divelab/Sys2Bench huggingface dataset:
Question: A vendor sells 50 percent of the apples he had and throws away 20 percent of the remainder. The next day, the vendor sells 50 percent of the remaining apples and throws away the rest. In total, what percent of his apples does the vendor throw away?
Options:
A)30
B)35
C)40
D)45
E)50
Rationale: Let x be the original number of apples.
On day one, the vendor throws away (0.2)(0.5)x=0.1x.
The remaining apples are (0.8)(0.5)x = 0.4x.
On day two, the vendor throws away (0.5)(0.4)x=0.2x.
The vendor throws away a total of 0.1x + 0.2x = 0.3x.
The vendor throws away 30 percent of the apples.
The answer is A.
Answer: A
Question: In what time will a railway train 64 m long moving at the rate of 46 kmph pass a telegraph post on its way?
Options:
A)3
B)5
C)4
D)6
E)7
Rationale: T = 64/46 * 18/5 = 5 sec
Answer:B
Answer: B
Question: If it takes two teams of factory workers 6 days to complete a task. How many days will it take each team working separately, to complete the same task if it will take one of the teams 3 days earlier to complete the task.
Options:
A)10 and 15
B)5 and 8
C)4 and 7
D)9 and 12
E)3 and 6
Rationale: Work = (A)(B)/(A+B) where A and B are the individual times of each entity.
Here, we're told that (working together) the two teams would complete a job in 6 days. This means that (individually) each team would take MORE than 6 days to do the job.
Answers E, B and C are illogical, since the individual times must both be greater than 6 days.
so we can TEST the values for Answers D and E.
Using the values for Answers D and A, we have...
Answer D: (9)(12)/(9+12) = 108/21 = 5.14 This is NOT a match
Answer A: (10)(15)/(10+115) = 150/25 = 6 This IS a match
Final Answer:
A
Answer: A
Question: A fair price shopkeeper takes 10% profit on his goods. He lost 60% goods during theft. His loss percent is:
Options:
A)72%
B)42%
C)56%
D)12%
E)22%
Rationale: Explanation:
Suppose he has 100 items. Let C.P. of each item be Re. 1.
Total cost = Rs. 100. Number of items left after theft = 40.
S.P. of each item = Rs. 1.10
Total sale = 1.10 * 40 = Rs. 44
Hence, loss % = 56/100 * 100 = 56%
Answer:C
Answer: C
Question: If green means red, red means yellow, yellow means blue, blue means orange and orange means green, what is the colour of blood ?
Options:
A)Blue
B)Red
C)Yellow
D)Green
E)Pink
Rationale: Explanation:
The colour of blood is 'red' and as given 'green' means 'red'.
so, the colour of blood is 'green'.
Answer: D
Answer: D
Question: For which of the following functions f is f(z) = f(1-z) for all z?
Options:
A)f (x) = 1 - x
B)f (z) = 1 - z^2
C)f (z) = z^2 - (1 - z)^2
D)f (z) = z^2*(1 - z)^2
E)f (x) = x/(1 - x)
Rationale: I remember seeing this problem in a GMATprep test. I think choice D should be F(z)=(z^2) (1-z)^2. If that is true then substituting (1-z) for will give us the same function back and the answer choice is D, where the function is multiplicative
Answer: D
Question: Which is a better investment 8% stock at 212 or 6 2/3 stock at 350?
Options:
A)8% stock at 212
B)6 2/3 stock at 350
C)None
D)Both are equally good
E)Cannot be compared, as the total amount of investment is not given
Rationale: Let investment in each case be Rs. (212 x 350).
Income in 1st case = Rs. 8 x 212 x 212/350= Rs. 1027.29.
Income in 2nd case = Rs.20 x 212 x 350/(3*350)= Rs. 1413.3
Clearly, 6 2/3 stock at 350 is better.
ANSWER:B
Answer: B
Question: If 24 men working for 12 hrs a day can do a work in 16 days, in how many days can 8 men working 6 hrs a day do it?
Options:
A)12 days
B)24 days
C)36 days
D)96 days
E)None of these
Rationale: Explanation :
24 men 12 hrs 16 days
8 men 6 hrs ? days (n)
n =16 X (12 / 6) X (24 / 8) ( since no of hrs reduced no of days has to increase and no of men reduced also increases no of days i.e., inverse proportional)
=> n = 96 days.
Answer : D
Answer: D
Question: A train running at the speed of 80 km/hr crosses a pole in 10 seconds. What is the length of the train?
Options:
A)450 m
B)350 m
C)150 m
D)250 m
E)240 m
Rationale: Speed=(90* 5/18) m/sec =25 m/sec Length of the train = (Speed x Time) = (25* 10) m = 250 m. Answer: D
Answer: D
Question: A truck carrying cans of paint contains P stacks. Each stack contains P/4 cases, and each case contains 2P cans. How many cans of paint are contained in 8 trucks?
Options:
A)4P
B)4P^3
C)P^2/8
D)P^3/4
E)2P^3
Rationale: There are 2P cans in each case.
There are P^2/2 cans in each stack.
There are P^3/2 cans in each truck.
There are 4P^3 cans in 8 trucks.
The answer is B.
Answer: B
Question: If on an item a company gives 25% discount, they earn 25% profit.If they now give 10% discount then what is the profit?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: let market price =100
then sp=75
but they earn 25% so= (100/125)*75
= 60
so cp=60
now again 10% discount on 100=90
so profit is =90-60
=30
ANSWER:A
Answer: A
Question: An amount of Rs.40,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?
Options:
A)2378
B)2697
C)10000
D)5000
E)6971
Rationale: Explanation:
We have, P = 2Q & S = 4R
Further Q = R & P + Q + R + S = 40,000
Thus we get, 2Q + Q + Q + 4Q = 40,000
8Q = 40,000 or Q = Rs. 5000
Thus, R = Rs. 2500, P = 10000 & S = Rs. 20000
Hence, the required difference = (S – P) = (20000 – 10000) = Rs. 10000
ANSWER:C
Answer: C
Question: A 160 meter long train crosses a man standing on the platform in 8 sec. What is the speed of the train?
Options:
A)96 kmph
B)94 kmph
C)92 kmph
D)86 kmph
E)72 kmph
Rationale: S = 160/8 * 18/5 = 72 kmph
ANSWER:E
Answer: E
Question: If $1088 are divided between worker A and worker B in the ratio 5:11,what is the share that worker B will get?
Options:
A)62.45%
B)64.55%
C)66.65%
D)68.75%
E)70.85%
Rationale: Worker B will get 11/16 = 68.75%
The answer is D.
Answer: D
Question: Tom and Jerry are running on the same road towards each other. If Tom is running at a speed of 2.5 meters per second and Jerry is running 36% slower, how much time will it take them to meet if the initial distance between the two is 50 meters and Tom started running 20 seconds before Jerry did?
A.
Options:
A)2 minute and 12 seconds.
B)two minutes.
C)44 seconds.
D)20 seconds.
E)12 seconds
Rationale: om is running alone for 20 seconds.
So he will cover a distance of 20*2.5 = 50 m in 20 seconds.
Basically, Jerry has not started yet , and Tom has covered the distance alone and met Jerry on the other side :)
D is the answer
Answer: D
Question: On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?
Options:
A)0
B)3
C)5
D)11
E)7
Rationale: Let x be the number and y be the quotient. Then,
x = 357 x y + 39
= (17 x 21 x y) + (17 x 2) + 5
= 17 x (21y + 2) + 5)
Required remainder = 5.
Answer :C
Answer: C
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
Options:
A)9
B)4
C)7
D)3
E)1
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
Answer: B
Question: Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
Options:
A)6
B)6.25
C)7.25
D)7.5
E)8
Rationale: Required run rate = 282 - (3.2 x 10) =	250 = 6.25
40	40
B
Answer: B
Question: Albert is 2 times Mary’s age and 4 times as old as Betty. Mary is 10 years younger than Albert. How old is Betty?
Options:
A)5
B)8
C)10
D)12
E)15
Rationale: A = 2M = M+10
M = 10
A = 20
A = 4B, and so B = 5
The answer is A.
Answer: A
Question: On a certain transatlantic crossing, 40 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 20 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
Options:
A)20%
B)40%
C)50%
D)60%
E)80%
Rationale: Let T be the total number of passengers.
Let x be the number of people with round trip tickets.
0.4T had round trip tickets and took their cars.
0.8x had round trip tickets and took their cars.
0.8x = 0.4T
x = 0.5T
The answer is C.
Answer: C
Question: If MEDICAL is written as EFNJDBM and VERSION is written as SFWTJPI then PROBLEM is written as
Options:
A)CPSQMFN
B)NQOCMFN
C)PSQCMFN
D)PSQCMFM
E)None
Rationale: M E D I C A L
13 4
E F N J D B M
5 14
1st and 3rd letters sum is same i.e.,13=5=18 and d+n=18
and the remaining letters are increased by 1 ((e,f),(i,j),(c,d),....
for version also sequence is same....
follow the same sequence for problem :
answer is : PSQCMFN
ANSWER:C
Answer: C
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Options:
A)1
B)2
C)7
D)4
E)9
Rationale: 1250 = D(100/4)2
D = 2
Answer:B
Answer: B
Question: A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
Options:
A)6 days
B)4 days
C)8 days
D)5 days
E)1 days
Rationale: 1/7 + 1/14 + 1/28 = 7/28 = 1/4
=> 4 days
Answer: B
Answer: B
Question: Look at this series: 8, 22, 8, 28, 8, ... What number should come next?
Options:
A)36
B)28
C)44
D)34
E)55
Rationale: D
34
This is a simple addition series with a random number, 8, interpolated as every other number. In the series, 6 is added to each number except 8, to arrive at the next number.
Answer: D
Question: Sam is training for the marathon. He drove 12 miles from his home to the Grey Hills Park and then ran 6 miles to Red Rock, retraced his path back for 2 miles, and then ran 5 miles to Rock Creek. If he is then n miles from home, what is the range of possible values for n?
Options:
A)1 ≤ n ≤23
B)3 ≤ n ≤21
C)5 ≤ n ≤19
D)6 ≤ n ≤18
E)9 ≤ n ≤15
Rationale: ANSWER: C To find the maximum and minimum range for his distance from home, assume that he traveled either directly toward his home or directly away from his home. The range then is between 12+6-2+5=21 for the maximum, and 12-6+2-5=3 for the minimum, so B is the answer
Answer: B
Question: An equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral triangle T1. A third equilateral triangle T3 is formed by joining the mid-points of T2 and this process is continued indefinitely. If each side of T1 is 30 cm, find the sum of the perimeters of all the triangles.
Options:
A)180 cm
B)220 cm
C)240 cm
D)270 cm
E)300 cm
Rationale: We have 30 for first triangle, when we join mid-points of first triangle we get the second equilateral triangle then the length of second one is 15 and continues.
So we have 30,15,7.5,...
We have ratio = 1/2, and it is GP type.
Sum of infinite triangle is a/1-r = 30/1-(1/2) = 60
Equilateral triangle perimeter is 3a = 3*60 = 180.
So option A.
Answer: A
Question: What is the decimal equivalent of (1/6)^2?
Options:
A)0.0016
B)0.0625
C)0.16
D)0.278
E)0.5
Rationale: (1/6)² = (1/6)(1/6)= 1/36
APPROACH #1: use long division to divide 36 into 1 to get 1/36 = 0.0278
D
Answer: D
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
Options:
A)2500 m^2
B)2510 m^2
C)2520 m^2
D)2540 m^2
E)2590 m^2
Rationale: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Answer: C
Question: A father is twice as old as his son. 20 years ago, the age of the father was 12 times the age of the son. The present age of the father (in years) is
Options:
A)33
B)44
C)45
D)46
E)47
Rationale: Let son’s age = x. Then father’s age = 2x
12 (x - 20) = (2x - 20)
10x = 220
x = 22
Father’s present age = 44 years.
ANSWER:B
Answer: B
Question: A swimmer can swim in still water at 4 km/h. If the speed of the water current is 2 km/h, how many hours will the swimmer take to swim against the current for 7 km?
Options:
A)3.0
B)3.25
C)3.5
D)3.75
E)4.0
Rationale: The swimmer can swim against the current at a speed of 4-2 = 2 km/h.
The time it will take is 7/2 = 3.5 hours.
The answer is C.
Answer: C
Question: Suresh borrowed some money at the rate of 6% p.a. for the first two years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow?
Options:
A)s.8500
B)s.6000
C)s.8500
D)s.9000
E)s.7000
Rationale: using the formula S.I=P*T*R/100
(x*6*2/100)+(x*9*5/100)+(x*13*3/100)=8160
x=8500
i.e money borrowed is Rs.8500
ANSWER:C
Answer: C
Question: If -4 < x < 8 and -6 < y < 3, which of the following specifies all the possible values of xy?
Options:
A)-42 < xy < 21
B)-42 < xy < 24
C)-48 < xy < 24
D)-24 < xy < 21
E)-24 < xy < 24
Rationale: The least value of xy is a bit more than 8*(-6)=-48 and the largest value of xy is a bit less than (-4)*(-6)=24.
Therefore -48 < xy < 24.
Answer: C.
Answer: C
Question: On Friday, Kramer purchases exactly 3 new shirts, 2 new sweaters, and 4 new hats, On the following day and each subsequent day thereafter, Kramer wears one of his new shirts together with one of his new sweaters and one of his new hats. Kramer avoids wearing the exact same combination of shirt, sweater, and hat for as long as possible. On which day is this no longer possible?
Options:
A)Tuesday
B)Wednesday
C)Thursday
D)Friday
E)Saturday
Rationale: Shirt combinations = 3!/1*(3-1)! = 3*2*1/1*2*1 = 3
Sweater combinations = 2!/1*(2-1)! = 2*1/1*1 = 2
Hat combinations = 4!/1!*(4-1)! = 4*3*2*1/1*3*2*1 = 4
Total Combinations = Shirt Combos*Sweater Combos*Hat Combos
3*2*4=24 combinations
24 / 7 (days of the week) = remainder of 3
Purchased on Friday, 3rd day is Monday. Next day, which he won't have a new combination for, is Tuesday. (A)
Answer: A
Question: In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 6 is
Options:
A)8
B)12
C)81
D)20
E)24
Rationale: I've never seen such kind of question in GMAT before.
OK there can be 4 cases:
|x+y| + |x-y| = 4
A. x+y+x-y = 6 --> x=3
B. x+y-x+y = 6 --> y=3
C. -x-y +x-y= 6 --> y=-3
D. -x-y-x+y=6 --> x=-3
The area bounded by 4 graphs x=3, x=-3, y=3, y=-3 will be square with the side of 4 so the area will be 9*9=81.
Answer: C
Answer: C
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is
Options:
A)25/42
B)25/44
C)25/409
D)25/45
E)25/41
Rationale: Total fruits = 9
Since there must be at least two apples,
(5C2 * 4C1)/8C1 +2C2/2C2 = 25/42.
Answer:A
Answer: A
Question: On a certain test, Bill scored 20 more points than John, but half as many points as Sue. If the sum of the scores of the three students was 160 points, how many points did Bill receive?
Options:
A)30
B)45
C)50
D)80
E)100
Rationale: consider john's points as x
so bill's points are x +20
So sue's points are 2x +40
total of all three students is 4x +60, but this total is given as 160
x = 25
so bill's points = 25 +20 = 45
correct answer option B
Answer: B
Question: A basket has 4 apples and 6 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked?
Options:
A)1/2
B)1/3
C)1/4
D)2/5
E)3/5
Rationale: The total possible choices are 10C3 = 120
The ways to choose 3 apples: 4C3 = 4
The ways to choose 2 apples: 4C2 * 6C1 = 36
P(at least 2 apples) = 40/120 = 1/3
The answer is B.
Answer: B
Question: A polling company reports that there is a 50% chance that a certain candidate will win the next election. If the candidate wins, there is a 60% chance that she will sign Bill X and no other bills. If she decides not to sign Bill X, she will sign either Bill Y or Bill Z, chosen randomly. What is the chance that the candidate will sign Bill Z?
Options:
A)11
B)10
C)6
D)4
E)5
Rationale: 50% - Candidate Elected
100%-60% = 40% - Candidate doesnotsigh Bill X
50% - Candidate randomly chooses between two bills.
These are multiplicative:
50% x 40% x 50%
0.5 x 0.4 x 0.5 = 0.10 = 10%
Answer (B)
Answer: B
Question: In a park there are two ponds with both brown ducks and green ducks. In the smaller pond there are 30 ducks and in the larger pond there are 50 ducks. If 20% of the ducks in the smaller pond are green and 12% of the ducks in the larger pond are green, then what percentage of ducks are green?
Options:
A)13%
B)14%
C)15%
D)16%
E)17%
Rationale: Number of ducks in small pond = 30
green ducks in small pond = 20 % of 30 = 6 ducks
Number of ducks in large pond = 50
green ducks in large pond = 12 % of 50 = 6 ducks
Total number of ducks = 30 + 50 = 80
total number of green ducks = 6 + 6 = 12 ducks
percentage of green ducks = 12/80 * 100 = 15%
Answer: C
Answer: C
Question: A man sells an article at a gain 15%. If he had bought it at 10% less and sold it for 6 less, he would have gained 25%. Find the cost price of the article.
Options:
A)150
B)160
C)170
D)180
E)240
Rationale: Let the C.P. be 100
First S.P. = 115
Second C.P. = 90
Second S.P = 125% of 90 = 112.50
Difference of two selling prices is 115 – 112.50 = 2.50 and C.P. of the article is 100
But actual difference is 6.
∴ C.P. = 100⁄2.50 × 6 = 240.
Answer E
Answer: E
Question: If 6 men and 8 women can do a piece of work in 10 days while 26 men and 48 women can do the same in 2 days, the time taken by 15 men and 20 women in doing the same type of work will be?
Options:
A)5
B)4
C)6
D)7
E)8
Rationale: Let 1 man's 1 day's work = x and 1 women's 1 day's work = y.
Then, 6x + 8y = 1 and 26x + 48y = 1 .
10 2
Solving these two equations, we get : x = 1 and y = 1 .
100 200
(15 men + 20 women)'s 1 day's work = 15 + 20 = 1 .
100 200 4
15 men and 20 women can do the work in 4 days.
Hence Answer will be B
Answer: B
Question: X = 101102103104105106107......146147148149150 (From numbers 101-150). Find out the remainder when this number is divided by 9.
Options:
A)2
B)4
C)5
D)6
E)7
Rationale: Sol:
The divisibility rule for 9 is sum of the digits is to be divisible by 9. So
We calculate separately, sum of the digits in hundreds place, tenths place, and units place.
Sum of the digits in hundreds place: 1 x 50 = 50
Sum of the digits in tenths place : 0 x 9 + 1 x 10 + 2 x 10 + 3 x 10 + 4 x 10 + 5 x 1 = 105
Sum of the digits in units place : (1 + 2 + 3 + ...+ 9) x 5 = 225
So total = 380
So remainder = 380 / 9 = 2
Answer:A
Answer: A
Question: Find the odd man out 8,27, 64,216,,512,1000
Options:
A)216
B)512
C)64
D)8
E)27
Rationale: 27 is cube of 3 which is odd number where as all others are cubes of even numbers.
ANSWER:E
Answer: E
Question: Ifaequals the sum of the even integers from 2 to 80, inclusive, andbequals the sum of the odd integers from 1 to 79, inclusive, what is the value of a - b ?
Options:
A)1
B)10
C)19
D)40
E)21
Rationale: This is a solution from Beatthegmat:
even numbers:
(80-2)/2 + 1 = 40 even integers.
(80+2)/2 = 41 is the average of the even set.
sum = avg*(#of elements) = 41*40 = 1640 = a
odd numbers:
(79-1)/2 + 1 = 40 odd integers.
(79+1)/2 = 40 is the average of the odd set.
sum = avg*(#of elements) = 40*40 = 1600 = b
a-b = 1640 - 1600 = 40. Answer : D
Answer: D
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)10 kmph
B)67 kmph
C)22 kmph
D)88 kmph
E)12 kmph
Rationale: Speed of the boat in still water
= (60+80)/2
= 70 kmph. Speed of the stream
= (80-60)/2
= 10 kmph.
Answer:A
Answer: A
Question: If x is an odd integer, which of the following is an odd integer?
Options:
A)2x+2
B)x^2
C)2x+4x
D)1+2x+x^2
E)3x-1
Rationale: Plug in an odd integer; in this case 3
(2*3)+2 = 8 Even
3^2 = 9 Odd
(2*3)+(4*3) = 6 + 12 = 18 Even
1+(2*3)+3^2 = 1+ 6 + 9 = 16 Even
(3*3)-1 = 9 - 1 = 8 Even
Answer: B
Answer: B
Question: The length of a rectangular plot is 10mtr more than its width. The cost of fencing the plot along its perimeter at the rate of Rs. 6.5mtr is Rs.1170. The perimeter of the plot is?
Options:
A)126
B)156
C)180
D)321
E)260
Rationale: Sol. Let width = x, Length = (10+x)
Perimeter = 2(x+(10+x))
= 2(2x=10)
& 2(2x+10)*6.5 = 1170
X = 40
Required perimeter = 2(40+50) = 180
C
Answer: C
Question: The ratio of two quantities is 3 to 7. If the first quantity is increased by 6, how much should the second quantity be increased to maintain the same ratio?
Options:
A)6
B)7
C)14
D)28
E)It cannot be determined from the information given
Rationale: 3:7 means 3x:7x...
The ratio is maintained when each of the Xs are the same...
3(1) + 6 equals 3(3)
7(3) equals 7(1) +14
ANSWER:C
Answer: C
Question: A Prototype fuel-efficient car (P-Car) is estimated to get 90% more miles per gallon of gasoline
than does a traditional fuel-efficient car (T-Car). However, the P-Car requires a special type
of gasoline that costs 60% more per gallon than does the gasoline used by a T-Car. If the two
cars are driven the same distance, what percent less than the money spent on gasoline for the
T-Car is the money spent on gasoline for the P-Car?
Options:
A)15.78%
B)33 1/3 %
C)50%
D)60%
E)66 2/3 %
Rationale: Assumption
Miles/Gallon
T = 100
P = 190 ( 90% more)
$/gallon
T = 100
P = 160 (60% more)
Miles
100 for both
Cost = (Miles X $/ Gallon)/ M/gallon
T = 100
P = 84.21
Hence 100 - 84.21 =15.78%
Ans A
Answer: A
Question: The volume of the sphere QQ is (dfrac{37}{64}%)less than the volume of sphere PP and the volume of sphere RR is (dfrac{19}{27}%) less than that of sphere QQ. By what is the surface areaof sphere RR less than the surfacearea of sphere PP?
Options:
A)50%
B)60%
C)75%
D)80%
E)89%
Rationale: Let the volume of sphere PP be 64 parts.
Therefore volume of sphere QQ
=64−3764%=64−3764% of 6464
=64−37=27=64−37=27 parts.
The volume of RR
=27−1927×27=27−1927×27
=27−19=8=27−19=8 parts.
Volume ratio:
=P:Q:R=64:27:8=P:Q:R=64:27:8
Radius ratio:
=P:Q:R=4:3:2=P:Q:R=4:3:2
The surface area will be 16:9:516:9:5
Surface area of RR is less than the surface area of sphere PP
16k−4k=12k16k−4k=12k
Now,
=12k16k×100=12k16k×100
=75%=75%
Thus surface area of sphere RR is less than the surface area of sphere P by 75%
C
Answer: C
Question: How long does a train 110 m long running at the speed of 90 km/hr takes to cross a bridge 132 m length?
Options:
A)12.9 sec
B)9.68 sec
C)17.9 sec
D)16.8 sec
E)14.9 sec
Rationale: Speed = 90 * 5/18 = 25 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/25 = 9.68 sec.
Answer: B
Answer: B
Question: In a partnership, A invests 1⁄6 of the capital for 1⁄6 of the time, B invests 1⁄3 of the capital for 1⁄3 of the time and C, the rest of the capital for whole time. Find A’s share of the total profit of 2,300
Options:
A)100
B)200
C)300
D)400
E)None of these
Rationale: Remaining capital = 1 - (1⁄6 + 1⁄3) = 1⁄2
Ratio of their profit
= 1⁄6 × [1⁄6 × 12] : 1⁄3 × [1⁄3 × 12] : 1⁄2 × 12
= 1⁄3 : 4⁄3 : 6 = 1 : 4 : 18
∴ A's share = 1 /1+4+18×2300 = 100
Answer A
Answer: A
Question: Two different solutions of alcohol with respective proportions of alcohol to water of 3:1 and 2:3 were combined. What is the concentration of alcohol in the new solution if the first solution was 4 times the amount of the second solution?
Options:
A)62
B)65
C)68
D)70
E)72
Rationale: SOL:
Lets assume that 40L of sol1 was mixed with 10L of sol2.
Alcohol in Sol1: 40*3/4 = 30L
Alcohol in Sol2: 10*2/5 = 4L
Total Alcohol in the mixed solution of 50L = 30 + 4 = 34L
Alcohol concentration in the new sol: (34/50)*100 = 68%
ANSWER:C
Answer: C
Question: A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together 8 hours a day?
Options:
A)2 days
B)5 days
C)7 days
D)3 days
E)9 days
Rationale: Sol. A can complete the work in (7 x 9) = 63 hours.
B can complete the work in (6 x 7) = 42 hours.
A’s 1 hour's work = (1/63) and B's 1 hour's work =(1/42)
(A + B)'s 1 hour's work =(1/63)+(1/42)=(5/126)
Both will finish the work in (126/5) hrs.
Number of days. of (42/5) hrs each =(126 x 5)/(5 x 42)=3 days
Ans: D
Answer: D
Question: What distance will be covered by a bus moving at 72 kmph in 30 seconds?
Options:
A)278
B)600
C)772
D)551
E)131
Rationale: 72 kmph = 72 * 5/18 = 20 mps
D = Speed * time = 20 * 30 = 600 m.
Answer: B
Answer: B