mathewhe/aqua_rat huggingface dataset:
Question: An outlet pipe can empty 2/3 rd of a cistern in 12 minutes. In 8 minutes, what part of the cistern will be emptied?
(A) 4/9
(B) 2/3
(C) 4/7
(D) 1/6
(E) 2/5
Rationale: Explanation:
2/3 ---- 12
? ----- 8 ==> 4/9
ANSWER IS A
Answer: (A) 4/9
Question: Of the following values of n, the value of (-1/6 )^(-n) will be greatest for n =
(A) 2
(B) 3
(C) 0
(D) -2
(E) -3
Rationale: imo -2
(-1/6)^-2=
1/(1/36)=36
oops i meant 2
A
Answer: (A) 2
Question: A line has a slope of 3/4 and intersects the point Q (-12, -39). At which point does this line intersect the x-axis?
(A) (40,0)
(B) (30,0)
(C) (0,40)
(D) (40,30)
(E) (0,30)
Rationale: Assume that the equation of the line is y=mx+c, where m and c are the slope and y-intercept.
You are also given that the line crosses the point (-12,-39), this means that this point will also lie on the line above.
Thus you get -39=m*(-12)+c , with m=3/4 as the slope is given to be 3/4.
After substituting the above values, you get c = -30.
Thus the equation of the line is y=0.75*x-30 and the point where it will intersect the x-axis will be with y coordinate = 0.
Put y=0 in the above equation of the line and you will get, x=40.
Thus, the point Q of intersection is (40,0).
A is the correct answer.
Answer: (A) (40,0)
Question: If 4b^4 − 41b^2 + 100 = 0, then what is the sum of the two greatest possible values of b ?
(A) 4
(B) 9/2
(C) 7
(D) 41/4
(E) 25
Rationale: just forget about the value of b^4 for the moment and let b^2= X. (its better to work with power of 2 than 4)
now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.
so b^2 = 4 and 25/4
so b= +2 and minus 2 and +5/2 and minus 5/2
The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = B
Answer: (B) 9/2
Question: (0.0048)(3.5) / (0.05)(0.1)(0.004)=
(A) 8.4
(B) 840
(C) 84.0
(D) 0.84
(E) 0.084
Rationale: (0.0048)(3.5) / (0.05)(0.1)(0.004) = 0.0048 *350/5 (0.1)(0.004)
= 0.048*70/1 (0.004)
=48*70/4 =12*70
=840
Answer : B
Answer: (B) 840
Question: Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 100 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?
(A) 250
(B) 300
(C) 350
(D) 400
(E) 500
Rationale: Nice problem. +1.
First timetogetherthey run half of the circumference.
Second timetogetherthey run full circumference.
First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.
Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 100 meters, thus the circumference is 200 + 100 = 300 meters.
Answer: B.
Answer: (B) 300
Question: Find 283/1983×100
(A) 14.29
(B) 14.21
(C) 14.22
(D) 14.27
(E) 14.23
Rationale: Never start finding common factors.
Adjust the denominator to 2000. So we are introducing an error of 17 which is 171983=1117171983=1117 th of the denominator.
283002000=14.15283002000=14.15
But this answer is slightly less than actual answer.
Now 14.1511714.15117 = 0.12 approximately.
Adding 0.12 to 14.25 gives 14.27.
Option B is correct.
Answer: (B) 14.21
Question: Of the four numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is ?
(A) 28
(B) 29
(C) 11
(D) 48
(E) 10
Rationale: Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 60 or x = (60 * 4) / 5 = 48.
Answer: D
Answer: (D) 48
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
(A) 99
(B) 87
(C) 57
(D) 54
(E) 23
Rationale: 30 * 33/2 = 5/2 * 2 * x => x
= 99
Answer:A
Answer: (A) 99
Question: Which of the following functions does not intersect with w = 3x^2 + 2x + 1
(A) W = 3x^2 + 3x + 1
(B) W = 2x^2 + 3x + 1
(C) W = 3x^2 + 2x + 3
(D) W = 4x^2 + 2x - 3
(E) W = x^2 + 2x + 3
Rationale: Let’s find the actual intersecting point of given function and each choice w
A. 3x^2 + 2x + 1 = 3x^2 + 3x + 1 --> x=0
B. 3x^2 + 2x + 1 = 2x^2 + 3x + 1 --> x^2 – x =0 --> x=0 or 1
C. 3x^2 + 2x + 1 = 3x^2 + 2x + 3 --> 1=3(X) --> they don’t have any intersect.
D. 3x^2 + 2x + 1 = 4x^2 + 2x - 3 --> x^2 –4=0 --> x= 2 or -2
E. 3x^2 + 2x + 1 = x^2 + 2x + 3 --> 2x^2 –2 =0 --> x= 1 or –1.
So only choice (C) has no intersecting point. The answer is (C).
Answer: (C) W = 3x^2 + 2x + 3
Question: In a certain city, 60% of the registered voters are democrats and the rest are republicans.In a mayoral race, if 75% of the registered voters who are democrats and 20% of the registered voters who are republicans are expected to vote for candidate A,What % of the registered voters are expected to vote for candidate A?
(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%
Rationale: Let total voters = 100
so D= 60, vote for the mayor 60*75%=45 (60*3/4)
R= 40, vote for the mayor 40*20%= (40*1/5)
45+8=53
53/100*100=53%
ANSWER:B
Answer: (B) 53%
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
(A) Rs.6620
(B) Rs.6500
(C) Rs.6800
(D) Rs.6400
(E) None of these
Rationale: Explanation:
A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer IS A
Answer: (A) Rs.6620
Question: In a sample of 800 high school students in which all students are either freshmen, sophomores, juniors, or seniors, 22 percent are juniors and 74 percent are not sophomores. If there are 160 seniors, how many more freshmen than sophomores are there among the sample of students?
(A) 42
(B) 48
(C) 56
(D) 208
(E) 256
Rationale: Sophomores= 26%
Juniors = 22%
Seniors = 160/800 =20%
Total: 68%
1-68%=32% (Freshmen)
0,32*800-0,26*800=256-208=48.
Answer choice B
Answer: (B) 48
Question: A company’s four cars running 12 hrs a day consume 1200 lts of fuel in 10 days. In the next 6 days, the company will need to run 9 cars for 12 hrs each so it rents 5 more cars which consume 20% less fuel than the company’s four cars. How many lts of fuel will be consumed in the next 6 days?
(A) 1200 lt
(B) 1440 lt
(C) 1664 lt
(D) 1728 lt
(E) 4800 lt
Rationale: Given that
4 cars running 12 hrs a day consume 1200 lts. of fuel in 10 days.
1 car consumption per hour per day = 1200 /4 *12 *10 = 2.5 litre
Now question say new car consume 20% less fuel than the company’s four cars = 80/100 of 2.5 = 2 ( 20 percent less than 2.5)
Hence we calculate total consumption for next 6 days, the company will need to run 5 new cars for 12 hrs = 2 *12 *6*5 =720
similarly = old 4 car consumption for next 6 days for 12 hrs =2.5*6*12*4 = 720
hence total is = 720+720= 1440 lt
Ans is B .
Answer: (B) 1440 lt
Question: The product of all the prime numbers less than 18 is closest to which of the following powers of 10 ?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5
Rationale: Product of Prime numbers less than 18 is 2*3*5*7*11*13*17
2*5=10 .
10*11*3*7*13*17 = 10*10*3*10*10*20 (approximately) ~ Product will be >10^5 <10^7 i.e. 10^6
D is the answer
Answer: (D) 10^6
Question: 6 workers should finish a job in 8 days. After 3 days came 4 workers join them. How many days X do they need to finish the same job?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let Rate of one worker be R
=> (6*R)*8 = 1 (Rate * Time = work)
=> R = 1/48
=> Work remaining after 3 days
1 - (3*6)/48 = 30/48
After 4 ppl joined in
((6+4)*Time)/48 = 30/48
Time X= 3 days to finish the task
IMO A
Answer: (A) 3
Question: The sum of four consecutive even numbers is 36. Find the sum of the squares of these numbers?
(A) 296
(B) 252
(C) 344
(D) 388
(E) None of these
Rationale: Let the four numbers be x, x + 2, x + 4 and x + 6.
=> x + x + 2 + x + 4 + x + 6 = 36
=> 4x + 12 = 36 => x = 6
The numbers are 6, 8, 10 and 12.
Sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344.
ANSWER:C
Answer: (C) 344
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
(A) 10.18 p.m
(B) 10.29 p.m
(C) 10.30 p.m
(D) 10.38 p.m
(E) 10.32 p.m
Rationale: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer:C
Answer: (C) 10.30 p.m
Question: If 10 gallons of grape juice are added to 40 gallons of a mixture, which contains 30 percent grape juice then what percent of the resulting mixture is grape juice?
(A) 14%
(B) 25%
(C) 48%
(D) 34%
(E) 50%
Rationale: OFFICIAL SOLUTION:
If we start with 40 gallons of a mixture that is 10% grape juice, then we have:
40 × 0.30 = 12 gallons of grape juice.
40 × 0.70 = 28 gallons of other components.
If we add 10 gallons of grape juice, we will end up with 24 gallons of grape juice and 36 gallons of other components, and we will have a total of 50 gallons of the mixture.
So 24/50 of the new mixture is grape juice. Now we convert this to a percent:Percent Grape Juice = 24/50 = 48/100= 48%.
The correct answer is choice (C)
Answer: (C) 48%
Question: Nicole cycles at a constant rate of 10 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 40 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?
(A) a) x minutes
(B) b) x/2 minutes
(C) c) 2x/3 minutes
(D) d) 3x/2 minutes
(E) e) 2x minutes
Rationale: Speed of nicole = 20km/h or 20/60 km/min = 1/3 km/min.
Once jessica passed the nicole, the distance between the nicole and jessica will increase at the rate of (30-20) = 10km/h or 1/6 km/min
now jessica is cycling for x minutes after passing the nicole, so in those x minutes distance between jessica and nicole would be (1/6)*x = x/6 km.
So, the time taken by nicole to travel x/6 km = (x/6)/(1/3) = 3x/2. hence answer should be D.
Answer: (D) d) 3x/2 minutes
Question: In a class of 38 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
(A) 3
(B) 5
(C) 8
(D) 13
(E) 15
Rationale: Total # of students = 38
Avg # of books per student = 2
Total # of books = 38*2 = 76
# of student borrowed at least 3 books = 38-2-12-10 = 14
# of books borrowed by above 14 students = 76-(12*1)+(10*2) = 44
Considering that 13 out of above 14 students borrowed only 3 books, # of books borrowed = 13*3 = 39
So maximum # of books borrowed by any single student = 44- 39= 5
Option B
Answer: (B) 5
Question: A fruit seller sells mangoes at the rate of Rs.10 per kg and thereby loses 15%. At what price per kg, he should have sold them to make a profit of 5%
(A) Rs 8.81
(B) Rs 9.35
(C) Rs 10.35
(D) Rs 12.35
(E) None of these
Rationale: Explanation:
85 : 10 = 105 : x
x= (10×105/85)
= Rs 12.35
Option D
Answer: (D) Rs 12.35
Question: If the cost price is 80% of the selling price, then what is the profit percent?
(A) 5%
(B) 11%
(C) 13%
(D) 25%
(E) 19%
Rationale: Let S.P. = $100
C.P. = $80
Profit = $20
Profit% = 20/80 * 100 = 25/6 = 25%
Answer is D
Answer: (D) 25%
Question: Anil and Ravi invest Rs.60,000 and Rs.40,000 and they got loss of Rs.5,000 at the end of year. Then what was the loss for Ravi in Percentage?
(A) 2%
(B) 3%
(C) 5%
(D) 6%
(E) 8%
Rationale: ratio of their investment is 3:2
so the lost of ravi is 2000rs
40000*(x/100)=2000
then x=5%
ANSWER:C
Answer: (C) 5%
Question: How many different pairs of positive integers (a, b) satisfy the equation 1/a+1/b=34/53 ?
(A) 6
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: There is no certain way to solve 2 unknown with 1 equation. The best way is to look at the question and retrospect the most efficient way. In this question, a and b are only positive integers. So that is a big relief. Now, we can start with putting a=1,2,.. and so on till the time we are confident about one of the options.
So, we start with
a=1, we get b as -ve. out
a=2, we get b as 6. Yes (Now (a,b) = (2,6). We can directly see that (a,b)=(6,2) will also satisfy. So we have 2 possible solutions)
a=3, we get b as 3. Yes (Now we have 3 possible solutions)
a=4, we get b as fraction. Out
a=5, we get b again as some fraction. Out
a=6 already taken.
We have A,B options left. C,D,E are out.
A is 6. To have 6 as the answer, we will need one more pair like2,6and one more solution where a=b.
When a=b, we have only 1 solution = 3. So, one more solution, where a=b is not possible.
So, answer will be C.
Answer: (C) 2
Question: Jhaveri invested in Upendra&Upendra,Celco and Winger shares at Rs. 300,Rs.200 and Rs.5 per share respectively. He bought 100 shares for Rs.1000.The number of Upendra&Upendra and Celco shares he bought are respectively
(A) 23,17
(B) 17,23
(C) 17,60
(D) 15,25
(E) 15,20
Rationale: 300a + 200 b + 5c = 10000
a + b + c = 100
295 a + 195 b = 9500
59 a + 39 b = 1900
using options a = 17 b = 23 we can solve it
ANSWER:D
Answer: (D) 15,25
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
(A) 1/2
(B) 2/5
(C) 8/15
(D) 9/20
(E) 7/8
Rationale: Explanation:
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) =	n(E)	/ n(S) = 9/20.
ANSWER IS D
Answer: (D) 9/20
Question: Which is the odd number?
1, 8, 27, 64, 125, 196, 216, 343
(A) 196
(B) 237
(C) 2087
(D) 277
(E) 011
Rationale: Explanation:
The pattern in the given question is 13, 23,,33...
In the series, 196 is not a perfect cube and therefore the odd number.
ANSWER: A
Answer: (A) 196
Question: A speaks english in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to speak english?
(A) 25%
(B) 26%
(C) 35%
(D) 45%
(E) 56%
Rationale: Let A = Event that A speaks the truth
B = Event that B speaks the truth
Then P(A) = 75/100 = 3/4
P(B) = 80/100 = 4/5
P(A-lie) = 1-3/4 = 1/4
P(B-lie) = 1-4/5 = 1/5
Now
A and B contradict each other =
[A lies and B true] or [B true and B lies]
= P(A).P(B-lie) + P(A-lie).P(B)
[Please note that we are adding at the place of OR]
= (3/5*1/5) + (1/4*4/5) = 7/20
= (7/20 * 100) % = 35%
C
Answer: (C) 35%
Question: Ram-Leela has $100 in her piggy bank. How much will she have in her bank 52 weeks from now if she puts $1 in the bank next week, $2 two weeks from now, $3 three weeks from now, and continues to increase the amount that she puts in by $1 each week?
(A) 1478
(B) 1578
(C) 1678
(D) 1778
(E) 1798
Rationale: The dollar deposits are in an A.P.
1,2,3,4...52 with common difference 1
Sum of the terms is n(n+1) / 2
i.e 52* (52+1) /2
= 52* 53/2 = 1378
Total deposit therefore with Chiu-Lihas is 100 + 1378= 1478$
Answer: (A) 1478
Question: The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is:
(A) 7
(B) 29
(C) 41
(D) 67
(E) 76
Rationale: x+(x+36)+y=100 => 2x+y=64
Therefore y must be even prime, which is 2.
Therefore 2x+2=64 => x=31
Third prime number= (x+36)= (31+36)= 67.
ANSWER:C
Answer: (C) 41
Question: The parameter of a square is equal to the perimeter of a rectangle of length 9 cm and breadth 6 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
(A) 11.72
(B) 11.52
(C) 11.97
(D) 10.91
(E) 11.79
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(9 + 6) = 30 cm Parameter of the square = 30 cm
i.e. 4a = 30
a = 7.5
Diameter of the semicircle = 7.5 cm
Circimference of the semicircle
= 1/2(âˆ)(7.5)
= 1/2(22/7)(7.5) = 165/14 = 11.79 cm to two decimal places
Answer: E
Answer: (E) 11.79
Question: If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 465, C will receive
(A) 6020
(B) 15
(C) 5
(D) 287
(E) 90
Rationale: Explanation:
Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6, and C =k/10 .
A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.
Hence, C's share (465 * 6/31) = Rs, 90.
Answer: E) Rs.90
Answer: (E) 90
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?
(A) 1000
(B) 2777
(C) 2889
(D) 27670
(E) 2771
Rationale: 1120 = P [1 + (5*12/5)/100]
P= 1000.Answer:A
Answer: (A) 1000
Question: In a certain company, a third of the workers do not have a retirement plan. 20% of the workers who do not have a retirement plan are women, and 30% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
(A) 80
(B) 95
(C) 105
(D) 120
(E) 210
Rationale: 20% of the workerswithoutretirement plan are women, this means 80% of the workerswithoutretirement plan are men right? Makes 100% = no retirement plan.
Then 40% of those wo have a retirement plan are men, which means 60% of those who have a retirement plan are women. These percentages are always refering to the subgroupsRetirement plan = YesandNo Retirement Plan.
Make the total workers equal x and work from there and it should be fine > x/3 have no retirement plan at all. I struggled with the question a lot, it was hard for me although usually I have no problems with sets questions like this. I believe it must be a 700+ question.
Yes, you are right. I read the question incorrectly! I glazed overnotfor some reason.
If20% of the workers who do not have a retirement plan are women,80% who do not have retirement plan are men. Also 40% who do have retirement plan are men. Since 1/3 do not have retirement plan and 2/3 do have, it becomes a simple weighted average question.
Cavg = (70*1 + 40*2)/3 = 50% are men
Total = 120*100/50 = 240
No. of women = 240 - 120 = 120
D
Answer: (D) 120
Question: In a kilometer race, A can give B a 100 m start and C a 150 m start. How many meters start can B give to C?
(A) 50
(B) 50/9
(C) 8500/9
(D) 500/9
(E) None of these
Rationale: A can give B a 100 m start and C a 150m. Start means when A runs 1000m, B runs 900m and C runs 850m. When B runs 1000m, C will run 1000 x (850/900) m (i.e. 8500/9 m) Thus, B can give C a start of - 1000 - (8500/9), i.e. 500/9 m.
Answer: D
Answer: (D) 500/9
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 10% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
(A) 1/2
(B) 1/3
(C) 2/5
(D) 2/7
(E) 3/7
Rationale: P (E) = 30 / 100 = 3 / 10 , P (H) = 20 / 100 = 1 / 5 and P (E ∩ H) = 10 / 100 = 1 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E ∩ H)
= (3 / 10) + (1 / 5) - (1 / 10) = 4 / 10 = 2/5
C
Answer: (C) 2/5
Question: three men invested sum. and their ratio is 5:7:6. profit is 7200.then b's share
(A) 2000
(B) 2100
(C) 2800
(D) 2300
(E) 2400
Rationale: b's share =7/18*7200=2800
ANSWER:C
Answer: (C) 2800
Question: A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
(A) 22
(B) 28
(C) 77
(D) 12
(E) 21
Rationale: 1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.Answer: B
Answer: (B) 28
Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat in still water and stream is
(A) 3:1
(B) 1:3
(C) 2:4
(D) 4:2
(E) 5:3
Rationale: Explanation:
Let speed downstream = x kmph
Then Speed upstream = 2x kmph
So ratio will be,
(2x+x)/2 : (2x-x)/2
=> 3x/2 : x/2 => 3:1
ANSWER IS A
Answer: (A) 3:1
Question: Oil cans x and y are right circular cylinders and the height and radius of y are each thrice those of x. If the oil in can x filled to capacity sells for $4, how much does the oil in y sell for if y is only 1/3rd filled?
(A) $30
(B) $25
(C) $36
(D) $40
(E) $28
Rationale: formula for vol of a cyl is PI*r^2*h
so Vy = 27*Vy
y when 1/3rd filled will cost 9 times x so ans is C
Answer: (C) $36
Question: P can do a work in 36 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.
(A) 7
(B) 8
(C) 9
(D) 10
(E) 15
Rationale: Work done by P in 1 day = 1/36
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3Ã—7/36 = 7/12
Remaining work = 1 â€“ 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/36) = 15
Option E
Answer: (E) 15
Question: A certain car averages 25 miles per gallon when driving in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 15 miles in the city and then 50 miles on the highway?
(A) 28
(B) 30
(C) 35
(D) 36
(E) 38
Rationale: Answer C
No of Miles per Gallon = Total no of miles/Total no of Gallons
=15+50/(15/25+50/40) ~ 35.13
Answer: (C) 35
Question: P and Q be centers of two circle having radius 200cms. These circle intersect each other at some point A and B. Length of PQ is 250 cms. What will the angle AQP be?
(A) between 0 to 45
(B) between 0 to 30
(C) between 0 to 60
(D) between 0 to 75
(E) between 0 to 95
Rationale: raw the diagram, in triangle AQP, AP = 200 , AQ = 200 and PQ = 250
cos(AQP)= (200^2+250^2-200^2)/(2*200*250)= 5/8 = .625 [using cal, cos(AQP)= 51]
or,
as cos45=.7 & cos60=.5 so, cos(AQP)=.625 lies betn angles 45 & 60
between 0 to 60
ANSWER:C
Answer: (C) between 0 to 60
Question: 306 Ã· ? Ã— 15 + 270 = 405
(A) 24
(B) 25
(C) 34
(D) 39
(E) 43
Rationale: Explanation:
306 Ã· ? Ã— 15 = 405 - 270 = 135
(306 Ã— 15)/? = 135
? = (306Ã— 15)/135 = 34
Answer: Option C
Answer: (C) 34
Question: A man leaves a point P at 6 a.m. and reaches the point Q at 10 a.m. another man leaves the point give at 8 a.m. and reaches the point P at 12 noon. At what time do they meet?
(A) 6
(B) 7
(C) 9
(D) 8
(E) 5
Rationale: 9 a.m.
Answer: C
Answer: (C) 9
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 67 seconds
(B) 32 seconds
(C) 40 seconds
(D) 87 seconds
(E) 12 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (2/25) = 40 seconds
Answer:C
Answer: (C) 40 seconds
Question: The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years
(A) 7:8
(B) 7:9
(C) 3:8
(D) 5:8
(E) None of these
Rationale: Explanation:
Let P age and Q age is 6x years and 7x years.
Then 7x - 6x = 4 <=> x = 4
So required ratio will be (6x+4): (7x+4) => 28:32 => 7:8
Option A
Answer: (A) 7:8
Question: In a class of 250 students, 150 study Spanish and 100 study French. If a student must study at least one of these two languages, what percent of the students study French but NOT Spanish?
(A) 80%
(B) 40%
(C) 30%
(D) 20%
(E) 10%
Rationale: No of students study french= 250- No of students study spanish = 250-150=100
% of the students study french but not spanish = (100/250)*100 % = 40 %
Answer:B
Answer: (B) 40%
Question: A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 4 percent and 8 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate?
(A)  3/8
(B)  4/5
(C)  1/2
(D)  3/5
(E)  3/4
Rationale: x * 4/100 * 1 + (20000 - x) * 8/100 * 1 = 1440
4x - 8x = 144000 - 160000
=> -4x = -16000
=> x = 4000/4
So 16000/20000 = 4/5
Answer - B
Answer: (B)  4/5
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 240 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
(A) 68 km/hr.
(B) 32 km/hr.
(C) 34 km/hr.
(D) 35 km/hr.
(E) 72 km/hr.
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (240 + 240 )/12
2x = 40
x = 20.
Speed of each train = 10 m/sec = 20 x 18/5 km/hr = 72 km/hr.
answer :E
Answer: (E) 72 km/hr.