mathewhe/aqua_rat huggingface dataset:
Question: The number of students enrolled at school XX this year is 7 percent more than it was last year. The number of students enrolled at school YY this year is 3 percent more than it was last year. If school XX grew by 40 more students than school YY did, and if there were 4000 total enrolled students last year at both schools, how many students were enrolled at school YY last year?
(A) 480
(B) 1600
(C) 1920
(D) 2080
(E) 2400
Rationale: Given Info:
No. of students enrolled in school X is= 7% more than previous year's strength= 7X/100
No. of students enrolled in school Y is= 3% more than previous year's strength= 3Y/100
Given that "THIS YEAR" school X have 40 students more than school Y. So the increase in strength can be written as
7X/100= 40 + 3Y/100
7X= 4000 + 3Y....................(1)
And total students on previous year are X + Y=4000......................(2)
Equating & Solving we get, Y=2400
ANS is E
Answer: (E) 2400
Question: In how many ways can live boys and three girls sit in a row such that all boys sit together?
(A) 2888
(B) 2885
(C) 2880
(D) 2876
(E) 2224
Rationale: Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements = 4! * 5! = 24 * 120 = 2880.
Answer:C
Answer: (C) 2880
Question: There is a 30% increase in the price of an article in the first year, a 20% decrease in the second year and a 10% increase in the next year. If the final price of the article is Rs. 2288, then what was the price of the article initially?
(A) Rs. 1500
(B) Rs. 1800
(C) Rs. 2000
(D) Rs. 2400
(E) None of these
Rationale: Let the price of the article, four years age be Rs. 100 in the 1st year, price of the article = 100 + 30 = Rs. 130. In the 2nd year, price = 130 - 20% of 130 = 130 - 26 = Rs. 104.
In the 3rd year, price = 104 + 10% of 104 = 104 + 10.4 = Rs. 114.40.
But present price of the article is Rs. 2288
for 114.4 ---> 100 ; 2288 ---> ?
Required price = (2288 * 100)/114.4 = 20 * 100 = Rs. 2000.
ANSWER:C
Answer: (C) Rs. 2000
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
(A) 12 days
(B) 15 days
(C) 16 days
(D) 18 days
(E) 20 days
Rationale: Explanation:
A's 2 day's work =(1/20 x 2)=1/10
(A + B + C)'s 1 day's work =(1/20 +1/30+1/60)=6/60=1/10
Work done in 3 days =(1/10 +1/10)=1/5
Now,	1/5work is done in 3 days
Whole work will be done in (3 x 5) = 15 days.
ANSWER IS B
Answer: (B) 15 days
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 18 as remainder
(A) 1235
(B) 1346
(C) 1378
(D) 1634.4
(E) 1489
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 18
5x = 1347
x = 269.4 number = 269.4+1365 = 1634.4
D
Answer: (D) 1634.4
Question: All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 154 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?
(A) 1232
(B) 1723
(C) 1129
(D) 2613
(E) 1372
Rationale: A
B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.
Quantity of milk in B = 8k - 5k = 3k.
Quantity of milk in container C = 8k - 3k = 5k
Container: A B C
Quantity of milk: 8k 3k 5k
It is given that if 154 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.
5k - 154= 3k + 154 => 2k = 308 => k = 154
The initial quantity of milk in A = 8k = 8 * 154 = 1232 liters.
Answer: (A) 1232
Question: What least number must be subtracted from 7538 so that remaining no.is divisible by 14
(A) 3
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Explanation:
On dividing 7538 by 14 we get the remainder 6, so 6 should be subtracted
Option C
Answer: (C) 6
Question: A is 2 times as fast as B. A alone can do the work in 20 days. If A and B working together in how many days will the work be completed?
(A) 23
(B) 13
(C) 21
(D) 24
(E) 25
Rationale: A can finish 1 work in 20 days
B can finish 1/2 work in 20 days - since A is 2 faster than B
This means
B can finish 1 work in 20*2 days = 40 days
Now using the awesome GMAT formula when two machines work together they can finish the job in = AB/ (A+B) = 20*40/(20+40) = 13 days
So answer is B
Answer: (B) 13
Question: What is the difference between the place value and face value of 1 in the numeral 54315?
(A) 9
(B) 11
(C) 5
(D) 1
(E) 10
Rationale: Difference between the place value and face value of 1 = 10-1 = 9
Answer is A
Answer: (A) 9
Question: There are two numbers such that the sum of twice the first and thrice the second is 39, while the sum of thrice the first and twice the second is 36. The larger of the two is
(A) 6
(B) 9
(C) 12
(D) 15
(E) 17
Rationale: Sol.
Let the numbers be x and y.
Then, 2x + 3y = 39 ................(i)
3x + 2y = 36 .................(ii)
On solving (i) and (ii), we get : x = 6 and y = 9.
∴ Larger number = 9.
Answer B
Answer: (B) 9
Question: If (3^4)(5^6)(7^3) = (35^n)(x), where x and n are both positive integers, how many different possible values of n are there?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
Rationale: Notice that the power of 7 in LHS is limiting the value of n, thus n cannot be more than 3 and since n is a positive integer, then n could be 1, 2, or 3.
Answer: C.
Answer: (C) 3
Question: A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?
(A) 1211
(B) 1218
(C) 1210
(D) 1212
(E) 1229
Rationale: π (232 – 122)
= 1210
Answer: C
Answer: (C) 1210
Question: What is the sum of all the numbers between 300 and 1000 which are divisible by 179?
(A) 1267
(B) 2876
(C) 1865
(D) 2506
(E) 1812
Rationale: Explanation:
358/179 â€¦.. 895/179
179(2 + 3 + 4 + 5) => 2506
Answer:D
Answer: (D) 2506
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are
(A) 42,30
(B) 42,31
(C) 42,32
(D) 42,33
(E) None of these
Rationale: Explanation:
Let their marks be (x+9) and x.
Then, x+9 = 56/100(x + 9 +x)
=> 25(x+9)
=> 14 (2x + 9)
=> 3x = 99
=> x = 33.
So, their marks are 42 and 33
Option D
Answer: (D) 42,33
Question: Find the value of 72519 x 9999 = y?
(A) 354517481
(B) 457687783
(C) 246567689
(D) 725117481
(E) 565776879
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: In a survey of parents, exactly 9/10 of the mothers and 3/4 of the fathers held full-time jobs. If 40 percent of the parents surveyed were women, what percent of the parents did not hold full-time jobs?
(A) 27%
(B) 21%
(C) 19%
(D) 18%
(E) 16%
Rationale: Fathers without full-time jobs are 1/4*3/5 = 3/20 of all the parents surveyed.
Mothers without full-time jobs are 1/10*2/5 = 2/50 of all the parents surveyed.
The percent of parents without full-time jobs is 3/20 + 2/50 = 19/100 = 19%
The answer is C.
Answer: (C) 19%
Question: The average age of a class of 20 students is 14 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) 36 years
Rationale: If age of the teacher was 14, average would not have changed.
Since average increased by 2,
Age of the teacher=14+22×1=36
ANSWER:E
Answer: (E) 36 years
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 20 m wide at the top and 12 m wide at the bottom and the area of cross-section is 800 sq m, the depth of cannel is?
(A) 76
(B) 50
(C) 27
(D) 80
(E) 25
Rationale: 1/2 * d (20 + 12) = 800
d = 50
Answer: B
Answer: (B) 50
Question: In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is
(A) 35
(B) 37
(C) 39
(D) 41
(E) 46
Rationale: Explanation:
Let B's age = x years.
Then, As age = (x+ 9) years.
(x+9+10)=2(x�10)
hence x=39.
Present age of B = 39 years
Answer: Option C
Answer: (C) 39
Question: Three pipes A, B and C can fill a tank in 5 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 6 hours. How many hours will take C alone to fill the tank?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: The rate of A+B+C is 1/5 of the tank per hour.
After 2 hours, the tank is 2/5 full.
The rate of A+B is 3/5 * 1/6 = 1/10 of a tank per hour.
The rate of C is 1/5 - 1/10 = 1/10
C can fill the tank in 10 hours.
The answer is B.
Answer: (B) 10
Question: The ratio of 2 numbers is 2:3 and their H.C.F. is 10. Their L.C.M. is ?
(A) 30
(B) 60
(C) 20
(D) 10
(E) 40
Rationale: Let the numbers be 2x and 3x
Their H.C.F. = 10
so the numbers are 2*10 , 3*10 = 20,30
L.C.M. = 60
Answer is B
Answer: (B) 60
Question: Truck X is 14 miles ahead of Truck Y, which is traveling the same direction along the same route as Truck X. If Truck X is traveling at an average speed of 57 miles per hour and Truck Y is traveling at an average speed of 63 miles per hour, how long will it take Truck Y to overtake and drive 4 miles ahead of Truck X?
(A) 5 hours
(B) 3 hours 20 minutes
(C) 3 hours
(D) 2 hours 45 minutes
(E) 8 hours
Rationale: Relative speed = 63-57 = 6 miles per hour
Dist required = 14+4 = 18 miles
Time taken to overtake = 18/6 = 3 hours. C is the answer.
Answer: (C) 3 hours
Question: A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if atleast one black ball is to be included in the draw?
(A) 64
(B) 36
(C) 52
(D) 86
(E) 24
Rationale: We may have (1 black and 2 non black) or (2 black and 1 non black) or (3 black)
Required number of ways = 3C1*6C2+3C2*6C1+3C3 = 64
Answer is A
Answer: (A) 64
Question: 9 points are marked on a straight line and another 10 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
(A) 91
(B) 105
(C) 196
(D) 27
(E) 14
Rationale: assuming that the top line can have either 2 points or 1 point...
9! / 1!8! - 9! / 2! 7! yields 27.
D
Answer: (D) 27
Question: Sandy can do a job in 6 days and Molly can do the same job in 12 days. If they work together, in how many days will they complete the job?
(A) 4 days
(B) 6 days
(C) 8 days
(D) 2 days
(E) 9 days
Rationale: Sandy can do 1/6 of the job each day.
Molly can do 1/12 of the job each day.
The combined rate is 1/6 + 1/12 = 1/4 of the job each day.
The job will take 4 days.
The answer is A.
Answer: (A) 4 days
Question: If each edge of cube increased by 15%, the percentage increase in
(A) 30.25
(B) 32.25
(C) 38.25
(D) 37.25
(E) 41.25
Rationale: 100 × (115)/100 × (115)/100 = 132.25 => 32.25%
Answer is B.
Answer: (B) 32.25
Question: Find the value of x in (x+1)/(x+3)=5
(A) 2.5
(B) -2.5
(C) 3.0
(D) 3.5
(E) -3.5
Rationale: (x-1)/(x+3)=5
Multiplying both sides with x+3 gives x+1=5(x+3)
= x+1=5x+15
Subtracting x from both sides gives 4x+15=1
Subtracting 15 from both sides gives 4x=-14
Dividing by 4 on both sides gives x=-3.5
Answer: E
Answer: (E) -3.5
Question: What will be the compound interest on a sum of Rs. 21,000 after 3 years at the rate of 12% p.a.?
(A) Rs. 8503.49
(B) Rs. 9720
(C) Rs. 10123.20
(D) Rs. 10483.20
(E) None
Rationale: Amount = [21000 * (1 + 12/100)3]
= 21000 * 28/25 * 28/25 * 28/25 = Rs. 29503.49
C.I. = (29503.49 - 21000) = Rs. 8503.49
ANSWER:A
Answer: (A) Rs. 8503.49
Question: Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours. C is closed A and B can fill the remaining par in 7 hours. The number of hours taken by C alone to fill the tank is?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: Part filled in 2 hours = 2/6 = 1/3.
Remaining part = 1 - 1/3 = 2/3
(A + B)'s 1 hour work = 2/21
C's 1 hour work = [(A + B + C)'s 1 hour work - (A + B)'s 1 hour work]
= (1/6 - 2/21) = 1/14
C alone can fill the tank in 14 hours.
ANSWER:C
Answer: (C) 14
Question: If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a eight-percent vinegar solution, what was the concentration of the original solution?
(A) 9.3%
(B) 17.3%
(C) 26.67%
(D) 35.5%
(E) 41.3%
Rationale: Let X be the quantity of non-vinegar in the strong vinegar solution
Thus vinegar quantity will be 12 - X
When 50 ounces of water were added the percentage of vinegar becomes 8%, thus (12 - X)/62 = 8/100
From this equation X = 7.04
Answer (12-7.04)/12 = 41.3%
ANSWER:E
Answer: (E) 41.3%
Question: If n + 12 is a positive odd integer, which of the following must be true about the sum of the next four integers?
(A) It is a multiple of 3
(B) It is a multiple of 4
(C) It is a prime number
(D) It is a multiple of 5
(E) It is a multiple of 2
Rationale: n+12 is a positive odd integer. This means n will be an odd integer
The next 4 integers would be: n + 12, n + 13, n + 14, n + 15
Sum = 4n + 54
This sum will always be even.
Option E
Answer: (E) It is a multiple of 2
Question: Which of these expressions has the greatest value?
(A) 1673211/1663212
(B) 1356741/1356745
(C) 1245671/1245675
(D) 1124471/1124476
(E) 1217861/1217864
Rationale: Using elimination method on options
1673211/1663212 = 1.00601186139...
ANSWER:A
Answer: (A) 1673211/1663212
Question: Replace X with the appropriate number in
5 , 6 , 8 , 9 , 13 , 15, 16, X
(A) 22
(B) 20
(C) 21
(D) 17
(E) 18
Rationale: E
list of consecutive numbers that has an 'i' in the spelling
Answer: (E) 18
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train catches and completely passes the slower train in 45 seconds. What is the length of each train (in meters)?
(A) 48.5
(B) 62.5
(C) 73.5
(D) 87.5
(E) 96.5
Rationale: The relative speed = 46 - 36 = 10 km/hr = 10 * 5/18 = 25/9 m/s
In 45 seconds, the relative difference in distance traveled is 45 * 25/9 = 125 meters
This distance is twice the length of each train.
The length of each train is 125/2 = 62.5 meters
The answer is B.
Answer: (B) 62.5
Question: . Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a?
(A) Rs.228
(B) Rs.229
(C) Rs.220
(D) Rs.200
(E) Rs.221
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800
= Rs.200
As this is positive, an overall profit of Rs. 200 was made.
Answer:D
Answer: (D) Rs.200
Question: A cook went to a market to buy some eggs and paid $12. But since the eggs were quite small, he talked the seller into adding two more eggs, free of charge. As the two eggs were added, the price per dozen went down by a dollar. How many eggs did the cook bring home from the market?
(A) 8
(B) 12
(C) 15
(D) 16
(E) 18
Rationale: Say the # of eggs the cook originally got was x;
he price per egg then would be 12x and the price per dozen would be 12∗12/x.
Now, since the cook talked the seller into adding two more eggs then he finally got x+2 eggs (notice that x+2 is exactly what we should find);
So, the price per egg became 12/x+2 and the price per dozen became 12∗12/x+2 .
As after this the price per dozen went down by a dollar then 12∗12/x−12∗12/x+2=1, which simplifies to 144/x−144/x+2=1. At this point it's better to substitute the values from answer choices rather than to solve for x. Answer choices E fits: if x+2=18 then 144/16−144/18=9−8=1 .
Answer: E
Answer: (E) 18
Question: A train is moving at a speed of 100 km/hour. The length of the train is 100 metre. In how much time will it cross a pole?
(A) 1 second
(B) 2.5 second
(C) 4 second
(D) 3.6 second
(E) 4.5 second
Rationale: In order to cross the pole, the train will need to cover its own length of 100 meter. To cover 100x1000 meter, train takes 60 minutes or 60 x 60 = 3600 second. So, to cover 100 meter, train would take 3600 x 100 / 100 x 1000 = 3.6 second.
Answer: D.
Answer: (D) 3.6 second
Question: If 4x+y=40, 2x-y=20, for integers of x and y, y^2=?
(A) 2
(B) 4
(C) 0
(D) 10
(E) 3
Rationale: 4x+y = 40
2x-y = 20
6x = 60
x = 10
y = 0
y^2 = 0
Answer is C
Answer: (C) 0
Question: The difference between a number and its two-fifth is 510. What is 20% of that number?
(A) 177
(B) 170
(C) 172
(D) 174
(E) 171
Rationale: Let the number be x. Then,
x - 2/5 x = 510
x = (510 * 5)/3 = 850
20% of 850 = 170.
Answer:B
Answer: (B) 170
Question: A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?
(A) 22
(B) 66
(C) 28
(D) 41
(E) 61
Rationale: (1 man + 1 woman)'s 1 day work = (1/3 + 1/4) = 7/12 Work done by 1 man and 1 woman in 1/4 day = (7/12 * 1/4) = 7/48
Remaining work = (1 - 7/48) = 41/48
Work done by 1 boy in 1/4 day = ( 1/12 * 1/4) = 1/48
Number of boys required = 41/48 * 41 = 41.
Answer: D
Answer: (D) 41
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 16 hours respectively. The ratio of their speeds is?
(A) 4:5
(B) 4:2
(C) 4:4
(D) 4:8
(E) 4:1
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √4
= 4:2
Answer: B
Answer: (B) 4:2
Question: In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?
(A) 7787
(B) 8000
(C) 1988
(D) 1277
(E) 2081
Rationale: x*110/100 * 90/100 = 7920
X*0.99=7920
X=7920/0.99
=> 8000
Answer:B
Answer: (B) 8000
Question: At 3:00 pm, a car has driven 30 miles east. It will continue to drive east at 0.6 minutes per mile and then turn around and drive at 0.6 minutes per mile back to its original starting point. How far can it drive before turning around in order to arrive back to its original starting point by 3:40 pm?
(A) a) 10
(B) b) 11
(C) c) 55/3
(D) d) 13
(E) e) 14
Rationale: 0.8 minutes --> 1 mile
1 minute --> 1/0.6 = 10/6 = 5/3 miles/minute
Distance covered in 40 minutes = 5/3 * 40 = 200/3 miles
Distance covered in the current direction = Distance covered from the opposite direction (since car returns back to starting point)
Let x be the miles driven before turning
30 + x = 200/3 - x
2x = 200/3 -30
x = 55/3
Answer: C
Answer: (C) c) 55/3
Question: In a certain sequence of 9 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: Non - Negative ( zero to positive infinity )
Solution to the question :
-5,-4,-3,-2,-1,0 , 1,2,3
Hence ans is 3 ..option D
Answer: (D) Three
Question: Given the two equations 10r + 5s = 115 and r + 2s = 16, by how much does r exceed s?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Solve by Simultaneous Equations.
My Answer is E.
r=10
s=3
Answer: (E) 7
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $432 per week. How much does she earn in dollars per hour?
(A) 2
(B) 8
(C) 9
(D) 11
(E) 12
Rationale: Explanation:
Total hours worked = 8 x 3 + 6 x 2 = 36
Total earned = 432. Hourly wage = 432 / 36 = 12
Answer: E
Answer: (E) 12
Question: Three candidates contested an election and received 1000, 7000 and 100 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 57%
(B) 60%
(C) 65%
(D) 90%
(E) 86.4%
Rationale: total votes are 8100 ( sum of votes obtained by 3 candidates)
percentage of the total votes recd by the winning candidate = 100*7000/8100 = 86.4%
ANSWER:E
Answer: (E) 86.4%
Question: The area of square ABCD above is 18. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?
(A) 18−9/4∗π
(B) 18−9/2∗π
(C) 9+9/4∗π
(D) 9+9/2∗π
(E) 9/2−9/4∗π
Rationale: =Square - Quarter circle
=18- pi*18/4
=18- pi*9/2
ANSWER:B
Answer: (B) 18−9/2∗π
Question: P and Q are the only two applicants qualified for a short-term research project that pays 300 dollars in total. Candidate P has more experience and, if hired, would be paid 50 percent more per hour than candidate Q would be paid. Candidate Q, if hired, would require 10 hours more than candidate P to do the job. Candidate P’s hourly wage is how many dollars greater than candidate Q’s hourly wage?
(A) $5
(B) $10
(C) $15
(D) $20
(E) $25
Rationale: Let Q's hourly wage be x, then P's hourly wage is 1.5x
Let T be the number of hours that Q needs, then P needs T-10 hours to do the job.
Since they both are paid an equal total amount of $300:
x*T=1.5x*(T-10)
T = 30 hours and Q's hourly wage is 300/30 = $10
P's hourly wage is 300/(T-10) = $15 which is $5 per hour more.
The answer is A.
Answer: (A) $5
Question: In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 50 percent of the male and 20 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
(A) A)0.9
(B) B)0.6
(C) C)0.45
(D) D)0.3
(E) E)0.25
Rationale: Percent of students who are 25 years old or older is 0.5*48+0.2*52=~34, so percent of people who are less than 25 years old is 100-3=66.
Answer: B.
Answer: (B) B)0.6
Question: How many numbers from 29 to 79 are exactly divisible by 11
(A) 5
(B) 7
(C) 8
(D) 9
(E) 11
Rationale: 29/11 = 2 and 79/11 = 7 ==> 7 - 2 = 5 Numbers
Option 'A'
Answer: (A) 5
Question: 7 boys take 12 days to complete a job. They worked for 5days, after 5days 2boys left the job. In how many days 5 boys will complete the job ?
(A) 5 days
(B) 6 days
(C) 7 days
(D) 9 days
(E) 9 ⅘ days
Rationale: 7 men can do 1/12 of the job per day
So after 5 days they have completed 5/12th job. Still 7/12 part of the job is to be completed.
5 men can do 1/12 × 5/7 = 5/84 of the job per day
So they will take 7/12 × 84 /5 = 9 ⅘ days to complete the job
(E)
Answer: (E) 9 ⅘ days
Question: What is the sum of the odd integers from 35 to 55, inclusive?
(A) 495
(B) 550
(C) 555
(D) 600
(E) 605
Rationale: The mean is 45.
Sum=Mean(# of elements)
There are 11 odd numbers between 35-55 inclusive. 11*45=495
A
Answer: (A) 495
Question: The average of five results is 46 and that of the first four is 40. The fifth result is?
(A) 50
(B) 88
(C) 70
(D) 66
(E) 51
Rationale: 5 * 46 â€“ 4 * 40
= 70
Answer: C
Answer: (C) 70
Question: The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere. If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams W?
(A) W=16
(B) W=32
(C) 64
(D) 128
(E) 512
Rationale: Weight directly proportional to 4 pi r^2
Now, 4pi is constant, so, weight is directly proportional to r^2.
When radius = 0.15, weight = 8, so (0.15) ^ 2 proportional to 8;
(0.15)^2 * 4 proportional to 8*4, solving further
(0.15)^2 * 2 ^2 = (0.15*2)^2 = 0.3 ^ 2; so answer = 32 (B)
Answer: (B) W=32
Question: An empty pool being filled with water at a constant rate takes 4 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?
(A) 5 hr 30 min
(B) 5 hr 20 min
(C) 4 hr 48 min
(D) 3 hr 12 min
(E) 2 hr 40 min
Rationale: (3/5) of a pool/ 4 hours = 3/20 (the rate)
(3 pools/20 hours) = (2/5* pool)/ x hours
Cross multiply 3x = (2/5) 20
x = 2 2/3
2/3 of an hour = 40 minutes
E
Answer: (E) 2 hr 40 min