mathewhe/aqua_rat huggingface dataset:
Question: Two trains 141 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 7.18
(B) 7.12
(C) 7.43
(D) 7.59
(E) 7.71
Rationale: T = (141 + 165)/ (80 + 65) * 18/5
T = 7.59
Answer:D
Answer: (D) 7.59
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800. Deepak's share is?
(A) Rs. 9600
(B) Rs. 8500
(C) Rs. 8450
(D) Rs. 8400
(E) Rs. 9400
Rationale: Ratio of their shares = 22500 : 35000 = 9 : 14
Deepak's share = Rs. (13800 * 14/23) = Rs. 8400 ANSWER "D
Answer: (D) Rs. 8400
Question: If there is exactly one root of the equation x^2 + ax + 2b, where a and b are positive constants, what is b in terms of a?
(A) a/2
(B) a
(C) 3a/2
(D) a^2/2
(E) a^2/8
Rationale: one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1
Here b = a
c= 2b
a = 1
substituting these values in 1, we have
a^2 = 8b => b =a^2/8
Answer is E.
Answer: (E) a^2/8
Question: If x > 0.5, which of the following could be the value of x?
(A) √0.007
(B) √0.006
(C) √0.008
(D) √0.5
(E) √0.009
Rationale: Answer : D
Answer: (D) √0.5
Question: A man sells a horse for Rs.860 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
(A) 287
(B) 879
(C) 967
(D) 900
(E) 998
Rationale: CP = SP + 1CP = SP - g
860 + x = 980 - 2x
3x = 120 => x
= 40
CP = 860 + 40
= 900
Answer:D
Answer: (D) 900
Question: (23341379 x 72) = ?
(A) 1680579288
(B) 1223441288
(C) 2142579288
(D) 2142339288
(E) None of these
Rationale: Explanation :
23341379 x 72 = 23341379(70 + 2) = (23341379 x 70) + (23341379 x 2)
= 1633896530 + 46682758 = 1680579288. Answer : Option A
Answer: (A) 1680579288
Question: Average marks of a,b,c is 48. When d joins average becomes 47. E has 3 more marks than d. Average marks of b,c,d,e is 48. What is the marks of a?
(A) 43
(B) 44
(C) 45
(D) 46
(E) 47
Rationale: a+b+c=144
a+b+c+d=188
d=44
e=47
b+c+d+e=192
b+c=101
a=43
ANSWER:A
Answer: (A) 43
Question: In a 2000 census, 51.27% of the population are male, and 48.73% are female. What is the ratio of men to every 100 women?
(A) 110:100
(B) 105:100
(C) 95:100
(D) 85:100
(E) 120:100
Rationale: The ratio of A to B, where
A = the percent of males, and
B = the percent of females.
A = 51.27
B = 48.73
A:B = 51.27:48.73
So, 100(5,127/4,873):100
Giving a male to female ratio of 105.20 men for every 100 women.
Answer is B
Answer: (B) 105:100
Question: During the first two weeks of January, the total rainfall in Springdale was 35 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall during the second week of January?
(A) 5 inches
(B) 6 inches
(C) 9 inches
(D) 10 inches
(E) 21 inches
Rationale: Total rainfall in 2 weeks = 35 inches.
Assume the rainfall in second week = 1.x
Rainfall in first week = x
Total rainfall = 2.5x = 35 inches
x = 14 and 1.5x = 21
Rainfall during second week = 21 inches
Option E
Answer: (E) 21 inches
Question: In Country X a returning tourist may import goods with a total value of $500 or less tax free, but must pay an 8 percent tax on the portion of the total value in excess of $500. What tax must be paid by a returning tourist who imports goods with a total value of $730 ?
(A) $58.40
(B) $40 .00
(C) $24.60
(D) $18.40
(E) $16.00
Rationale: The tourist must pay tax on $730 - $500 = $230. Thus the amount to be paid is 0.08*$230 = $18.40.
Answer: D.
Answer: (D) $18.40
Question: The length of the bridge, which a train 145 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 76 m
(B) 178 m
(C) 230 m
(D) 187 m
(E) 176 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (145 + x)/30 = 25/2
=> 2(145 + x)= 750 => x = 230 m.
Answer: C
Answer: (C) 230 m
Question: The ratio of the number of red cars in a certain parking lot to the number of black cars is 3 to 8. If there are 90 black cars in the lot, how many red cars are there in the lot?
(A) 11
(B) 33
(C) 24
(D) 27
(E) 32
Rationale: B is correct
R/B = 3/8 and B =90
R = 90*3/8 = 33
Answer: (B) 33
Question: If P (A) = 0.18, P (B) = 0.5 and P (B|A) = 0.2, find P(A n B)?
(A) 0.28
(B) 0.36
(C) 0.45
(D) 0.56
(E) 0.7
Rationale: P(B|A) = P(A n B)/P(A)
P(A n B) = P(B|A) × P(A)
P(A n B) = 0.2 × 0.18
P(A n B) = 0.36
B)
Answer: (B) 0.36
Question: A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
(A) 250
(B) 276
(C) 280
(D) 285
(E) None of these
Rationale: Explanation:
Since the month begins with a Sunday, to there will be five Sundays in the month.
Required average
= {510 x 5 + 240 x 25 }/30
=	8550/30
= 285
ANSWER:D
Answer: (D) 285
Question: P, Q and R have Rs.8000 among themselves. R has two-thirds of the total amount with P and Q. Find the amount with R?
(A) Rs.3200
(B) Rs.3600
(C) Rs.2400
(D) Rs.4000
(E) None of these
Rationale: Let the amount with R be Rs.r
r = 2/3 (total amount with P and Q)
r = 2/3(8000 - r) => 3r = 16000 - 2r
=> 5r = 16000 => r = 3200.
ANSWER:A
Answer: (A) Rs.3200
Question: Which of the following numbers is prime?
(A) 2^16+1
(B) 2^31+3^31
(C) 4^66+7^66
(D) 5^82−2^82
(E) 5^2881+7^2881
Rationale: Let's check which of the options is NOT a prime:
A. 2^16 + 1 --> the units digit of 2 in positive integer power repeats in blocks of four {2, 4, 8, 6}. Hence, the units digit of 2^16 is 6 and the units digit of 2^16 + 1 is 7 --> 2^16 + 1 CAN be a prime.
B. 2^31 + 3^31 --> the units digit of 2^31 is 8 and the units digit of 3^31 is 7 (the units digit of 3 in positive integer power repeats in blocks of four {3, 9, 7, 1}). Hence, the units digit of 2^31 + 3^31 is 5 (8+7). Thus 2^31 + 3^31 is divisible by 5. Not a prime.
C. 4^66 + 7^66 --> the units digit of 4^66 is 6 (the units digit of 4 in positive integer power repeats in blocks of two {4, 6}) and the units digit of 7^66 is 9 (the units digit of 7 in positive integer power repeats in blocks of four {7, 9, 3, 1}). Hence, the units digit of 4^66 + 7^66 is 5 (6+9). Thus 4^66 + 7^66 is divisible by 5. Not a prime.
D. 5^82 - 2^82 --> we can factor this as (5^41 - 2^41)(5^41 + 2^41). Not a prime.
E. 5^2881+ 7^2881 --> 5^2881 + 7^2881 = odd + odd = even. Not a prime.
Only option A can be prime.
Answer: A.
Answer: (A) 2^16+1
Question: In how many different ways can the letters of the word BOOKLET be arranged such that B and T always come together?
(A) 360
(B) 720
(C) 480
(D) 5040
(E) None of these
Rationale: Treat B and T as a single letter. Then the remaining letters (5 + 1 = 6) can be arranged in 6! ways. Since, O is repeated twice, we have to divide by 2 and the B and T letters can be arranged in 2! ways.
Total no. of ways = 6!×2!/2=720
Answer B
Answer: (B) 720
Question: In an examination, 34% of total students failed in Hindi, 44% failed in English and 22% in both. The percentage of these who passed in both the subjects is :
(A) 23
(B) 37
(C) 28
(D) 44
(E) 81
Rationale: Explanation:
Formula n(aâˆªb) = n(a) + n(b) âˆ’ n(aâˆ©b)
Fail in Hindi or English = 34 + 44 â€“ 22 = 56
Therefore students who passed = 100 â€“ 56 = 44.
Answer: D
Answer: (D) 44
Question: The radius of a cylinder is 10 m, height 12 m. The volume of the cylinder is:
(A) 2200
(B) 5500
(C) 3300
(D) 3771.4
(E) 4400
Rationale: Cylinder volume = Ï€r(power2)h
= 22/7 Ã— 10 Ã— 10 Ã— 12
= 3771.4 m(power3)
Answer is D.
Answer: (D) 3771.4
Question: A boat has a speed of 14kmph in standing water. The stream has a speed of 1.2kmph. What time does the boat take to go to a distance of 4864 km and come back? (hours)
(A) 700
(B) 378
(C) 2696
(D) 1207
(E) 1712
Rationale: Explanation:
A boat travels at the speed of 14 km/hr in still water.
=> Speed of stream = 1.2 kmph
=> Speed of boat downstream becomes 14 + 1.2 = 15.2 kmph
=> Speed of boat upstream becomes 14 - 1.2 = 12.8 kmph
Total time taken in the journey = Journey downstream + Journey upstream
Therefore, 4864(1/12.8 + 1/15.2) = 700 hours
ANSWER: A
Answer: (A) 700
Question: If n is a prime number greater than 7, what is the remainder when n^2 is divided by 12 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: There are several algebraic ways to solve this question, but the easiest way is as follows:since we cannot have two correct answers just pick a prime greater than 7, square it and see what would be the remainder upon division of it by 12.
n=11 --> n^2=121 --> remainder upon division 121 by 12 is 1.
Answer: B.
Answer: (B) 1
Question: 700 + 6 × 4 = ?
(A) 820
(B) 202
(C) 420
(D) 724
(E) None of these
Rationale: 700 + 6 × 4 = ?
or, ? = 700 + 24 = 724
Answer D
Answer: (D) 724
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?
(A) 32 years
(B) 36 years
(C) 40 years
(D) 48 years
(E) 58 years
Rationale: Let the mother's present age be x years. Then, the person's present age = 2/5 x years.
(2/5 x + 8) = 1/2 (x + 8)
2(2x + 40) = 5(x + 8) => x = 40
ANSWER:C
Answer: (C) 40 years
Question: 5 letters have to be put in 5 different envelopes numbered 1 through 5 such that each of the letters go into only 1 envelope.The letter is said to be put in correct position if for example letter 1 goes into envelope 1.Now what is the probability that all letters be put into wrong envelopes?
(A) 1/3
(B) 2/3
(C) 11/120
(D) 11/30
(E) 76/120
Rationale: This Q is based on derangement, a permutation in which all elements are in the wrong position.
Number of derangements = n!(12!−13!+14!+...+((−1)n)n!)n!(12!−13!+14!+...+((−1)n)n!).. Of Course it can be derived but thats not required..
Since there are 5 letters and 5 envelopes:-
Derangements=5!(12!−13!+14!−15!)Derangements=5!(12!−13!+14!−15!)
=> 120(1/2−1/6+1/24−1/120)=60−20+5−1=44.120(1/2−1/6+1/24−1/120)=60−20+5−1=44.
Total possible ways = 5! = 120.
therefore required prob, P=44/120=11/30.
ans D
Answer: (D) 11/30
Question: A and B walk around a circular track. They start at 9 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 11:00 a.m.?
(A) 8
(B) 7
(C) 6
(D) 15
(E) 3
Rationale: Sol.
Relative speed = (2 + 3) = 5 rounds per hour.
So, they cross each other 5 times in an hour.
Hence, they cross each other 15 times before 11:00 a.m.
Answer D
Answer: (D) 15
Question: In track last week, the boys ran 20 laps. The girls ran 10 more
laps. Each lap is a 1/10th of a mile. How many miles did the girls run?
(A) 1 mile
(B) 3 miles
(C) 5 miles
(D) 7 miles
(E) 9 miles
Rationale: The girls ran 20 + 10 = 30 laps. 30 x 1/10 = 30/10, which reduces to 3.
The girls ran 3 miles
correct answer B
Answer: (B) 3 miles
Question: Which of the following is a prime number
(A) 9
(B) 2
(C) 4
(D) 8
(E) 7
Rationale: Explanation:
A prime number is a natural number greater than 1 which has no positive divisors other than 1 or itself.
So from above options 2 is that number
Option B
Answer: (B) 2
Question: In covering a distance of 30 km, Amla takes 2 hours more than Peter. If Amla doubles his speed, then he would take 1 hour less than Peter. Amla’s speed is :
(A) 7 kmph
(B) 6.5 kmph
(C) 5.5 kmph
(D) 5 kmph
(E) None
Rationale: Sol.
Let Peter’s speed be x km/hr.
Then, 30/x - 30/2x = 3
⇔ 6x = 30
⇔ x = 5 km/hr
Answer D
Answer: (D) 5 kmph
Question: If n=4p where p is a prime number greater than 2, how many different positive even divisors does n have, including n?
(A) two
(B) three
(C) four
(D) six
(E) eight
Rationale: We're told that N = 4P and that P is a prime number greater than 2. Let's TEST P = 3; so N = 12
The question now asks how many DIFFERENT positive EVEN divisors does 12 have, including 12?
12:
1,12
2,6
3,4
How many of these divisors are EVEN? 2, 4, 6, 12 …..4 even divisors.
ANSWER:C
Answer: (C) four
Question: S, T and U are inner angles in a triangle. If S= T+ U, what can't be the size of T?
(A) 960 DEGREES
(B) 9770 DEGREES
(C) 9570 DEGREES
(D) 940 DEGREES
(E) 90 DEGREES
Rationale: Given S= T+ U, and S, T and U are inner angles in a triangle. Thus S+ T+ U= 180
T+ U+ T + U= 180 => 2(T+ U) = 180 => T+ U= 90. Thus beta will be less than 90.
Hence the answer is E.
Answer: (E) 90 DEGREES
Question: When n is divided by 11, the remainder is 6. When n is divided by 19, the quotient is equal to Z, and the remainder is equal to 6. Z must be divisible by which of the following numbers?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: N = 11 q + 6
N = 19 z + 6
Equating
11 Q + 6 = 19z+6
19z=11q
19z/11 = q
since q is an integer Z must be divisible by 19.
Hence A
Answer: (A) 11
Question: A beggar on the street can make one cigarette out of every 6 cigarette butts he finds. After one whole day of searching and checking public ashtrays,the beggar finds a total of 72 cigarette butts. How many cigarettes can he make and smoke from the butts he found?
(A) 4
(B) 14
(C) 34
(D) 27
(E) 46
Rationale: If the begger can make a whole cigarette from 6 butts then he can make 12 cigarettes from the 72 he found. Once he smokes those, he then will have another 12 butts, which gives him enough to make another 2 cigarettes. A total of 14.
correct answer is B)14
Answer: (B) 14
Question: If pqr = 0 , rst = 1 , and spr = 0, which of the following must be zero?
(A) P
(B) Q
(C) R
(D) S
(E) T
Rationale: rst = 1 which means neither r / s/ t is 0
r x pq = 0 , we know r is not 0 from above hence either p or q must be 0.
s x p x r = 0, we know from first expression that r an p are not 0 hence p =0.
option A
Answer: (A) P
Question: In the rectangular coordinate system, if the line x = 8y + 5 passes through points (m,n) and (m + 2,n + p), what is the value of p?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: x = 8y+5, and thus y = x/8 - 5/8
The slope is 1/8.
The slope of a line through points (m,n) and (m + 2,n + p) is (n+p-n)/(m+2-m) = p/2
p/2 = 1/8 and thus p = 1/4
The answer is C.
Answer: (C) 1/4
Question: A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 540 kilos of plankton, how many kilos did he consume on the sixth hour?
(A) 38
(B) 47
(C) 50
(D) 53
(E) 63
Rationale: If you list the amount eaten each hour, you'll get an equally spaced list, increasing by 3 each hour. In any equally spaced list, the median equals the mean. Here, the mean is 540/9 = 60, so the median is also 60, and that is the amount eaten in the 5th hour. We need to add 3 to find the total eaten in the next hour, so the answer is 63.
option E.
Answer: (E) 63
Question: A dealer marks his goods 20% above cost price. He then allows some discount on it and makes a profit of 8%. The rate of discount is :
(A) 8%
(B) 11%
(C) 21%
(D) 10%
(E) none of the above
Rationale: Let C.P.=Rs.100
Marked price = Rs.120, S.P. = Rs.108
Discount = [12120×100][12120×100]% = 10%
Ans is : D
Answer: (D) 10%
Question: In a bag there are 10 black balls and 25 blue balls and 15 white balls. A ball is drawn at random. What is the probability of getting a white ball?
(A) 2/5
(B) 3/10
(C) 4/10
(D) 5/10
(E) 3/5
Rationale: total balls = 10+25+15=50
probability of getting a white ball= 15/50 = 3/10 . correct option is B
Answer: (B) 3/10
Question: Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 6 : 3?
(A) 16
(B) 45
(C) 277
(D) 92
(E) 11
Rationale: Let the distances between city A to B and B to C be 6x km and 3x km respectively.
Total time taken to cover from A to C
= (6x)/40 + (3x)/60 = (18x + 6x)/120 = 24x/120 = x/5 Average speed = (6x + 3x)/(x/5) = 45 kmph.
Answer:B
Answer: (B) 45
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 30 1/3%
(B) 33 1/3%
(C) 23 1/3%
(D) 35 1/3%
(E) 29 1/3%
Rationale: B
33 1/3%
675 ---- 225
100 ---- ? => 33 1/3%
Answer: (B) 33 1/3%
Question: A train running at the speed of 60 km/hr crosses a pole in 18 seconds. Find the length of the train?
(A) 150 meter
(B) 170 meter
(C) 156 meter
(D) 300 meter
(E) 154 meter
Rationale: Speed = 60*(5/18) m/sec
= 50/3 m/sec
Length of Train (Distance)
= Speed * Time
(50/3) * 18
= 300 meter
Answer:D
Answer: (D) 300 meter
Question: Walking at 40% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance?
(A) 16
(B) 36
(C) 42
(D) 48
(E) 54
Rationale: speed is inversly proprtional to time
walking at 40% of speed meand 2/5s takes 5/2t.
It takes 24 minutes extra to cover the distance. then
5/2t=t+24
5t=2t+48
3t=48
t=16.
Option A is correct
Answer: (A) 16
Question: If x^4 + y^4 = 85, then the greatest possible value of x is between:
(A) 0 to 2
(B) 2 to 4
(C) 4 to 6
(D) 6 to 8
(E) 8 to 10
Rationale: The answers to this question provide a great 'hint' as to how to go about solving it; since they're all essentially 'ranges', you can use them to figure out which solution contains the maximum value of X.
We're told that X^4 + Y^4 = 100. To maximize the value of X, we need to minimize the value of Y^4. The smallest that Y^4 could be is 0 (when Y = 0), so we'll have....
X^4 = 100
Looking at the answers, it makes sense to see what 3^4 equals....
3^4 = 81
Since that is BELOW 85, and 6^4 will clearly be MORE than 85, we have the correct answer.
Final Answer:
B
Answer: (B) 2 to 4
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
(A) 33 1/7%
(B) 33 6/3%
(C) 33 1/3%
(D) 39 1/3%
(E) 33 1/4%
Rationale: 1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: Two water pumps, working simultaneously at their respective constant rates, took exactly 9 hours to fill a swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?
(A) 12
(B) 14
(C) 15
(D) 16
(E) 18
Rationale: Let the rate of the slow pump be x. Then the rate of the fast pump is 1.5x.
(x+1.5x) = 2.5x = 1/9 of the capacity of the whole pool per hour.
The rate of the fast pump is (1.5/2.5)*1/9 = 1/15 of the whole pool per hour.
The time it takes the faster pump to fill the pool would be 15 hours.
The answer is C.
Answer: (C) 15
Question: A sum of Rs. 125000 amounts to Rs. 14500 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) 7%
Rationale: S.I. = (14500 - 12500) = Rs. 2000\
Rate = (100 * 2000) / (12500 * 4) = 4%
ANSWER:B
Answer: (B) 4%
Question: The largest 4 digit number exactly divisible by 77 is?
(A) 9935
(B) 9933
(C) 9944
(D) 9954
(E) 9960
Rationale: Largest 4-digit number = 9999
77) 9999 (129
9933
Answer : B
Answer: (B) 9933
Question: Q=√[2√63 + 2/(8+3√7)] =
(A) 8 + 3√7
(B) 4 + 3√7
(C) 8
(D) 4
(E) √7
Rationale: In these type of question u multiply the nominator and denominator with conjugate...Conjugate of 8 +3sqrt(7) is 8 -3sqrt(7)
sqrt[2sqrt(63) + 2 { 8 - 3sqrt(7)}/{64 - 63}]
Q=sqrt[2sqrt(63) +16 - 2sqrt(63)] =4
Answer is 4.=D
Answer: (D) 4
Question: A library has an average of 140 visitors on Sundays and 80 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is :
(A) 90
(B) 100
(C) 105
(D) 110
(E) 125
Rationale: Explanation:
Since the month begins with a Sunday, so there will be five Sundays in the month,
Required average = (140 * 5 + 80 * 25) / 30 = 2700/30 = 90
Answer: A) 90
Answer: (A) 90
Question: If 4a = 16b and 5b = 13c, Find a:b:c?
(A) 52:13:5
(B) 13:7:52
(C) 7:13:52
(D) 7:13:54
(E) None of these
Rationale: Explanation:
(4a = 16b ==> a/b = 16/4)
and (5b = 13c ==> b/c = 13/5)
==> a:b = 16:4 and b:c = 13:5
a:b:c =52:13:5
Answer: Option A
Answer: (A) 52:13:5
Question: 50 persons like apple. 7 like orange and mango dislike apple. 10 like mango and apple and dislike orange. 4 like all. How many people like apple?
(A) 47
(B) 46
(C) 54
(D) 57
(E) 62
Rationale: orange+mango-apple=7
mango+apple-orange=10
apple=50
orange+mango+apple=4
50+10+4-7=57 like apple
ANSWER:D
Answer: (D) 57
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 130. If legs are counted, there are 580. The number of hares in the zoo is?
(A) 120
(B) 182
(C) 190
(D) 137
(E) 160
Rationale: 130*2 = 260
580
-----
320
1----2
?----320 = 160
Answer:E
Answer: (E) 160
Question: If the sales tax be reduced from 4 (1/2) % to 3 (1/2) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 10500?
(A) Rs. 105
(B) Rs. 150
(C) Rs. 146
(D) Rs. 135
(E) None of these
Rationale: Explanation:
Required difference = (4 (1/2) of Rs. 10500) - (3 (1/2) of Rs. 10500)
= (9/2– 7/2) % of Rs. 10500
= (1) x (1/100) x 10500
= Rs. 105
ANSWER A
Answer: (A) Rs. 105
Question: The average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
(A) 26
(B) 56
(C) 22
(D) 29
(E) 21
Rationale: 1 to 11 = 11 * 50 = 550
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 550
= 56
Answer:B
Answer: (B) 56
Question: A relay has a series of 5 circuits in a line. The even-numbered circuits are control circuits; the odd are buffer circuits. If both a control circuit and the buffer circuit immediately following it both fail in that order, then the relay fails. The probability of circuit one failing is 3/8; circuit two, 5/8; circuit three, 3/10; circuit four, 3/4; and circuit five, 2/5 .What is the probability that the relay fails?
(A) 9/80
(B) 3/10
(C) 303/800
(D) 69/160
(E) 497/800
Rationale: The first circuit doesn't matter.
Prob(relay fails) = 1 - Prob(relay succeeds)
Prob(2+3 work) = 1 - 3/16 = 13/16
Prob(4+5 work) = 1 - 3/10 = 7/10
Prob(relay fails) = 1 - Prob(2+3 work AND 4+5 work) = 1 - (13/16)(7/10) = 1 -91/160 = 69/160
D
Answer: (D) 69/160
Question: 30 pens and 75 pencils were purchased for 630. If the average price of a pencil was 2.00, find the average price of a pen.
(A) 10
(B) 11
(C) 12
(D) 13
(E) 16
Rationale: Since average price of a pencil = 2
∴ Price of 75 pencils = 150
∴ Price of 30 pens = (630 – 150) = 480
∴ Average price of a pen = 480⁄60 = 16
Answer E
Answer: (E) 16
Question: Which one of the following numbers is divisible by 11?
(A) 4823718
(B) 8423718
(C) 8432718
(D) 4832718
(E) 4852718
Rationale: Explanation:
4832718 = (4+3+7+8) – (8+2+1) = 11
So, the given number is divisible by 11
Answer:D
Answer: (D) 4832718
Question: In an electric circuit, three resistors with resistances r1, r2 and r3 are connected in parallel. In this case, if R is the combined resistance of these three resistors, then the reciprocal of R is equal to the sum of the reciprocals of r1, r2 and r3. What is R in terms of r1, r2 and r3?
(A) (r1 + r2 + r3)
(B) r1r2r3
(C) 1/(x + y)
(D) r1r2r3/(r1 + r2 + r3)
(E) (r1 + r2 + r3)/r1r2r3
Rationale: The wording is a bit confusing, though basically we are told that 1/R = 1/r1 + 1/r2 + 1/r3, from which it follows that r=r1r2r3/(r1 + r2 + r3).
Answer: D.
Answer: (D) r1r2r3/(r1 + r2 + r3)
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot at the rate of 26.50 per metre is 5,300, what is the length of the plot (in metres)?
(A) 40
(B) 120
(C) 50
(D) Data inadequate
(E) None of these
Rationale: Perimeter of the rectangular plot = [(b + 20) + b] × 2
= 5300/26.5=200=200
∴ (2b + 20)2 = 200
⇒ b = 40
⇒ l = 40 + 20 = 60 m
Answer E
Answer: (E) None of these
Question: In a hostel there were 100 students. To accommodate 15 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
(A) A)Rs.6900
(B) B)Rs.5480
(C) C)Rs.5400
(D) D)Rs.5900
(E) E)Rs.5430
Rationale: 100x + 400
= 115(x – 5)
x = 65
100 * 65 + 400
= 6900
Answer:A
Answer: (A) A)Rs.6900