mathewhe/aqua_rat huggingface dataset:
Question: A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Let the total number of shots be x. Then,
Shots fired by A = 5/8x
Shots fired by B = 3/8x
Killing shots by A = 1/3 of 5/8x = 5/24x
Shots missed by B = 1/2 of 3/8x = 3/16x
Therefore, 3x/16 = 27 or x = (27 x 16/3)= 144.
Birds killed by A = 5x/24 = (5/24 x 144)= 30.
Answer is C.
Answer: (C) 30
Question: A shopkeeper professes to sell his goods at cost price but uses a weight of 800 gm instead of kilogram weight.Thus, he makes a profit of
(A) 20%
(B) 22%
(C) 25%
(D) None of these
(E) Cannot be determined
Rationale: Solution
Therefore,Profit	=(200/800×100)%
= 25%.
Answer C
Answer: (C) 25%
Question: A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 99 cookies, what is the minimum number of chocolate chip cookies he makes?
(A) 7
(B) 14
(C) 21
(D) 28
(E) 35
Rationale: 7C+6P=99
We need to maximize P to minimize C so that the eq is also satisfied
Try substitution for CP to solve so that eqn is satisfied
The least value of C for which equation gets satisfied is 5
i.e. 7*3+6*13=21+78=99
Hence C is the answer
Answer: (C) 21
Question: You are renting an apartment and you need √784 for each side, how many feet are you looking to measure?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 28
Rationale: Try filling the numbers into the answer y x y =
Find the closest to 784.
Answer E
Answer: (E) 28
Question: A farmer spent $35 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 10% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?
(A) $36.55
(B) $38.50
(C) $39.20
(D) $39.50
(E) $40.60
Rationale: A farmer spent 40% money on chicken feed, so he spent 0.4*$35=$14 on chicken feed, thus he spent the remaining 35-14=$21 on goat feed.
Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.9=$14 --> x=$15.55.
Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 15.55+21=$36.55.
Answer: A.
Answer: (A) $36.55
Question: If -2/(a - 6) = 4/(a + 4), then a = ?
(A) 2/3
(B) 1/2
(C) 5/3
(D) 8/3
(E) 7/3
Rationale: Multiply all terms of the given equation by (a - 6)(a + 4), simplify and solve
(a - 6)(a + 4)[ -2/(a - 6) ] = (a - 6)(a + 4) [ 4/(a + 4) ]
- 2 (a + 4) = 4 (a - 6)
a = 8/3
correct answer D
Answer: (D) 8/3
Question: A cube of sides 9 is first painted red and then cut into smaller cubes of side 3. How many of the smaller cube have painted on exactly 2 sides?
(A) 30
(B) 24
(C) 12
(D) 8
(E) 9
Rationale: n=side of big cube/side of small cube
and no. Of smaller cubes with two surfaces painted is (n-2)*12
(3-2)*12=12 ans
ANSWER:C
Answer: (C) 12
Question: 25 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?
(A) 87
(B) 18
(C) 17
(D) 16
(E) 30
Rationale: Binders Books Days
25 1400 21
x 1600 20
x/25 = (1600/1400) * (21/20) => x = 30
Answer:E
Answer: (E) 30
Question: Given that E and F are events such that P(E) = 10 P(F) = 2 and P(E n F) = 10,
find P (E|F) and P(F|E)
(A) 1
(B) 69
(C) 24
(D) 5
(E) 12
Rationale: Here, E and F are events
P(E|F) = P(EnF)/P(F) = 10/10= 1
P(F|E) = P(EnF)/P(E) = 10/2 = 5.
D)
Answer: (D) 5
Question: A sum was put a simple interest at a certain rate for 7 years. Had it been put at 2% higher rate, it would have fetched Rs. 350 more. The sum is:
(A) s.500
(B) s.1000
(C) s.1500
(D) s.2000
(E) s.2500
Rationale: Explanation :
Let the sub be Rs.x and the initial rate be R%.Then
x Ã— (R+2) Ã— 7/100âˆ’xÃ—RÃ—7/100=350
â‡’x Ã— 2Ã—7/100=350
â‡’x Ã— 7 /100=175
â‡’7x=17500
â‡’x=2500
Answer : Option A
Answer: (A) s.500
Question: Assuming i have an infinite supply of coins.
What is the fewest number of coins would be required in order to make sure each and every coin touched exactly three other coins.
(A) 3
(B) 7
(C) 4
(D) 8
(E) 2
Rationale: C
4
Three placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.
Answer: (C) 4
Question: Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities.
How many mystical fruits remain after he goes through all the thirty check points?
(A) 25
(B) 26
(C) 27
(D) 28
(E) 29
Rationale: Solution:
25 Fruits
Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can.
For the first sack:
He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M,
(Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M
M = 10
Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each.
Now he must get rid of the second sack.
For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints.
(Space in First Sack) N = (Remaining fruits in second sack) 30 – N
N = 15
Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points.
Answer A
Answer: (A) 25
Question: 25% of 30% of 45% is equal to?
(A) 0.03375
(B) 0.03372
(C) 0.03379
(D) 0.03372
(E) 0.03328
Rationale: (25/100) * (30/100) * (45/100)
1/4 * 3/10 * 9/20
27/800 = 0.03375
Answer: A
Answer: (A) 0.03375
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
(A) 2
(B) 6
(C) 5
(D) 4
(E) 8
Rationale: Explanation:
Explanation:
Let rate = R% and time = R years.
Then,
Answer: B) 6
Answer: (B) 6
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.1 years, The ratio of the number of boys to the number of girls in the class is
(A) 7 : 6
(B) 2 : 3
(C) 9 : 3
(D) 6 : 3
(E) 2 : 5
Rationale: Explanation:
Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.1 = (k + 1) * 15.8
<=> (16.4 - 15.8) k = (15.8 - 15.1) <=> k = 0.7/0.6 = 7/6.
Required ratio = 7/6 : 1 = 7 : 6.
Answer: A
Answer: (A) 7 : 6
Question: A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 24 inches. Find b.
(A) 8
(B) 16
(C) 24
(D) 32
(E) 48
Rationale: From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) andbis 4 (=2^2), sob=2^x, where x>=2.
From the second premise, we know that the LCM of 12 (2^2*3) andbis 24 (2^3*3), sob=2^3 or 2^3*3 (8 or 24).
Combining 2 premises shows the answer is A(8).
Answer: (A) 8
Question: Two trains leave a station traveling the same direction. Train A leaves the station traveling at a constant speed of 60 mph, and train B leaves the station traveling at a constant speed of 80 mph. If both trains maintain constant speeds, in how many minutes will train B overtake train A if train A left 40 minutes prior to train B?
(A) 90
(B) 100
(C) 110
(D) 120
(E) 130
Rationale: We can use D=RT [distance=rate*time]
Train A will have traveled for 40 minutes longer than train B when B overtakes A, so
time of train A: T+40minutes = T+(2/3) hours (use hours since the rate is in hours)
time of train B: T
rate of train A: 60 mph
rate of train B: 80 mph
the distances traveled by each will be equal when train B overtakes train A, so we can set the right sides of D=RT equal for the two trains
(rate of train A)*(time of train A) = (rate of train B)*(time of train B)
60*(T+2/3)=80*T
60T + 40 = 80T
40 = 20T
2 = T
2 hours = 120 minutes
D
Answer: (D) 120
Question: 10 - [9 - {8 - (7 - 6)}] - 5 is equal to ?
(A) -5
(B) 1
(C) 3
(D) 9
(E) 8
Rationale: Answer
Given expression = 10 - [ 9 - {8 - 1}] - 5
= 10 - [9 - 7] - 5
= 10 - 2 - 5
= 3
Option: C
Answer: (C) 3
Question: By selling an umbrella for Rs. 300, a shop keeper gains 200%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
(A) 50
(B) 25
(C) 400
(D) 200
(E) 150
Rationale: Marked price = Rs. 300
C.P. = 100/300 * 300 = Rs. 100
Sale price = 90% of Rs. 300 = Rs. 270
Required gain % = 200/100 * 100 = 200%.
Answer:D
Answer: (D) 200
Question: The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 72° of the circle, what percentage of MegaTek employees are in manufacturing?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 72%
Rationale: 72° divided by 360° equals 0.2, therefore the sector is equal to 20% of the total
ANSWER: A
Answer: (A) 20%
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of5% p.a. was Rs.246. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
(A) Rs.2535
(B) Rs.2646
(C) Rs.2546
(D) Rs.2656
(E) Rs.2565
Rationale: Let the sum be Rs.P
P{ [ 1 + 5/100]2 - 1 } = 246
P(5/100)(2 +5/100) = 246 [a2 - b2 = (a - b) ( a + b)] P = 246 / (0.05)(2.05) = 2400. Amount =Rs.2646 Answer :B
Answer: (B) Rs.2646
Question: Victor gets 92 % marks in examinations. If these are 184 marks, find the maximum marks.
(A) 334
(B) 500
(C) 200
(D) 288
(E) 271
Rationale: Let the maximum marks be m
Then 92 % of m = 184
⇒ 92/100 × m = 184
⇒ m = (184 × 100)/92
⇒ m = 18400/92
⇒ m = 200
Therefore, maximum marks in the examinations are 200.
Answer: C
Answer: (C) 200
Question: Which of the following equations is NOT equivalent to 4x^2 = z^2 - 9 ?
(A)  4x^2 + 9 = z^2
(B)  4x^2 - z^2 = -9
(C)  4x^2= (z + 3)(z - 3)
(D)  2x = z - 3
(E) x^2 = (z^2-9)/4
Rationale: 4X^2 = z^2 - 9
The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt.
Looking at Answer D, we have....
2X = z - 3
While you COULD take the square root of both sides of the original equation, it's important to note that the square root of z^2 - 9 is NOT (z-3).
z^2 - 9 can be factored into (z-3)(z+3), but neither of these parentheses is the square root of z^2 - 9.
You can see the proof when you square either of the two parentheses:
(z-3)^2 = z^2 - 6X + 9
(z+3)^2 = z^2 + 6x + 9
Thus, D is NOT equivalent to the prompt.
Answer: (D)  2x = z - 3
Question: From a pack of 52 cards, two cards are drawn together at random. What is the probability that the one is heart and other two is diamond?
(A) 238/5525
(B) 176/5534
(C) 253/5523
(D) 234/5525
(E) 1/5525
Rationale: Solution
Let S be the sample space. Then,
n(S) = 52C3	= 22100
Let E = event of getting 1 face card.
n(E) = number of ways of choosing 1 face card out of 26
=13C1 * 13C2= 13*72 = 936
P(E) = n(E) / n(S)	= 936 / 22100 = 234/5525
= 234/5525.
Answer D
Answer: (D) 234/5525
Question: In a recent election, Ms. Robbins received 6,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 15 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 40 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?
(A) 0.06N + 3,200
(B) 0.09N + 6,000
(C) 0.4N + 7,200
(D) 0.1N + 8,000
(E) 0.06N + 8,000
Rationale: I will go with option B
According to question 40 percent of total votes (N) cas were cast by independent voters. This implies 60 percent of N are voters that belong to political party. And she received 6000 votes from independent voters and 15 percent from registered voters (i.e 0.15 * 0.6 * N = 0.09N). Hence total votes = 6000 + 0.09N ....option B
Answer: (B) 0.09N + 6,000
Question: There were 400 ducks in a pond and 15 percent of them just left. How many ducks are remaining?
(A) 300
(B) 280
(C) 220
(D) 340
(E) 250
Rationale: 400/100 = 4
4 x 15 = 60
400 - 60 = 340
Answer is D
Answer: (D) 340
Question: A student was asked to find the arithmetic mean of the number 3,11,7,9,15,13,8,19,17,21,14 and x. He found the mean to be 12. what should be the number in place of x ?
(A) 3
(B) 7
(C) 17
(D) 31
(E) 32
Rationale: Solution
Clearly, we have(3+11+7+9+15+13+8+19+17+21+14+X/12) = 12
or 137+x = 144 or x = 144-137 = 7. Answer B
Answer: (B) 7
Question: If 76 is divided into four parts proportional to 7,5,3,4 then the smallest part is
(A) 12
(B) 15
(C) 16
(D) 19
(E) None
Rationale: Sol.
Given ratio = 7 : 5 : 3 : 4, sum of ratio terms = 19.
∴ Smallest part = (76 x 3/19) = 12.
Answer A
Answer: (A) 12
Question: What is the smallest integer b for which 27^b> 3^24?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 12
Rationale: 27^b> 3^24
Converting into the same bases:
27^b> 27^8
Therefore for the equation to hold true, b> 8 or b = 9
Option C
Answer: (C) 9
Question: The area of a square playground is A square feet and the perimeter is p feet. If 4A=8p+36, what is the perimeter of the playground, in feet?
(A) 28
(B) 40
(C) 36
(D) 56
(E) 64
Rationale: You can also solve this via using the given numbers in the answer choices!
Of course you need to be aware of the basic properties as outlined by the other posts above (a = x^2 and p = 4x)
Starting with D you will notice that x=14 is way too big for your area (14^2) and will not satisfy: 4A=8p+36 or A=2p+9
--> Eliminate D and E
Now pick C (its either too big, then its A, or too small then you know its C or it is B itsself)
And picking C indeed solves the problem! (36/4 --> 9; a= 9^2 = 81 and 81=2x36+9)
Answer: (C) 36
Question: An event manager has ten patterns of chairs and eight patterns of tables. In how many ways can he make a pair of table and chair?
(A) 100
(B) 80
(C) 110
(D) 64
(E) None of these
Rationale: Explanation :
He has has 10 patterns of chairs and 8 patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 8 ways
Hence one chair and one table can be arranged in 10 x 8 ways = 80 ways. Answer : Option B
Answer: (B) 80
Question: If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling nine books ?
(A) 2025
(B) 2677
(C) 1800
(D) 2778
(E) 76611
Rationale: Explanation:
Least Cost Price = Rs. (200 * 9) = Rs. 1800.
Greatest Selling Price = Rs. (425 * 9) = Rs. 3825.
Required profit = Rs. (3825 - 1800) = Rs. 2025.
Answer: A) 2025
Answer: (A) 2025
Question: At a dinner party, 7 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
(A) 1) 5
(B) 2) 720
(C) 3) 724
(D) 4) 732
(E) 5) 120
Rationale: for number of distinct arrangements of 'n' items around a circular table, we get the arrangements by way of (n-1)!
in this case, there are 7 guests, so number of distinct arrangements = 6! = 720
Answer : B
Answer: (B) 2) 720
Question: Two trains of equal lengths take 10 sec and 15 sec, respectively, to cross a telegraph post. If the length of each train is 120 m, in what time will they cross each other, travelling in opposite directions?
(A) 17 sec
(B) 12 sec
(C) 18 sec
(D) 19 sec
(E) 52 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.
Answer: B
Answer: (B) 12 sec
Question: A box contains 3 yellow balls and 6 black balls. One by one, every ball is selected at random without replacement. What is the probability that the fourth ball selected is black?
(A) 4/7
(B) 3/5
(C) 5/8
(D) 2/3
(E) 3/4
Rationale: Each ball has an equal chance (1/9) of being selected fourth.
The probability that a black ball is selected fourth is 6/9 = 2/3.
The answer is D.
Answer: (D) 2/3
Question: A certain no. when divided by 95 leaves a remainder 25, what is the remainder if the same no.be divided by 15?
(A) 3
(B) 4
(C) 6
(D) 8
(E) 9
Rationale: Explanation:
95 + 25 = 120/15 = 8 (Remainder)
D
Answer: (D) 8
Question: If a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability R that this product will be a multiple of 45?
(A) 1/32
(B) 1/28
(C) 1/24
(D) 1/16
(E) 1/14
Rationale: There are 3 single digit multiple of 3, that is, 3,6,9.
There are 8 prime nos less than 20 - 2,3,5,7,11,13,17,19
Total outcome - 8*3 = 24
Favourable outcome = 1 (9*5)
Hence required probability R= 1/24. Answer C.
Answer: (C) 1/24
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $504 per week. How much does she earn in dollars per hour?
(A) 2
(B) 8
(C) 9
(D) 14
(E) 24
Rationale: Explanation:
Total hours worked = 8 x 3 + 6 x 2 = 36
Total earned = 504. Hourly wage = 504 / 36 = 14
Answer: D
Answer: (D) 14
Question: Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in --- days.
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: Explanation :
Work done by Kamal in 1 day = 1/20
Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16
=> Suresh can complete the work in 16 days
Answer : Option B
Answer: (B) 16
Question: The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?
(A) 12/35
(B) 35/12
(C) 45/12
(D) 4/9
(E) 6/15
Rationale: Let the numbers be a and b. Then, a + b = 12 and ab = 35.
a + b/ab	=12/35
1/b+	1/a=	12/35
Sum of reciprocals of given numbers =12/35
answer E
Answer: (E) 6/15
Question: Danny and Steve are running towards each other, each one from his own house. Danny can reach Steve's house in 31 minutes of running, which is half the time it takes Steve to reach Danny's house. If the two started to run at the same time, how much time longer will it take Steve to reach the halfway point between their houses than Danny to reach the halfway point between their houses?
(A) 15.5 minutes
(B) 31 minutes
(C) 35 minutes
(D) 62 minutes
(E) 93 minutes
Rationale: Danny's time is 31 minutes. The time to reach halfway is 15.5 minutes.
Steve's time is 62 minutes. The time to reach halfway is 31 minutes.
The time difference is 31 - 15.5 = 15.5 minutes
The answer is A.
Answer: (A) 15.5 minutes
Question: Twenty percent of the skiers that tried out for the ski patrol were selected. Of those that were not selected, 20 skiers were CPR certified and 28 were not. How many skiers tried out for the ski patrol?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Not Selected = 80%
If total is x.
Then 0.8x=20+28=48
x=60
Hence answer is C.
Answer: (C) 60
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
(A) 222
(B) 377
(C) 277
(D) 400
(E) 281
Rationale: 2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer: D
Answer: (D) 400
Question: Find the sum of divisors of 544 which are perfect squares.
(A) 32
(B) 64
(C) 42
(D) 21
(E) None of these
Rationale: 544= 25 + 171 =(2)0+(2)1+(2)2+(2)3+(2)4+(2)5 x (17)0 + (17)1.
Here 20=1 =11 A perfect Square,
22 and 24=16=44 are perfect Squares, Hence,
1 + 4 + 16= 21. Correct answer is : D
Answer: (D) 21
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 320 m
(B) 350 m
(C) 650 m
(D) 750 m
(E) None of these
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
ANSWER:B
Answer: (B) 350 m
Question: Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 50 years. What is Deepak present age
(A) 14
(B) 15
(C) 33
(D) 22
(E) 23
Rationale: Explanation:
Present age is 4x and 3x,
=> 4x + 6 = 50 => x = 11
So Deepak age is = 3(11) = 33
Answer: Option C
Answer: (C) 33
Question: The profit earned by selling an article for Rs.753 is equal to the loss incurred when the same article is sold for Rs.455.What should be the sale price for making 50% profit ?
(A) 706
(B) 786
(C) 906
(D) 896
(E) 696
Rationale: Let C.P =Rs. x
Then as given, (753 - x ) = (x - 455) 2x = 1208 x = 604
There fore S.P= 150% of 604 => Rs. = Rs.906
ANSWER:C
Answer: (C) 906
Question: A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 140, how much must C pay as his share of rent?
(A) 45
(B) 36
(C) 55
(D) 65
(E) none
Rationale: Sol.
A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9.
âˆ´ Câ€™s rent = Rs. [140 * 9/35] = Rs. 36.
Answer B
Answer: (B) 36
Question: A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 10% on conveyance. If his savings at the end of the month is Rs. 1200, then his salary per month in rupees is:
(A) 12000
(B) 6000
(C) 8000
(D) 10000
(E) None of these
Rationale: Total expenditure = 40 + 25 + 15 + 10 = 90%
Saving = (100 - 90) = 10%
10/100 × Salary = 1200, Salary = 12000 Rs.
Answer:A
Answer: (A) 12000
Question: If |x^2 − 12| = x, which of the following could be the value of x?
(A) –4
(B) –3
(C) 1
(D) 2
(E) 3
Rationale: Here ONE important point is that LHS is positive, so RHS will also be positive, SO x will be +IVE..
A and B are eliminated..
Now try to substitute remaining choices
C. 1
|x^2 − 12| = x..
|1^2-12|=1.. 11=1.. NO
D. 2
|x^2 − 12| = x..
|2^2-12|=2.. 7=2.. NO
E. 3
|x^2 − 12| = x..
|3^2-12|=3.. 3=3.. YES
ANSWER:E
Answer: (E) 3
Question: We invested a total of $1,000. We invested one part of the money at 3% and the rest of the money at 5%. The total investment with interest at the end of the year was $1,046. How much money did we invest at 3%?
(A) $200
(B) $240
(C) $280
(D) $320
(E) $360
Rationale: Let x be the money invested at 3%.
1.03x+1.05(1000-x)=1046.
0.02x=1050-1046.
0.02x=4.
2x=400.
x=200.
The answer is A.
Answer: (A) $200
Question: Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 5.5 km apart, if they walk in the same direction?
(A) 11 hrs
(B) 14 hrs
(C) 15 hrs
(D) 17 hrs
(E) None
Rationale: Sol.
to be 0.5 km apart, they take 1 hour.
To be 5.5 km apart, they take [1/0.5 * 5.5] hrs = 11 hrs.
Answer A
Answer: (A) 11 hrs
Question: You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?
(A) 5
(B) 6
(C) 9
(D) 12
(E) 18
Rationale: Consider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:
XYZ
YZX
ZXY
And:
XYZ
ZXY
YZX
Now, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible is 2*6=12.
Answer: D.
Answer: (D) 12