mathewhe/aqua_rat huggingface dataset:
Question: P is three times as old as Q. In 10 years, P will be twice as old as Q. How old was P three years ago?
(A) 27
(B) 30
(C) 33
(D) 36
(E) 39
Rationale: P = 3Q so Q = P/3
P+10 = 2(Q+10) = 2(P/3+10)
P/3 = 10
P = 30
Three years ago, P was 27.
The answer is A.
Answer: (A) 27
Question: A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 17%
(B) 72%
(C) 12%
(D) 82%
(E) 16%
Rationale: Original price = 100
CP = 80
S = 80*(140/100) = 112
100 - 112 = 12%
Answer:C
Answer: (C) 12%
Question: The true discount on a bill of Rs. 2260 is Rs. 360. What is the banker's discount?
(A) Rs. 428
(B) Rs. 422
(C) Rs. 412
(D) Rs. 442
(E) None of these
Rationale: Explanation :
F = Rs. 2260
TD = Rs. 360
PW = F - TD = 2260 - 360 = Rs. 1900
True Discount is the Simple Interest on the present value for unexpired time
=>Simple Interest on Rs. 1900 for unexpired time = Rs. 360
Banker's Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2260 for unexpired time
=360/1900 × 2260 = 0.19 × 2260 = Rs. 428 Answer : Option A
Answer: (A) Rs. 428
Question: If n = 20! + 19, then n is divisible by which of the following?
I. 15
II. 17
III. 19
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Rationale: 19 divides 20! so 19 also divides 20! + 19.
15 and 17 divide 20! so they do not divide 20! + 19.
The answer is C.
Answer: (C) III only
Question: A can fill the tank in 28hrs
B can fill the tank in 14 hrs
and C takes 7hrs.
If all three pipes are opened simultaneously ,how long it will take to fill the tank?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Solution:time taken=(28*14*7*)/(28*14 + 14*7 + 28*7)
To solve this quicker find out LCM(28,14,7)
we get 28
Time taken =28/(28/28 + 28/14 + 28/7)
=28/(1+2+4)
=28/7
=4
Answer A
Answer: (A) 4
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
(A) 100
(B) 110
(C) 112
(D) 115
(E) 119
Rationale: Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer: (A) 100
Question: Three friends (Amar, Mohan and Sham) started partnership business by investing Rs. 1,00,000, Rs. 1,40,000 and Rs. 1,60,000 respectively. After eight months, Ramesh joins them with his capital of Rs. 50,000. If, at the end of the year, a profit of Rs. 30,500 was made, what would be the difference between the shares of Sham and Mohan?
(A) 1464
(B) 1462
(C) 2679
(D) 2776
(E) 9782
Rationale: Explanation:
Amar invests Rs. 1,00,000 for 12 months : Mohan invests Rs. 1,40,000 for 12 months : Sham invests Rs.1,60,000 for 12 months : Ramesh invests Rs. 50,000 for 4 months
Amar : Mohan : Sham : Ramesh = 30 : 42 : 48 : 5
Sham's share = (48/125) * 30,500 = 11712
Mohan's share = (42/125) * 30,500 = 10248
Difference between shares of Sham's and Mohan's = 1464
ANSWER: A
Answer: (A) 1464
Question: the total age of A and B is 12 year more than the total age of B and C. C is how many years younger than A ?
(A) 12
(B) 24
(C) data inadequate
(D) None of these
(E) 34
Rationale: Solution
(A + B ) - (B + C) = 12 ⇔ A - C = 12. Answer A
Answer: (A) 12
Question: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 110 mangoes.
(A) 367
(B) 380
(C) 400
(D) 406
(E) 412
Rationale: Mr. John used to purchase certain number of mangoes for $360 Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes.
Method 1:
Let price per mango = x. Let number of mangoes be n. Then, nx = 360.
Now price = 0.9x; number of mangoes = n + 12. Total amount = 0.9x*(n+12) = 360.
nx = 0.9nx + 10.8x => 0.1nx = 10.8x => n = 108 => x = 360/108 = 3.33
Original price of 110 mangoes = 110*3.33 = 367.
Answer A
Answer: (A) 367
Question: 5+3+2 = 151022
9+2+4 = 183652
8+6+3 = 482466
5+4+5 = 202541
THEN ;
7+2+5 = ?
(A) 253547
(B) 143681
(C) 143547
(D) 147614
(E) 255547
Rationale: C
143547
Answer: (C) 143547
Question: In a mayoral election, Candidate X received 1/4 more votes than candidate Y, and Candidate Y received 1/6 fewer votes than Z. If Z received 24,000 votes how many votes did candidate X received?
(A) 18000
(B) 22000
(C) 24000
(D) 25000
(E) 32000
Rationale: Z=24 --> Y received 1/4 fewer votes than Z --> Y=Z-1/6*Z=20;
X received 1/4 more votes than Y --> X=Y+1/4*Y=25.
Answer: D.
Answer: (D) 25000
Question: The average (arithmetic mean) of 20, 40, and 60 is 5 more than the average of 10, 70, and what number?
(A) 15
(B) 25
(C) 35
(D) 45
(E) 55
Rationale: a1 = 120/3 = 40
a2 = a1 -5 = 35
sum of second list = 35*3 = 105
therefore the number = 105 -80 = 25
ANSWER:B
Answer: (B) 25
Question: There are, in a certain league, 8 teams, and each team face another team for a total of 12 times. How many games are played in the season?
(A) 150
(B) 121
(C) 144
(D) 180
(E) 1200
Rationale: By using the formula, t[n(n - 1) / 2], where t = no. of games between two teams and n = total no. of teams, we get: 144
Option C.
Answer: (C) 144
Question: Six years ago I was three times as old as my brother, and now I am twice as old my brother. Find my brother's age.
(A) 8 years
(B) 24 years
(C) 12 years
(D) 16 years
(E) 26 years
Rationale: Let brother's age = x
And my age = 2x
6 years ago:
Brother age = x-6
My age = 2x-6
I was 3 time his age then,
2x-6 = 3(x-6)
2x-6 = 3x-18
3x-2x = 18-6
x = 12
Brother's age = 12years
My age now = 2x
= 2(12)
= 24years
ANSWER:B
Answer: (B) 24 years
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 5 days. How long will C take to do it?
(A) 120/7 days
(B) 110/11 days
(C) 100/9 days
(D) 90/13 days
(E) 80/3 days
Rationale: 2c = 1/4 + 1/5 – 1/3 = 7/60
c = 7/120 => 120/7 days
The answer is A.
Answer: (A) 120/7 days
Question: In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 5 metres then what will be the area of the square so formed?
(A) Cannot be determined
(B) 2600 cm2
(C) 2500 cm2
(D) 3025 cm2
(E) None of these
Rationale: Let the side of the square be x m.
∴ Perimeter of the square = 48 × 5 = 4x ∴ x = 60 m
∴ Area = (60)2 = 3600 m2
Answer E
Answer: (E) None of these
Question: The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places)?
(A) Rs.20043.94
(B) Rs.20043.97
(C) Rs.20043.99
(D) Rs.20043.90
(E) Rs.20043.91
Rationale: Let the rate of interest be R% p.a.
(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.
Answer:A
Answer: (A) Rs.20043.94
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ?
(A) 62.5
(B) 65
(C) 61
(D) 64
(E) 60
Rationale: Let the capacity of 1 bucket = x.
Then, the capacity of tank = 25x.
New capacity of bucket = 2/5 x
Therefore, Required number of buckets = (25x)/(2x/5)
= (25x) x 5/2x
= 125/2
= 62.5
Answer is A.
Answer: (A) 62.5
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?
(A) 16
(B) 18
(C) 20
(D) 24
(E) 26
Rationale: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways
4: Or 4p = — 4:- 4X3X2X1- 24 ways
D
Answer: (D) 24
Question: A man borrowed Rs. 800 at 10% per annum simple interest and immediately lent the whole sum at 10% per annum compound interest. What does he gain at the end of 2 years ?
(A) Rs. 6
(B) Rs. 8
(C) Rs. 10
(D) Rs. 12
(E) Rs. 14
Rationale: S.I FOR RS.800 FR 2 YEARS IS RS.160, WHEREAS AMOUNT IS 168 RS. HENCE GAIN IS 168-160=8
ANSWER:B
Answer: (B) Rs. 8
Question: If a and b are nonzero integers such that a = 5b/2, then each of the following must be true EXCEPT
(A) 0 < b/a < 1
(B) ab is positive.
(C) On the number line, b lies between 0 and a.
(D) The ratio of a to b is equivalent to 10/4.
(E) a – b is positive.
Rationale: This question can be solved by TESTing VALUES. Based on its wording, you would likely need to do 2 TESTs to get to the correct answer though.
We're told that A and B are NONZERO INTEGERS and that A = 5B/2 or 2A = 5B. We're told that each of the answer is always true EXCEPT for one of them...
Before we get to the actual work, it's important to note a few details:
1) We are NOT told that A and B are positive - we're just told that they're NONZERO - that's interesting - it means that we have to consider the possibility that they're both NEGATIVE...
2) 4 of the answers will always be true, while one of them will EITHER be sometimes true OR never true. We'll have to keep working until we find 1 answer that is not true (for whatever reason) - that will be the solution to this question.
Since 2A = 5B, I'm going to run 2 pairs of TESTs at the same time...
A = 5
B = 2
AND
A = -5
B = -2
Answer A: 0 < B/A < 1
2/5 and -2/-5 both = 2/5. Answer A appears true.
Answer B: AB is positive
(2)(5) and (-2)(-5) both = +10. Answer B appears true.
Answer C: B is between 0 and A on the number line
0....2....5
-5....-2....0
Answer C appears true.
Answer D: A/B = 10/4
5/2 = -5/-2
10/4 = 5/2
Answer D appears true.
Answer E: A - B is positive
5 - 2 = 3
-5 - (-2) = -3 *****This is NOT always true.
Final Answer:
E
Answer: (E) a – b is positive.
Question: For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 52 units per day, what is the value of n ?
(A) 30
(B) 19
(C) 10
(D) 9
(E) 7
Rationale: (average production for n days) * n = (total production for n days) --> 50n=(total production for n days);
(total production for n days) + 90 = (average production for n+1 days) * (n+1) --> 50n + 90 = 52 * (n+1) --> n=19.
Or as 40 extra units increased the average for n+1 days by 2 units per day then 40/(n+1)=2 --> n=19.
Answer:B.
Answer: (B) 19
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
(A) 855 1/2 grams
(B) 833 1/3 grams
(C) 833 1/2 grams
(D) 875 2/7 grams
(E) 865 2/7 grams
Rationale: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3 = 833 1/3 grams.
ANSWER:B
Answer: (B) 833 1/3 grams
Question: Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 7 years?
(A) 4x (1+n/100)^6 - x
(B) 5x (1+n/100)^5- x
(C) 3x (1+n/100)^4 - x
(D) x (1+n/100)^4 - x
(E) x (1+n/100)^7 - x
Rationale: Amount after 7 years compounded yearly = x (1+n/100)^7
Thus profit = Final amount - original principle = x (1+n/100)^7 - x . Answer : E
Answer: (E) x (1+n/100)^7 - x
Question: A starts a business with a capital of Rs. 5,000. B joins in the business with Rs.2000 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
(A) 5 months
(B) 6 months
(C) 7 months
(D) 10 months
(E) None of these
Rationale: Explanation :
Let B joins for x months. Then
A:B = 5000*12 : x* 2000 = 3 : 1
=> 5*12 : 2x= 3 : 1
=> 5*12/ 2x = 3/1 = 3
=> 5*4 /2x = 1
=> 10/x = 1
=> x = 10. Answer : Option D
Answer: (D) 10 months
Question: A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job?
(A) 23
(B) 22
(C) 21
(D) 36
(E) 48
Rationale: C
21
WC = 1:2
2x + x = 1/14 => x = 1/42
2x = 1/21 => 21 days
Answer: (C) 21
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 10.9
(B) 10.7
(C) 10.3
(D) 10.8
(E) 10.2
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 140 + 160 = 300 m.
Required time = 300 * 9/250 = 54/5 = 10.8 sec.
'Answer: D
Answer: (D) 10.8
Question: There has been successive increases of 20% and then 10% in the price of gas from the previous month. By what percentage should a driver reduce gas consumption so that the expenditure does not change?
(A) 16%
(B) 20%
(C) 24%
(D) 28%
(E) 32%
Rationale: Let P be the original price per unit of gas.
Let x be the original gas consumption.
Let y be the reduced gas consumption.
y*1.1*1.2*P = x*P
y = x / (1.1*1.2) which is about 0.76x which is a decrease of about 24%.
The answer is C.
Answer: (C) 24%
Question: The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 17 terms of the arithmetic progression?
(A) 300
(B) 120
(C) 150
(D) 170
(E) 270
Rationale: n th term of A.P. is given by a+(n-1)d
4 th term = a+3d
12 th term = a+11d
Given a+3d+a+11d=20 --> 2a+14d=20 --> a+7d = 10
Sum of n term of A.P = n/2[2a+(n-1)d]
subsitiuing n = 17 ...we get 17/2[ 2a + 14d] = 17 [a+7d] = 17*10 = 170...
Answer is D...
Answer: (D) 170
Question: What is the least number which when divided by 6, 7, 9 and 18 leaves remainder 4 in each care?
(A) 130
(B) 140
(C) 136
(D) 156
(E) 166
Rationale: Explanation:
LCM of 6, 7, 9 and 18 is 126
Required number = 126 + 4 = 130
Answer: Option A
Answer: (A) 130
Question: If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true?
I. x > z
II. 2(x+ y) > 2z
III. yz > xz
IV. xy > y + z
(A)  I only
(B)  II only
(C)  II and III only
(D)  II and IV only
(E)  III and IV only
Rationale: we do not know the values or the relative values but that the three are consecutive..
so the max difference in any two number is 2 and min 1..
lets see the choices..
I. x > z...
we do not know the values or the relative values... need not be true..
II. 2(x+ y) > 2z or x+ y > z
we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true
III. yz > xz
we do not know the values or the relative values between x and y..need not be true
IV. xy > y + z
xy-y>z or y(x-1)>z...
again lets take the worst scenario..
we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true
only ii is true
ans B
Answer: (B)  II only
Question: If Rs 1050 is divided into three parts, proportional to (1 / 3) : (3 / 4) : ( 4 / 6), then what is the first part?
(A) 500
(B) 300
(C) 200
(D) 100
(E) 150
Rationale: EXPLANATION:
Given:
1050 =	1/3	:	3/4	:	4/6
1) L.C.M. of 3, 4 and 6 is 12
Therefore, multiply numerator and denominator of (1/3) with 4, to obtain denominator 12. Similarly multiply (3/4) with 3 and (4/6) with 2
4/12	:	9/12	:	8/12 = 4 : 9 : 8
2) If a number a is divided in three ratios x : y : z,
First Part:	ax/(x + y + z) ------- (a is the number divided)
Therefore,
First Part:	(1050 x 4) /(4 + 9 + 8)=200
ANSWER IS C
Answer: (C) 200
Question: A charity collected $1,499 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have?
(A) 77
(B) 78
(C) 79
(D) 74
(E) 65
Rationale: Min fund = 20
Total = 1499
The closest multiple of 20 to 1499 is : 73
Which implies 73 people gave 20 and 1 person gave 39
Ans. D
Answer: (D) 74
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 299
(B) 200
(C) 240
(D) 111
(E) 161
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 36 = 15
x + 300 = 540
x = 240 m. Answer:C
Answer: (C) 240
Question: Find the invalid no.from the following series 3, 7, 15, 27, 63, 127, 255
(A) 3
(B) 15
(C) 27
(D) 127
(E) 255
Rationale: Go on multiplying the number by 2 and adding 1 to it to get the next number.So, 27 is wrong.
C
Answer: (C) 27
Question: If the number 52,1n6, where n represents the tens digit, is a multiple of 3, then the value of n could be which of the following?
(A) 6
(B) 5
(C) 3
(D) 4
(E) 0
Rationale: The sum of the digits 5 + 2 + 1 + n + 6 must be a multiple of 3
14 + n must be a multiple of 3
substituting the numbers n must = 4
Answer D
Answer: (D) 4
Question: P,Q and R started a business in which P invested Rs.10,000/- for 2year, Q invested Rs.20,000/- for 3 years, R invested Rs.30,000/- for 4 years. At the end of the profit received by them is Rs.10,000/-. What is Q’s share?
(A) Rs. 2,500
(B) Rs. 2,000
(C) Rs. 1,000
(D) Rs. 1,500
(E) Rs. 3,000
Rationale: Solution: A : B : C = (10,000 * 2) : (20,000 * 3) : (30,000 * 4) = 1 : 3 : 6.
So Q's share = Rs. (10,000 * 3/10) = Rs. 3,000.
Answer: Option E
Answer: (E) Rs. 3,000
Question: If 2^2n + 2^2n + 2^2n + 2^2n = 4^20, then n =
(A) 3
(B) 6
(C) 19
(D) 23
(E) 24
Rationale: 2^2n + 2^2n + 2^2n + 2^2n = 4^20
=> 4 x 2^2n = 4^20 = 2^40
=> 2^2 x 2^2n = 2^40
=> 2^(2n+2) = 2^40
=> 2n+2 = 40=> n =19
So. Answer will be C.
Answer: (C) 19
Question: When a certain number X is divided by 63, the remainder is 25. What is the remainder when X is divided by 8?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: When a certain number X is divided by 63, the remainder is 25. What is the remainder when X is divided by 8?
Putting a value say x = 255 we get remainder as 25 when divided by 63.
When 25 divided by 8 we get 1 as remainder.
A is the answer.
Answer: (A) 1
Question: In a race of length L metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)
(A) L(L-N) / L-M
(B) M+
(C) L-N
(D) M-N
(E) L(N-M)/ L-M
Rationale: For my work, i took the following numbers:
L = 100
M = 10
N =20.
So basically, L beat G by 10 meters. Now whatever options comes close to the figure 10 is the right ans..
looking the the opion C to E, one can make out that they are incorrect, leaving us with just two options..A and B.
Out of which, i choose E.
Answer: (E) L(N-M)/ L-M
Question: John throws a coin until a series of three consecutive heads or three consecutive tails appears. What is the probability that the game will end after the fourth throw?
(A) 1/16
(B) 2/16
(C) 3/16
(D) 7/16
(E) 9/16
Rationale: Let's consider the routes that would lead to ending the game on the fourth toss. In order to be a win at that point, tosses #2 & #3 & #4 would all have to be the same, either H or T, and in order for the game NOT to end on the third toss, the first toss would have to be different from the other four. Thus, the only two possible sequences are
H-T-T-T ----> P = (1/2)^4 = 1/16
T-H-H-H ----> P = (1/2)^4 = 1/16
Either one of these would satisfy the condition, so we could have one or the other. OR means add in probability.
1/16 + 1/16 = 2/16
Answer (B).
Answer: (B) 2/16
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: 264 is divisible by 3, 4 and 11
=> 264 is divisible by 132
396 is divisible by 3, 4 and 11
=> 396 is divisible by 132
462 is divisible by 3 and 11, but not divisible by 4
=> 462 is not divisible by 132
792 is divisible by 3, 4 and 11
=> 792 is divisible by 132
968 is divisible by 4 and 11, but not divisible by 3
=> 968 is not divisible by 132
2178 is divisible by 3 and 11, but not divisible by 4
=> 2178 is not divisible by 132
5184 is divisible by 3 and 4, but not divisible by 11
=> 5184 is not divisible by 132
6336 is divisible by 3, 4 and 11
=> 6336 is divisible by 132
Hence, only 264, 396 ,792 and 6336 are divisible by 132. So the answer is 4
B)
Answer: (B) 4
Question: Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 5000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?
(A) 100000
(B) 100500
(C) 105000
(D) Data inadequate
(E) None of these
Rationale: Let the investment of X in 1995 be x.
∴ Profit = x⁄5
∴ Income = (x + x⁄5) = 6⁄5x
Investment of company X in 1996 would be (x – 5000) From the question,
(x - 500) × 126⁄100 = 6⁄5x ⇒ x = 105000
Answer C
Answer: (C) 105000
Question: A man has some hens and cows. If the number of heads be 44 and the number of feet equals 128, then the number of hens will be
(A) 22
(B) 24
(C) 26
(D) 20
(E) 28
Rationale: Explanation :
Let number of hens = h and number of cows = c
number of heads = 44
=> h + c = 44 ---(Equation 1)
number of feet = 128
=> 2h + 4c = 128
=> h + 2c = 64 ---(Equation 2)
(Equation 2) - (Equation 1) gives
2c - c = 64 - 44
=> c = 20
Substituting the value of c in Equation 1, we get
h + 22 = 44
=> h = 44 - 20 = 24
i.e., number of hens = 24
Answer : B
Answer: (B) 24
Question: 4, 7, 16, 43, 124, (...)
(A) 22
(B) 367
(C) 27
(D) 32
(E) 25
Rationale: Explanation :
4
4 × 3 - 5 = 7
7 × 3 - 5 = 16
16 × 3 - 5 = 43
43 × 3 - 5 = 124
124 × 3 - 5 = 367
Answer : Option B
Answer: (B) 367
Question: The average of 11 results is 20. The average of first 5 of them is 15 and that of last 5 is 22 . Find the 6th result?
(A) 35
(B) 50
(C) 100
(D) 120
(E) 150
Rationale: 6th result = sum of 11 results - sum of 10 results
= 11*20-5*15-5*22
= 220-75-110
= 35
Answer is A
Answer: (A) 35
Question: The output of a factory is increased by 10% to keep up with rising demand. To handle the holiday rush, this new output is increased by 30%. By approximately what percent would the output of the factory now have to be decreased in order to restore the original output?
(A) 20%
(B) 24%
(C) 30%
(D) 32%
(E) 79%
Rationale: take it as original output =100.
to meet demand increase by 10%, then output=110.
to meet holiday demand , new output increase by 30% then output equals 143
To restore new holidy demand output to original 100.
final -initial/final*100
=43/143*100=30% approxiamately.
option C is correct.
Answer: (C) 30%
Question: Three taps A, B and C can fill a tank in 24, 30 and 40 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in :
(A) 8 hours
(B) 10 hours
(C) 14 hours
(D) 16 hours
(E) 18 hours
Rationale: (A+B)'s 1 hour's work = (1/24 + 1/30) = 9/120 = 3/40.
(A+C)'s 1 hour's work = (1/24 + 1/40) = 8/120 = 2/30.
Part filled in 2 hours = (3/40 + 2/30) = 17/120.
Part filled in 12 hours = (6 * 17/120) = 17/20.
Remaining part = (1 - 17/20) = 3/20.
now, it is the time of A and B and 3/20 part is filled by A and B in 1 hour, then, 3/40 part will filled in 2 hours.
.'. total time taken to fill the tank = (12 + 2) = 14 hours Answer : C
Answer: (C) 14 hours
Question: If a and b are positive integers such that a/b = 4.37, which of the following must be a divisor of a?
(A) 19
(B) 13
(C) 12
(D) 7
(E) 17
Rationale: 1) A and B are positive INTEGERS
2) A/B = 4.37
A = 437
B = 100
437/100 = 4.37
These values are the smallest values as 437 is neither divisible by 5 or 2, the factors of 100.
The value of B is irrelevant to the question. We're asked for what MUST divide into A....
Since A is a multiple of 437, we have to 'factor-down' 437. This gives us (19)(23). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.
Answer: A
Answer: (A) 19