40 = 81 ( l + b ) = 9 perimeter = 2 ( l + b ) = 18 cm . answer : a | null |
Question: the pilot of a small aircraft with a 60 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 10 miles per gallon , will not get him there . by how many miles per gallon must the aircraft β s fuel efficiency be improved to make the flight to cleveland possible ?
A.5.
B.12.
C.2.
D.4.
e ) 6C.
"actual miles / gallon is = 480 / 60 = 8 miles / gallon . current engine miles / gallon is 10 miles / gallon . additional 2 miles / gallon is required to match the actual mileage . answer : c" | null |
Question: there is a square with sides of 12 . what is the circumference of the biggest circle that can be cut out of this square ?
['A.75.4', 'B.31.42', 'C.36', 'D.18.85', 'e ) 37.7']E.
circumference of a circle = c = 2 Γ― β¬ r square is 12 wide , so circle ' s diameter would be 12 , and radius would be 6 c = 2 Γ― β¬ 6 which is approximately 37.7 answer is e | null |
Question: convert 0.36 in to a vulgar fraction ?
A.18 / 50.
B.16 / 50.
C.17 / 50.
D.9 / 25.
e ) noneD.
"answer 0.36 = 36 / 100 = 9 / 25 correct option : d" | null |
Question: a box contain the number of balls which is as much greater than 44 is less than 70 . the number of balls is ?
A.47.
B.114.
C.74.
D.67.
e ) 57E.
answer let the number be x . then , x - 44 = 70 - x Γ’ β‘ β 2 x = 70 + 44 = 114 Γ’ β‘ β 2 x = 114 Γ’ Λ Β΄ x = 57 correct option : e | null |
Question: robert ' s salary was decreased by 20 % and subsequently increased by 20 % . how much percentage does he lose ?
A.4 %.
B.20 %.
C.25 %.
D.30 %.
e ) 50 %A.
"let original salary be $ 100 salary after decreasing 20 % = 100 - 100 x 20 / 100 = $ 80 salary after increasing 20 % on $ 80 = 80 + 80 x 20 / 100 = $ 96 percentage of loss = 100 - 96 = 4 % answer : a" | null |
Question: the average of temperatures at noontime from monday to friday is 55 ; the lowest one is 45 , what is the possible maximum range of the temperatures ?
A.20.
B.25.
C.40.
D.45.
e ) 75C.
"there are 5 days so the sum of temperature can be 55 * 5 = 275 lowest is 45 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 45 = 180 . on the fifth day it is 275 - 180 = 95 range is therefore 95 - 45 = 40 answer c" | null |
Question: 12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 6 .
A.150.
B.152.
C.154.
D.159.
e ) 144D.
"d = d * q + r d = 17 * 9 + 6 d = 153 + 6 d = 159 answer d" | null |
Question: what is the probability that the sum of two dice will yield a 5 , and then when both are thrown again , their sum will again yield a 5 ? assume that each die has 4 sides with faces numbered 1 to 4 .
A.1 / 144.
B.1 / 36.
C.1 / 12.
D.1 / 16.
e ) 1 / 3D.
"solution - rolling dices is an independent event . the combinations to get 5 are ( 1,4 ) , ( 4,1 ) , ( 2,3 ) , ( 3,2 ) , and total combinations of both dices is 16 . the probability of getting 5 in first attempt is 4 / 16 = 1 / 4 . probability of getting 5 again in second attempt = ( 1 / 4 ) * ( 1 / 4 ) = 1 / 16 . ans d" | null |
Question: a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2400 ?
A.s . 800.
B.s . 810.
C.s . 820.
D.s . 900.
e ) s . 920A.
"2400 * 1 / 3 = 800 option a" | null |
Question: yesterday ' s closing prices of 2,420 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ?
A.484.
B.726.
C.1,100.
D.1,320.
e ) 1,694D.
"lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 2420 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) & ( 2 ) to get h = 1320 . d is answer ." | null |
Question: a shopkeeper sells 200 metres of cloth for rs . 12000 at a loss of rs . 12 per metre . find his cost price for one metre of cloth ?
A.s . 59.
B.s . 72.
C.s . 62.
D.s . 50.
e ) s . 13B.
"sp per metre = 12000 / 200 = rs . 60 loss per metre = rs . 12 cp per metre = 60 + 12 = rs . 72 answer : b" | null |
Question: before 7 years , dog a β s age was 4 times of dog b β s age and after 4 years , dog a β s age will be 3 times of dog b β s age . what is the difference of dog a β s age and dog b β s now ?
A.36.
B.42.
C.54.
D.60.
e ) 70E.
"a - 7 = 4 ( b - 7 ) - - > a - 4 b = - 21 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 29 - - > a = 3 ( 22 ) = 99 a - b = 99 - 29 = 70 answer : e" | null |
Question: a pipe can empty 2 / 3 rd of a cistern in 12 mins . in 6 mins , what part of the cistern will be empty ?
A.2 / 3.
B.3 / 7.
C.4 / 9.
D.3 / 8.
e ) 1 / 3E.
"2 / 3 - - - - 12 ? - - - - - 6 = = > 1 / 3 e" | null |
Question: a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6400 ?
A.rs . 5870.
B.rs . 8270.
C.rs . 6020.
D.rs . 6850.
e ) none of theseB.
"explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6400 * 6 ) β 30,130 ] = rs . ( 38400 β 30,130 ) = rs . 8270 answer b" | null |
Question: 1401 x 1401 = ?
A.1962800.
B.1962801.
C.1960000.
D.1951611.
e ) 1951613B.
"1401 x 1401 = ( 1401 ) 2 = ( 1400 + 1 ) 2 = ( 1400 ) 2 + ( 1 ) 2 + ( 2 x 1400 x 1 ) = 1960000 + 1 + 2800 = 1960001 + 2800 = 1962801 . b )" | null |
Question: the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 9 and 39 inclusive .
A.351.
B.384.
C.410.
D.424.
e ) 450B.
"we ' re dealing with a sequence of consecutive odd integers : 9 to 39 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 9 + 39 = 48 2 ) now look at the ' next smallest ' and the ' next biggest ' : 11 + 37 = 48 now we have proof that there is no middle term . we have 8 bunches of 48 8 ( 48 ) = 384 b" | null |
Question: huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 12 inches on a side and costs $ 10 , and a large pizza that measures 18 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
A.5 square inches.
B.36 square inches.
C.15 square inches.
D.25 square inches.
e ) 350 square inchesB.
"in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 12 * 12 = 144 ) for the small pizza and ( 18 * 18 = 324 ) for the large pizza . in total sq inches that would be ( 144 + 324 ) * 2 = 936 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 324 = 972 sq inches . hence , the difference is 36 square inches more ( 972 - 936 ) . the correct answer is b" | null |
Question: two goods trains each 75 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
A.2.3 sec.
B.4.2 sec.
C.48 sec.
D.7.2 sec.
e ) 9 secD.
"relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 75 + 75 = 150 m . required time = 150 * 6 / 125 = 7.2 sec . answer : d" | null |
Question: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 153 games will be played during the tournament . find the number of participants .
A.15.
B.16.
C.17.
D.18.
e ) 19D.
"if the number of participants is 3 ( say a , b , c ) the number of games played will be 2 ( a plays against b and c ) + 1 ( b plays against c ) = 3 using the same logic , if the number of participants is n , the number of games played will be ( n - 1 ) + ( n - 2 ) + ( n - 3 ) + . . . 3 + 2 + 1 given that this sum = 153 = 1 + 2 + 3 + . . . ( n - 1 ) sum of first m positive integers is given by m ( m + 1 ) / 2 . so sum of first ( n - 1 ) positive integers is ( n - 1 ) * n / 2 153 = ( n - 1 ) * n / 2 ( n - 1 ) * n = 306 17 * 18 = 306 ( we know that 15 ^ 2 = 225 so the two consecutive numbers must be greater than 15 . also , 20 ^ 2 = 400 so the two numbers must be less than 20 . the pair of numbers in between 15 and 20 whose product ends with 6 is 17 and 18 ) so n = 18 answer ( d )" | null |
Question: find the ones digit of 73 ^ 340
A.3.
B.5.
C.6.
D.7.
e ) 9A.
"cyclicity of 3 is 3,9 , 7,1 after 4 multiplication again the cycle repeats . so divide 340 by 4 and we get 87 as quotient and 2 as remainder . so cycle will run for 87 times and then 2 times more . so pick up the 2 nd item from the cycle . hence answer a ." | null |
Question: if a lends rs . 2000 to b at 15 % per annum and b lends the same sum to c at 17 % per annum then the gain of b in a period of 4 years is ?
A.155.
B.162.
C.157.5.
D.160.
e ) 157.12D.
"( 2000 * 2 * 4 ) / 100 = > 160 answer : d" | null |
Question: how much time will a train of length 400 m moving at a speed of 72 kmph take to cross another train of length 300 m , moving at 36 kmph in the same direction ?
A.40 sec.
B.50 sec.
C.60 sec.
D.70 sec.
e ) 80 secD.
"the distance to be covered = sum of their lengths = 400 + 300 = 700 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 700 / 10 = 70 sec . answer : d" | null |
Question: length of a rectangular plot is 26 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
A.53 m.
B.63 m.
C.73 m.
D.83 m.
e ) 93 mB.
"let breadth = x metres . then , length = ( x + 26 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 26 ) + x ] = 200 2 x + 26 = 100 2 x = 74 x = 37 hence , length = x + 26 = 63 m b" | null |
Question: on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 34 inch from the base of the mountain . how many km is he from the base of the mountain ?
['A.14.83', 'B.14.81', 'C.14.8', 'D.14.82', 'e ) 14.12']D.
explanation : since 312 inch = 136 km so 1 inch = 136 / 312 km so 34 inch = ( 136 Γ 34 ) / 312 = 14.82 km answer : d | null |
Question: the sum of the present ages of a father and his son is 42 years . 6 years ago , father ' s age was 4 times the age of the son . after 6 years , son ' s age will be :
A.14.
B.16.
C.18.
D.20.
e ) 22C.
let the present ages of son and father be x and ( 42 - x ) years respectively . then , ( 42 - x ) - 6 = 4 ( x - 6 ) 36 - x = 4 x - 24 x = 12 the son ' s age after 6 years will be 18 . the answer is c . | null |
Question: two trains a and b starting from two points and travelling in opposite directions , reach their destinations 9 hours and 16 hours respectively after meeting each other . if the train a travels at 80 kmph , find the rate at which the train b runs .
A.40.
B.160.
C.120.
D.80.
e ) 100B.
"if two objects a and b start simultaneously from opposite points and , after meeting , reach their destinations in β a β and β b β hours respectively ( i . e . a takes β a hrs β to travel from the meeting point to his destination and b takes β b hrs β to travel from the meeting point to his destination ) , then the ratio of their speeds is given by : sa / sb = β ( b / a ) i . e . ratio of speeds is given by the square root of the inverse ratio of time taken . sa / sb = β ( 4 / 16 ) = 2 / 4 = 1 / 2 this gives us that the ratio of the speed of a : speed of b as 1 : 2 . since speed of a is 80 kmph , speed of b must be 80 * ( 2 / 1 ) = 160 kmph b" | null |
Question: a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes tom can make using this recipe ?
A.5.
B.6.
C.7.
D.8.
e ) 9A.
less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a | null |
Question: the c . p of 10 pens is equal to the s . p of 5 pens . find his gain % or loss % ?
A.50 %.
B.40 %.
C.30 %.
D.60 %.
e ) 20 %A.
10 cp = 5 sp 10 - - - 5 cp gain 100 - - - ? = > 50 % ( gain ) answer : a | null |
Question: the average of 6 no . ' s is 3.95 . the average of 2 of them is 4.2 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?
A.4.2.
B.4.4.
C.4.6.
D.3.8.
e ) 5.7D.
"sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 4.2 * 2 ) + ( 3.85 * 2 ) ] = 7.60 . required average = ( 7.6 / 2 ) = 3.8 . d" | null |
Question: 20 one identical machines , running continuously at the same constant rate , take 9 days to complete a shipment . how many additional machines , each running at the same constant rate , would be needed to reduce the time required to complete a shipment by two days ?
A.2.
B.3.
C.4.
D.6.
e ) 9D.
from the question you know that 21 r = 1 / 9 . the question asks you ( partially ) to make the rate from 1 / 9 to 1 / 7 ( drop from 9 day to 7 ) . so the only thing that you need to do is to find the magic number than can convert 1 / 9 to 1 / 7 . so 1 / 9 * x = 1 / 7 ( 1 equation with one unknown ) . so by solving this you get x = 9 / 7 . thats it then ! take the magic number 9 / 7 and multiply both sides of the original equation and you have : 21 * ( 9 / 7 ) * r = ( 9 / 7 ) * 1 / 9 27 * r = 1 / 7 , hence 27 r = 1 / 7 , therefore 6 more machines ! d | null |
Question: a furniture dealer purchased a desk for $ 150 and then set the selling price equal to the purchase price plus a markup that was 40 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
A.$ 40.
B.$ 60.
C.$ 80.
D.$ 90.
e ) $ 100E.
"purchase price = 150 selling price = x 150 + 0.4 * x = x 0.6 * x = 150 x = 250 profit = 250 - 150 = 100 answer : e" | null |
Question: the number of sailors on a ship is 78 % more than the number of officers . the ratio of sailors to officers would be
A.33 : 25.
B.47 : 20.
C.47 : 25.
D.89 : 50.
e ) 97 : 50D.
sailor = 1.78 * officer sailor / officer = 1.78 / 1 = 178 / 100 = 89 / 50 answer will be d | null |
Question: three 7 faced dice are thrown together . the probability that all the three show the same number on them is ?
A.1 / 38.
B.1 / 49.
C.1 / 39.
D.1 / 42.
e ) 1 / 29B.
"it all 3 numbers have to be same basically we want triplets . 111 , 222 , 333 , 444 , 555 , 666 and 777 . those are seven in number . further the three dice can fall in 7 * 7 * 7 = 343 ways . hence the probability is 7 / 343 = 1 / 49 answer : b" | null |
Question: how much more would rs . 10000 fetch , after two years , if it is put at 20 % p . a . compound interest payable half yearly than if is put at 20 % p . a . compound interest payable yearly ?
A.241.
B.725.
C.992.
D.837.
e ) 923A.
"10000 ( 11 / 10 ) 4 - 10000 ( 6 / 5 ) 2 = 241 answer : a" | null |
Question: what is the decimal equivalent of ( 1 / 4 ) ^ 2 ?
A.0.0016.
B.0.0625.
C.0.16.
D.0.25.
e ) 0.5B.
"1 / 4 = 25 / 100 = > ( 25 / 100 ) ^ 2 = 625 / 10000 = 0.0625 answer : b" | null |
Question: a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 33 pints of perfect pink paint ?
A.9.
B.16.
C.17.
D.25 1 / 3.
e ) 28 1 / 2C.
"3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 33 pints will require 9 / 17 * 33 = 17 pints . . c" | null |
Question: a rectangular field has area equal to 150 sq m and perimeter 50 m . its length and breadth must be ?
['A.15 m.
15 m', 'B.15 m.
90 m', 'C.16 m.
10 m', 'D.15 m.
10 m', 'e ) 15 m.
30 m']D.
lb = 150 2 ( l + b ) = 50 = > l + b = 25 l β b = 5 l = 15 b = 10 answer : d | null |
Question: if 5 + 7 / x = 6 - 5 / x , then x =
A.7.
B.14.
C.12.
D.6 / 7.
e ) 5C.
we ' re given the equation 5 + 7 / x = 6 - 5 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we need to multiply both sides of the equation by x , giving us . . . 5 x + 7 x / x = 6 x - 5 x / x we can then eliminate that denominator , which gives us . . . . 5 x + 7 = 6 x - 5 12 = x c | null |
Question: the average of 15 numbers is calculated as 30 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
A.12.
B.26.
C.16.
D.45.
e ) 12D.
"15 * 30 + 36 β 26 = 450 / 10 = 45 answer : d" | null |
Question: kelly has had 3 pay cuts in her salary in the past 6 months . if the first pay cut was 8 % , the second pay cut was 14 % and the third was 18 % . what will be the percentage decrease , if the salary is decreased in a single shot ?
A.35.9 %.
B.34.12 %.
C.32.12 %.
D.35.12 %.
e ) 31.12 %D.
let rs . 100 be initial salary . salary after 1 st decrease , 8 % = 92 salary after 2 nd decrease , 14 % = 79.12 i . e . reduced by 14 percent of 92 salary after 3 rd decrease , 18 % = 64.88 i . e . reduced by 18 percent of 79.12 so if its decreased in single shot = i = ( ( b - a ) / b ) * 100 = 35.12 % answer : d | null |
Question: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 400 when the rate to profit rises from 5 to 7 percent . find the capital of c ?
A.3377.
B.2899.
C.5000.
D.2778.
e ) 1991C.
"a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 400 c ' s capital = 30000 * 1 / 6 = 5000 answer : c" | null |
Question: how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | β€ 11 ?
A.15.
B.16.
C.17.
D.8.
e ) 19D.
"so i can write this as in - 3 i + 4 < = 11 or in - 3 i < = 7 so n can have - 4 to 10 = 8 true values . . . . d" | null |
Question: in the coordinate plane , a circle centered on point ( - 3 , - 4 ) passes through point ( 1 , 2 ) . what is the area of the circle ?
A.9 Ο.
B.18 Ο.
C.25 Ο.
D.37 Ο.
e ) 52 ΟE.
"r ^ 2 = ( - 3 - 1 ) ^ 2 + ( - 4 - 2 ) ^ 2 = 16 + 36 = 52 area of circle = Ο r ^ 2 = 52 Ο answer : e" | null |
Question: a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a ?
A.240.
B.278.
C.209.
D.267.
e ) 262A.
"( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 630 = 240 answer : a" | null |
Question: what is the sum of the 1 st 5 prime numbers greater than 20 ?
A.121.
B.151.
C.168.
D.164.
e ) 161E.
"required sum = ( 23 + 29 + 31 + 37 + 41 ) = 161 note : 1 is not a prime number answer e" | null |
Question: the population of a bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1000 to 1000000 bacteria
A.10.
B.12.
C.14.
D.16.
e ) 20E.
the question basically asks how many minutes it takes for a population to increase by factor 1000 ( 1000000 / 1000 = 1000 ) . now you know that every two minutes the population doubles , i . e . is multiplied by 2 . so the equation becomes : 2 ^ x > = 1000 , where x represents the number of times the population doubles . a lot of people remember that 2 ^ 10 = 1024 . i . e . the population has to double 10 times . since it takes the population 2 minutes to double once it takes 10 * 2 minutes = 20 minutes to double nine times . thus , solution e = 20 is correct . | null |
Question: a woman bought a pack of 36 eggs , but the seller told her that there were 3 rotten eggs in the pack . she forgot it and begun to prepare a recipe that needs 2 eggs . what is the probability that both choosen eggs will be rotten ?
A.1 / 210.
B.2 / 210.
C.3 / 210.
D.1 / 119.
e ) 2 / 119A.
there are 3 rotten eggs in a pack of 36 . thus the probability of picking 2 rotten eggs is : ( 3 / 36 ) ( 2 / 35 ) = 1 / 210 . the correct answer is a . | null |
Question: if a person walks at 20 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
A.20 km.
B.56 km.
C.60 km.
D.70 km.
e ) 80 kmA.
"let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 14 20 x = 10 x + 200 10 x = 200 x = 20 km . answer : a" | null |
Question: 20 % of a number is more than 30 % of 120 by 80 . find the number ?
A.520.
B.560.
C.580.
D.620.
e ) 610C.
( 20 / 100 ) * x β ( 30 / 100 ) * 120 = 80 1 / 5 x = 116 x = 580 answer : c | null |
Question: find the average of all prime numbers between 40 and 80 .
A.59.4.
B.56.
C.39.8.
D.44.9.
e ) noneA.
"sol . there are five prime numbers between 40 and 80 . they are 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 Γ’ Λ Β΄ required average = [ 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 / 10 ] = 594 / 10 = 59.4 answer a" | null |
Question: the population of a bacteria colony doubles every day . if it was started 9 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
A.512.
B.768.
C.1024.
D.2048.
e ) 4096C.
"it started 9 days ago . so bacterias keep growing for 9 days + today = 10 days 2 ^ 10 = 1024 c is the answer" | null |
Question: in may , the groundskeeper at spring lake golf club built a circular green with an area of 65 Ο square feet . in august , the groundskeeper doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
A.105 Ο.
B.130 Ο.
C.200 Ο.
D.260 Ο.
e ) 320 ΟD.
"area = Ο r ^ 2 , so doubling the radius results in an area that is 4 times the original area . 4 ( 65 Ο ) = 260 Ο the answer is d ." | null |
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