mathewhe/aqua_rat huggingface dataset:
Question: Jar X is 1/2 full of water. Jar Y, which has half the capacity of Jar X, is 1/4 full of water. If the water in Jar Y is poured into Jar X, then Jar X will be filled to what fraction of its capacity?
(A) 3/4
(B) 5/8
(C) 7/8
(D) 5/12
(E) 7/12
Rationale: Let P be the capacity of Jar X.
The amount of water in Jar Y is 1/4*P/2=P/8
Then the total amount in Jar X is P/2+P/8=5P/8
The answer is B.
Answer: (B) 5/8
Question: Two pumps are connected to an empty tank. Pump X fills the tank with water at a constant rate, while pump Y drains water out of the tank at a constant rate. The two pumps finish filling the tank in three times the duration it would take pump X alone to fill the tank. If pump Y alone can empty a whole tank in 36 minutes, then how many minutes does it take pump X alone to fill the tank?
(A) 18
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: Let V be the volume of the tank.
Let R be the rate per minute that pump X fills the tank.
Let T be the time it takes pump X to fill the tank.
The rate at which pump Y empties the tank is V/36 per minute.
(R - V/36)*3T=V=RT.
(R-V/36)*3=R
2R=V/12.
R=V/24.
It takes pump X 24 minutes to fill the tank.
The answer is B.
Answer: (B) 24
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
(A) 2
(B) 8
(C) 7
(D) 62
(E) 21
Rationale: Explanation:
96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: (B) 8
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?
(A) 1/166
(B) 1/186
(C) 1/196
(D) 2/106
(E) 1/126
Rationale: Out of nine, five are good and four are defective. Required probability
= 4C4/9C4
= 1/126
Answer:E
Answer: (E) 1/126
Question: How much 60% of 50 is greater than 40% of 30?
(A) 18
(B) 27
(C) 26
(D) 29
(E) 21
Rationale: (60/100) * 50 – (40/100) * 30
30 - 12 = 18
Answer: A
Answer: (A) 18
Question: Two friends A and B are running up hill and then to get down! length of road is 440 yards. A on his return journey met B going up at 20 yards from top, A has finished the race 5 minutes earlier than B, then how much time A had taken to complete the race.
(A) 51.5minutes
(B) 52.5minutes
(C) 53.5minutes
(D) 54.5minutes
(E) 55.5minutes
Rationale: When A travels 460m (=440+20), B travels 420m (=440-20). So, ratio of speed = 460:420 = 23:21. Let A's speed be 23x, and that of B's be 21x.
23x = ((2*440) / t) which implies 23t = 880/x;
21x = ((2*440) / (t+5)) which implies 21(t+5) = 880/x.
From these two equations, 23t = 21(t+5). Solving, t = 52.5minutes
ANSWER:B
Answer: (B) 52.5minutes
Question: If pq = p^5 + q^2 – 2pq, for what value of q is pq equal to p^5 for all values of p?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: C
p5 + q2 â€“ 2pq = p5
=> q2 - 2pq = 0
=> q (q - 2p) = 0
=> q = 0 or q = 2p
im not following the logic you used here.. how did you replace pq with 0 could someone help explain it in MORE DETAI
C
Answer: (C) 0
Question: A merchant gains or loses, in a bargain, a certain sum. In a second bargain, he gains 380 dollars, and, in a third, loses 70. In the end he finds he has gained 250 dollars, by the three together. How much did he gain or lose bv the first ?
(A) 80
(B) 60
(C) -60
(D) -70
(E) None
Rationale: In this sum, as the profit and loss are opposite in their nature, they must be distinguished by contrary signs. If the profit is marked +, the loss must be -.
Let x = the sum required.
Then according to the statement x + 380 - 70 = 250
And x = -60.
Answer C
Answer: (C) -60
Question: The editor of an anthology of short stories will select authors from a pool of 11 authors, of which 5 are female. If the anthology is to include the work of 6 authors of which at least 2 are female, in how many ways can the editor select the authors?
(A) 420
(B) 431
(C) 442
(D) 453
(E) 464
Rationale: 11C6 = 462
The number of ways to select 6 males is 6C6 = 1
The number of ways to select 5 males and 1 female is 6C5*5C1 = 30
462 - 1 - 30 = 431
The answer is B.
Answer: (B) 431
Question: A certain league has five divisions. The respective divisions had 6, 7, 8, 9 and 11 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
(A)  81
(B)  83
(C)  85
(D)  86
(E)  89
Rationale: Overall, there can be 81 minuses. Tus, it is A.
Answer: (A)  81
Question: The area of a triangle is with base 4m and height 5m?
(A) 11 m2
(B) 10 m2
(C) 18 m2
(D) 19 m2
(E) 12 m2
Rationale: 1/2 * 4 * 5
= 10 m2
Answer: B
Answer: (B) 10 m2
Question: The sum s of prime numbers that are greater than 60 but less than 70 is
(A)  67
(B)  128
(C)  191
(D)  197
(E)  260
Rationale: A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.
Let's list the numbers from 61 to 69.
61, 62, 63, 64, 65, 66, 67, 68, 69
Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.
We are now left with: 61, 63, 65, 67, 69
We can next eliminate 65 because 65 is a multiple of 5.
We are now left with 61, 63, 67, 69.
To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.
We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.
Thus, we can eliminate 63 and 69 from the list because they are not prime.
Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum s of 61 and 67 is 128.
Answer B.
Answer: (B)  128
Question: A room is 15m long, 4m broad and 3m height. Find the cost of white washing its four walls at 50p per m2 ?
(A) 33
(B) 57
(C) 88
(D) 26
(E) 19
Rationale: 2 *3(15 + 4) = 114
114 * 1/2 = Rs.57
\Answer:B
Answer: (B) 57
Question: If x varies inversely as (y2 - 1) and is equal to 24 when y = 10, the value of x when y = 5 will be ?
(A) 100
(B) 101
(C) 99
(D) 98
(E) 97
Rationale: Let X = K/(Y2 - 1).
Now 24 = K/(100 - 1)
Or K = 24 x 99.
X = K/(Y2 – 1)
When Y = 5, X = 24 × 99/(25 - 1 ) = 99
ANSWER:C
Answer: (C) 99
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
(A) 230
(B) 278
(C) 266
(D) 555
(E) 255
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer:A
Answer: (A) 230
Question: if 50% of (x-y) = 20% of (x+y) then what percent of x is y?
(A) 2.5%
(B) 10%
(C) 5%
(D) 15%
(E) 43%
Rationale: 50% of (x-y)=20% of(x+y)
(50/100)(x-y)=(20/100)(x+y)
5(x-y)=2(x+y)
3x=7y
x=7/3y
therefore required percentage
=((y/x) X 100)% = ((y/(7/3)y) X 100) =43%
Answer is E.
Answer: (E) 43%
Question: A bag of candy contained 360 pieces. A group of 25 students divided the candy so that the 11 boys received twice as much candy as the girls. How many pieces of candy did the boys get?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: girls candy = x
boys candy = 2x
# boys = 11
# girls = 25 - 11 = 14
14x + 11(2x) = 360
14x + 22x = 360
36x = 360
x = 10
boys candy = 2x = 2(10) = 20
Answer: E
Answer: (E) 20
Question: a boy perform 5 times a reaction and his reading are 2,2.1,2,2.2 but unfortunately
5th reading clearly not visible because a drop of chemical fall onto it.but luckily he
have mean of all reading which is 2.please help him in finding 5th reading.
(A) 2
(B) 1.7
(C) 1.9
(D) 1.8
(E) 2.1
Rationale: solution
let 5th reading be x
(2+2.1+2+2.2+x)/5=2
8.3+x=10
x=1.7
answer B
Answer: (B) 1.7
Question: Out of a group of 10 contestants, 2 are to be selected at random. What is the maximum number of male contestants possible if the probability that both selected contestants are male is less than 20% ?
(A)  0
(B)  1.51
(C)  2
(D)  2.12
(E)  4
Rationale: Let y be the number of males.
Total contestants = 10
Probability that the first contestant selected is a male = y/10
Probability that the second contestant selected is also a male = y-1/9
Total probability = y(y-1)/ 90 < 1/20 (this probability is less than 20%)
Solving for y we get, y(y-1)< 9/2. This implies that the maximum value of y can be 2.12.
Answer D!
Answer: (D)  2.12
Question: A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the
second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take
both the punctures together to make it flat ?
(A) 315min
(B) 325min
(C) 335min
(D) 345min
(E) None of these
Rationale: Explanation:
Do not be confused, Take this question same as that of work done question's. Like work done by 1st
puncture in 1 minute and by second in 1 minute.
Lets Solve it:
1 minute work done by both the punctures =
(19+16)=(518)
So both punctures will make the type flat in
(185)mins=335mins
Answer: C
Answer: (C) 335min
Question: Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
(A) 40
(B) 80
(C) 90
(D) 100
(E) 120
Rationale: Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
Answer: Option A
Answer: (A) 40
Question: The average of seven numbers is 22. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
(A) 25
(B) 27
(C) 29
(D) 32
(E) 55
Rationale: The total of seven numbers = 7X22 = 154
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (154 - 99 ) = 55
E
Answer: (E) 55
Question: In a graduating class, 40 percent of the students are male. In this class, 60 percent of the male students and 40 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) 0.4
(B) 0.44
(C) 0.48
(D) 0.52
(E) 0.56
Rationale: Let x be the total number of students.
The number students who are younger than 25 is 0.4*0.4x+0.6*0.6x = 0.52x
The answer is D.
Answer: (D) 0.52
Question: Oak trees line both sides of a street for a length of 7/10 of a kilometer. If there is 14 meters of space between the trees, and each tree is 1 meter wide, how many trees are there along the street?
(A) a)	22
(B) b)	23
(C) c)	24
(D) d)	44
(E) e)	48
Rationale: There is a gap of 16 m between every 2 trees , each tree is 1 m wide.
7/10 of 1 km = 700 m
Lets assume that x trees are planted So equation is
x*1 +(x-1)*14 = 700
Solve for x and we get x = 48, answer is E
Answer: (E) e)	48
Question: P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 6), the remainder is also D. If P/Q = 1020.75 and P/(Q + 6) = 816.6, then which of the following gives the correct set of {D, Q}?
(A) {6, 12}
(B) {6, 15}
(C) {9, 12}
(D) {9, 15}
(E) {18, 24}
Rationale: p/q= d=p/q+6
d= .75 q
d= .6(q+6)
we get d = 18 and q = 24. Answer = E.
Answer: (E) {18, 24}
Question: In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 655200 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
(A) 1300000
(B) 12500
(C) 14000
(D) 12000
(E) None of these
Rationale: Explanation :
Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 655200.
(75/100 * 96/100 * 70/100 * x) = 655200.
=> x = (655200*100*100*100)/(75*96*70) = 1300000
Answer : A
Answer: (A) 1300000
Question: Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:
(A) three times as much
(B) twice as much
(C) the same
(D) half as much
(E) A third as much
Rationale: Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
Speed = Distance/Time.
I.E Time = Distance/Speed.
times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.CORRECT ANSWER : B
Answer: (B) twice as much
Question: Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?
(A) 18
(B) 20
(C) 24
(D) 36
(E) 42
Rationale: Use weighted average:
2% and 12% solutions mix to give 5% solution.
w1/w2 = (A2 - Avg)/(Avg - A1) = (12 - 5)/(5 - 2) = 7/3
You need 7 parts of 2% solution and 3 parts of 12% solution to get 10 parts of 5% solution.
If total 5% solution is actually 60 litres, you need 7*6 = 42 litres of 2% solution and 3*6 = 18 litres of 12% solution.
Answer (E)
Answer: (E) 42
Question: If a, b and c are the sides of a triangle, and a2 + b2 + c2 = bc + ca + ab, then the triangle is
(A) equilateral
(B) isosceles
(C) right-angled
(D) obtuse-angled
(E) None of these
Rationale: Explanation :
We know that (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac = 3ab + 3bc + 3ac
Now assume values of a, b, c and substitute in this equation to check the options.
Shortcut:
(a – b)2 + (b – c)2 + (c – a)2 = 0.
Hence, a = b = c.
Answer : A
Answer: (A) equilateral
Question: jhon has 10 choclates, jennifer has 5 choclates. Totally how many choclates they have in all?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 14
Rationale: 10+5=15. Answer is C
Answer: (C) 15
Question: One vessel contains a mixture of 5 parts pure wine and 3 parts soda, whereas the other vessel contains a mixture of 9 parts pure wine and 3 parts soda. Compare the strength of the wine.
(A) 35;36
(B) 15 : 18
(C) 7 : 4
(D) 14 : 5
(E) None of these
Rationale: 5/8 : 9/12
LCM of 8,12 = 24
(5/8)*24 : (9/12)*24
15:18
Answer is B.
Answer: (B) 15 : 18
Question: Find the third proportional to 63 and 29.9?
(A) 14.09
(B) 14.29
(C) 14.19
(D) 14.16
(E) None of these
Rationale: Explanation:
Formula = Third proportional = (b × b)/a
A = 63 and B = 29.9
(29.9 × 29.9)/ 63 = 894.01/63 = 14.19
Answer: Option C
Answer: (C) 14.19
Question: A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent?
(A) 120%
(B) 190%
(C) 100 percent
(D) 200%
(E) 101%
Rationale: MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer:C
Answer: (C) 100 percent
Question: The ratio of the number of females to males at a party was 1:2 but when 3 females and 3 males left, the ratio became 1:3. How many people were at the party originally?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: The total number of people are x females + 2x males.
3*(x-3) = 2x - 3
x = 6
There were 3x = 18 people at the party originally.
The answer is C.
Answer: (C) 18
Question: The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 10, 50, and what number?
(A) 40
(B) 45
(C) 55
(D) 45
(E) 50
Rationale: a1 = 120/3 = 40
a2 = a1 -5 = 35
sum of second list = 35*3 = 105
therefore the number = 105 -60 = 45
D
Answer: (D) 45
Question: In a certain candy store, 22% of the customers are caught sampling the candy and are charged a small fine, but 8% of the customers who sample the candy are not caught. What is the total percent of all customers who sample candy?
(A) 22%
(B) 23.9%
(C) 24%
(D) 25%
(E) 34%
Rationale: Since 8% of the customers who sample the candyare notcaught, then 88% of the customers who sample the candyarecaught:
{% of customers who sample candy}*0.92 = 0.22;
{% of customers who sample candy} = 0.239.
Answer: B.
Answer: (B) 23.9%
Question: The least number which must be subtracted from 6709 to make it exactly divisible by 9 is:
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: On dividing 6709 by 9, we get remainder= 4
Therefore, required number to be subtracted= 4
ANSWER:C
Answer: (C) 4
Question: If 3^k - 3^(k-1) = 162 then k(k-1) =
(A) 12
(B) 16
(C) 20
(D) 30
(E) 81
Rationale: It seems like you were really close but you solved for k - 1 instead. I am curious - how did you reason through the question? Perhaps you figured the answer has to be in the form of k(k -1), e.g. (3)(4) = 12. Even then, had you figured k has to be a little bigger (plugging in 4 for k gives you 81 which is too low), So when you reasoned the answer to be 4 you may have plugged the 4 in the (k - 1) exponent place.
Again, a quick plugging in should get you (C) 20 as, the only other answer with consecutive integers as factors is far too big.
Answer: (C) 20
Question: 10 is added to a certain number, the sum is multiplied by 2, the product is divided by 2 and 2 is subtracted from the quotient. The remainder left is half of 88. What is the number?
(A) 21
(B) 20
(C) 25
(D) 36
(E) 45
Rationale: Let number is X.
When 10 added to it,
= (X+10)
2 multiplied to sum,
= 2 *(X +10)
Now,
= [{2 *(X +10)} /2]
And,
= [{2 *(X +10)} /2] - 2
According to question,
[{2 *(X +10)} /2] - 2 = half of 88
[(2X + 20) /2) = 44 +2
X + 10 = 46
X + 10 = 46
X = 46 - 10
X = 36
So, required number is: 36.
ANSWER : D
Answer: (D) 36
Question: If f(a)=4a+6b+8, what is the value of (f(3a)-f(2b)) ?
(A) 6a+8b+6
(B) 8a-6b
(C) 5a+3b-8
(D) 6a+7b+3
(E) 8a-2b+9
Rationale: f(a)=4a+6b+8
f(3a) = 12a+6b+8
f(2b) = 4a+12b+8
(f(3a)-f(2b)) = 12a+6b+8-4a-12b-8 = 8a-6b
Answer is B
Answer: (B) 8a-6b
Question: A train 200 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: S = (200 + 300)/45 = 500/45 * 18/5 = 40
ANSWER:D
Answer: (D) 40
Question: A square and a rectangle have equal areas. If their perimeters are p1 and p2 respectively, then
(A) p1 < p2
(B) p1 = p2
(C) p1 > p2
(D) none of these
(E) Cannot be determined
Rationale: Solution
A square and a rectangle with equal areas will satisfy the relation p1 < p2.
Answer A
Answer: (A) p1 < p2
Question: Mr. stenley employed a certain number of typist for his project. 8 days later 20% of the typist left the job and it was found that it took as much time to complete the rest work from then as the entire work needed with all the employed typists. The average speed of a typist is 20 pages/hour. Minimum how many typist could be employed?
(A) 10
(B) 5
(C) 15
(D) 4
(E) 3
Rationale: Explanation:
Since 20% (i.e 1/5) typists left the job. So, there can be any value which is multiple of 5 i.e, whose 20% is always an integer. Hence, 5 is the least possible value.
Answer: B
Answer: (B) 5
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) Rs. 4980
(B) Rs. 4991
(C) Rs. 4996
(D) Rs. 4997
(E) Rs. 5000
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991.
B)
Answer: (B) Rs. 4991
Question: An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 5 o’clock in the afternoon?
(A) 60°
(B) 90°
(C) 270°
(D) 320°
(E) None of these
Rationale: Sol.
Angle traced by the hour hand in 9 hours = [360/12 * 9]° = 270°
Answer C
Answer: (C) 270°
Question: A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. He sellis the radio for Rs 300. The profit percent of the retailer is
(A) 22
(B) 32
(C) 25
(D) 88
(E) 11
Rationale: Explanation:
cost price = (225 + 15) = 240 sell price = 300
gain = (60/240)*100 = 25%
Answer: C) 25%
Answer: (C) 25
Question: A train 125 m long passes a person, running at 5 km/hr in the same direction in which that the train is going, in 10 seconds. The speed of the train is:
(A) 40 km/hr
(B) 60 km/hr
(C) 55 km/hr
(D) 50 km/hr
(E) 65 km/hr
Rationale: speed of train related to a person = 125/10 m/s
=>25/2
(25/2*18/5) km/hr
=45 km/hr
so speed consider as x and relative speed consider (x-5)
x-5 = 45 => x = 50 km/hr
ANSWER D
Answer: (D) 50 km/hr
Question: How many three-digit numbers that do not contain the digits 2 or 5 are there?
(A) 488
(B) 996
(C) 228
(D) 456
(E) 1986
Rationale: We can have 7 digits ( 1,3,4,6,7,8,9) for the first place ( hundred's place).
and similarly 8 digits for tenth's and unit digit. ( 0,1,3,4,6,7,8,9)
So in total 7*8*8= 488
Hence B
Answer: (B) 996
Question: Each of the following equations T has at least one solution EXCEPT
(A) T=–2^n = (–2)^-n
(B) T=2^-n = (–2)^n
(C) T=2^n = (–2)^-n
(D) (–2)^n = –2^n
(E) (–2)^-n = –2^-n
Rationale: While it is possible to reason out which of these choices must not work, we may not have time or the confidence to do so. However, this problem has variable in its answer choice, and relatively simple math. Therefore, an easy alternative is picking numbers.
Since we're dealing with exponents, we want to keep things as easy as possible. Hence, we'll start with the easiest exponent possible: n = 1. A, B, and C are not solved (x^-n = 1/(x^n), so we're comparing integers to fractions), but choices D and E both end up valid, eliminating them from contention.
In the process of doing this, however, we've uncovered a major clue to our next step: A, B, and C, all compared integers to fractions, and the only integer equal to it's reciprocal is 1, which is equal to 1/1. This, in turn, tells us the we need to pick n = 0. Remember, for all non-zero x, x^0 = 1.
If we plug n = 0 into choices B and C, we end up with 1 = 1 both times. Choice A, however, results in the false 1 = -1. Thus, we conclude that the first choice has no valid solutions, and is therefore the correct answer.
Answer: (A) T=–2^n = (–2)^-n
Question: A and B complete a work in 4 days. A alone can do it in 8 days. If both together can do the work in how many days?
(A) 3.75 days
(B) 3.78 days
(C) 3.25 days
(D) 3.15 days
(E) 2.7 days
Rationale: 1/4 + 1/8 = 3/8
8/3 = 2.7 days
Answer: E
Answer: (E) 2.7 days
Question: The average age of students in section A of 50 students is 14 years and the average age of students in section B of 30 students is 6 years. Find the average age of students in both sections taken together?
(A) 20years
(B) 15years
(C) 18years
(D) 9years
(E) 11years
Rationale: The required average = (50*14+30*6)/50+30 = 11 years
Answer is E
Answer: (E) 11years
Question: The length of the bridge, which a train 150 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 266
(B) 288
(C) 245
(D) 776
(E) 225
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (150 + X)/30 = 25/2 ==> 2(150 + X) = 750 ==> X
= 225 m.
Answer:E
Answer: (E) 225
Question: Find the middle one when The sum of three consecutive even numbers is 36?
(A) 10
(B) 12
(C) 14
(D) 15
(E) 16
Rationale: 3 consecutive numbers can be a - 1, a, a + 1
So sum of numbers = 3a = 36.
Hence a = 12.
B
Answer: (B) 12
Question: What is the value of âˆš81% ?
(A) 25%
(B) 36%
(C) 42%
(D) 60%
(E) 90%
Rationale: Explanation: br>âˆš81%
=âˆš81/âˆš100
=9/10
=90/100=90%
correct answer is E)90%
Answer: (E) 90%
Question: 26 men can complete a piece of work in 8 days. In how many days will 25 men complete the same work?
(A) 7 1/3 days
(B) 9 1/3 days
(C) 8 2/3 days
(D) 8 1/3 days
(E) 9 1/3 days
Rationale: Let the required number of days be p
More men, less days (indirect proportion)
Hence we can write as
26 : 25 :: p : 8
26*8=25*p
p=26*8/25
p=8 1/3 days
ANSWER:D
Answer: (D) 8 1/3 days