mathewhe/aqua_rat huggingface dataset:
Question: What is the Compound Interest on Rs.8500 at 7.5% p.a. compounded half-yearly for 2 1/2 years.
(A) 1409.85
(B) 1717.85
(C) 1427.85
(D) 2717.85
(E) 1817.85
Rationale: Compound interest : A = P(1 + r/n)nt
A = 10,217.85
C.I. >> 10,217.85 - 8500 >> Rs. 1717.85
Answer:B
Answer: (B) 1717.85
Question: An analyst will recommend a combination of 3 industrial stocks, 2 transportation stocks, and 2 utility stocks. If the analyst can choose from 4 industrial stocks, 5 transportation stocks, and 3 utility stocks, how many different combinations of 7 stocks are possible?
--
(A) 12
(B) 19
(C) 60
(D) 180
(E) 720
Rationale: 4C3 * 5C2 * 3C2 = 4*60*3 = 720.
Answer: E.
Answer: (E) 720
Question: Find the odd man out
3,12, 24,48, 56, 96
(A) 48
(B) 8
(C) 16
(D) 56
(E) 2
Rationale: 3*2 = 6
6*2 =12
12*2=24
24*2=48
48*2=96
ANSWER:D
Answer: (D) 56
Question: Two bullet train s 140 m and 210 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
(A) 15.8 sec.
(B) 12.6 sec.
(C) 11.8 sec.
(D) 10.8 sec.
(E) 08.8 sec.
Rationale: Relative speed = (60 + 40) km/hr = 100x5/18 = 250/9 m/ sec.
Distance covered in crossing each other = (140 + 210) m = 350 m.
Required time = 350x9/250 = 54/5 = 12.6 sec.
ANSWER B
Answer: (B) 12.6 sec.
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A & B leaves after 2 days simultaneously from the beginning. How long will work lost?
(A) 14 1/3
(B) 10 1/3
(C) 11 1/3
(D) 12 1/3
(E) 13 1/3
Rationale: 2/10 + 2/15 + x/20 = 1
x = 40/3 = 13 1/3
Answer: E
Answer: (E) 13 1/3
Question: A computer system uses alphanumeric case sensitive characters for its passwords. When the system was created it required users to create passwords having 4 characters in length. This year, it added the option of creating passwords having 5 characters in length. Which of the following gives the expression for the total number of passwords the new computer system can accept?
Assume there are 65 unique alphanumeric case sensitive characters.
(A) 63^4
(B) 62^5
(C) 62(62^4)
(D) 66(65^4)
(E) 63(62^6)
Rationale: Total number of passwords = number of 4 character password +number of 5 character password
= 65^4 + 65^5 (Since there is no limitation on repetition , each character can be chosen in 62 ways )
=65^4(1+ 65)
=65^4 * 66
Answer D
Answer: (D) 66(65^4)
Question: 155 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
(A) 12 liters
(B) 62 liters
(C) 41 liters
(D) 50 liters
(E) 34 liters
Rationale: Milk = 3/5 * 155 = 93 liters
Water = 62 liters
93 : (62+P) = 3:4
186 + 3P = 372 => P = 62
62 liters of water are to be added for the ratio become 3:4.
Answer:B
Answer: (B) 62 liters
Question: Let a be a positive integer. If q is divisible by 2^a and q is also divisible by 3^(2a), then it is possible that q is NOT divisible by
(A) 6
(B) 3 × 2^a
(C) 2 × 3^(2a)
(D) 6^a
(E) 6^(2a)
Rationale: Since, q is divisible by 2^a and 3^(2a), it must be divisible by 6. As least value of a = 1
Only for E, 6^(2a) doesn't satisfy, if a = 1 and q=18, it is not divisible by 6^2 (i.e 36)
Hence answer is E
Answer: (E) 6^(2a)
Question: A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/3 chance that engine one will fail. There is a 55% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?
(A)  7/12
(B)  1/4
(C)  1/2
(D)  7/24
(E)  17/24
Rationale: In probability questions the trap answer is just the multiple of the numbers in the question.
i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer
The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer
So lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct.
C
Answer: (C)  1/2
Question: A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is
(A) 2 mph
(B) 2.5 mph
(C) 3 mph
(D) 4 mph
(E) None
Rationale: Solution
Speed downstreams	=(10 + x)mph.
Speed upstreams	=(10 - x)mph.
= 18 kmph.
36/(10-x) - 36/(10+x)	= 90/60
= 72x ×60
= 90(100 - x²)
x²+48x+100= 0.
x= 2mph.
Answer A
Answer: (A) 2 mph
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 22 1/9 kmph
(B) 22 8/2 kmph
(C) 22 1/8 kmph
(D) 22 1/2 kmph
(E) 22 1/4 kmph
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 21/2 kmph
Answer:D
Answer: (D) 22 1/2 kmph
Question: Find the value of 10 + 2 â€¢ (8 â€“ 3)
(A) 25
(B) 13
(C) 17
(D) 20
(E) 15
Rationale: 10 + 2 â€¢ (8 â€“ 3)
= 10 + 2 (5)
= 10 + 2 *5
= 10 + 10
= 20
correct answer D
Answer: (D) 20
Question: A person crosses a 300 m long street in 4 minutes. What is his speed in km per hour?
(A) 1.6
(B) 4.5
(C) 8.2
(D) 6.5
(E) 2.9
Rationale: distance = 300 meter
time = 4 minutes = 4 x 60 seconds = 240 seconds
Speed = distance/time=300/240=1.25 m/s=1.25Ã—18/5 km/hr=4.5 km/hr
Answer :B
Answer: (B) 4.5
Question: At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Raja,Kamal, Baskar, and Dinesh get lockers with the numbers 100, 400, 150, and 420, respectively, who is the most popular student?
(A) Baskar
(B) They have equal popularity
(C) Dinesh
(D) Raja
(E) Kamal
Rationale: Distinct prime factors of 100 (Raja) : 2,5
Distinct prime factors of 400 (Kamal): 2 and 5.
Distinct prime factors of 150 (Baskar): 2,3, and 5
Distinct prime factors of 420 (Dinesh): 2,3,5 and 7.
So most popular student - Dinesh
Answer C
Answer: (C) Dinesh
Question: The radius of a wheel is 25.4 cm. What is the distance covered by the wheel in making 500 resolutions?
(A) 724 m
(B) 798.3 m
(C) 287 m
(D) 278 m
(E) 927 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 25.4 = 79829 cm
= 798.3 m
Answer:B
Answer: (B) 798.3 m
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are?
(A) 6Rs
(B) 2Rs
(C) 4Rs
(D) 9Rs
(E) 3Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 90 Rs.
5M + 5M + 5M ----- 90 Rs.
15M ------ 90 Rs. => 1M = 6Rs.
Answer: A
Answer: (A) 6Rs
Question: Two brothers took the exam, the higher score is X and the lower one is Y. If the difference between the two scores is equal to their average, what is the value of Y/X ?
(A) 3
(B) 2.
(C) 1/2.
(D) 1/3.
(E) There isn't enough data to answer the question
Rationale: X-Y = (X+Y)/2
2 X - 2 Y = X + Y
X = 3 Y
Y/X = 1/3
D is the answer.
Answer: (D) 1/3.
Question: The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?
(A) 10 and 50
(B) 12 and 18
(C) 24 and 64
(D) 21 and 63
(E) 22 and 44
Rationale: 64 has only the prime 2 (64=2^6) in its prime factorization, so it can not have a PAIR of distinct prime divisors in common with ANY of the numbers.
The answer is C.
Answer: (C) 24 and 64
Question: Rahul went to a shop and bought things worth Rs. 28, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) Rs 15
(B) Rs 12.10
(C) Rs 22.70
(D) Rs 26.80
(E) None of these
Rationale: Explanation :
Let the cost of the tax items = x
Given that tax rate = 6%
Cost of tax items, x*(6/100) = 30/100
x = 5 rs
Now non taxable item = total cost - cost for taxable item - tax
= 28 - 5 - 0.30
=22.70
Answer : C
Answer: (C) Rs 22.70
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
(A) 16 : 5
(B) 14 : 5
(C) 16 : 7
(D) 19 : 5
(E) None of these
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
ANSWER:D
Answer: (D) 19 : 5
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of three rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after ___ minutes?
(A) 11 min
(B) 12 min
(C) 10 min
(D) 15 min
(E) 30 min
Rationale: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B = 3 - 1 =2 rounds per hour.
Time taken to complete one round at this speed = 1/2 hr = 30 min.
E
Answer: (E) 30 min
Question: 0, 1, 5, 14, 30, ____
(A) 25
(B) 35
(C) 45
(D) 65
(E) 55
Rationale: 0,1,5, 14, 30,.....
0+1*1=1
1+2*2=5
5+3*3=14
14+4*4=30
So 30+5*5=55
ANSWER:E
Answer: (E) 55
Question: What is the least number of digits (including repetitions) needed to express 10^300 in decimal notation?
(A) a) 4
(B) b) 100
(C) c) 301
(D) d) 1000
(E) e) 1001
Rationale: 10^n is a decimal number with a 1 followed by n zeros.
So 10^300 will include 300 0's + 1 digit for 1 = 301
So the answer is C.
Answer: (C) c) 301
Question: A train 120 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.
(A) 67 kmph
(B) 50 kmph
(C) 55 kmph
(D) 60 kmph
(E) 70 kmph
Rationale: Explanation:
Let the speed of the train be x kmph.
Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.
Therefore 120/((x+5)×5/18)=6 <=> 30 (x + 5) = 2160 <=> x = 67
Speed of the train is 67 kmph.
Answer: Option A
Answer: (A) 67 kmph
Question: A boat can move upstream at 25 kmph and downstream at 31 kmph, then the speed of the current is?
(A) 3
(B) 6
(C) 7
(D) 54
(E) 8
Rationale: US = 25
DS = 31
M = (31 - 25)/2 = 3.Answer:A
Answer: (A) 3
Question: 9 - 3 ÷ 1/3 + 1 = ?
(A) 1
(B) 3
(C) 6
(D) 9
(E) 12
Rationale: 9 - 3 1/3 + 1
=9-3÷1/3+1
=9-(3X3) +1
=9-9+1
=1
CORRECT ANSWER : A
Answer: (A) 1
Question: In the last set of tests, a student scored marks in each of 5 subjects in the ratio 4:5:6:7:8 and got an overall average score of 72%. If a mark of 50% in a subject is a pass and the maximum marks of each subject is the same, how many subjects did the student pass?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The tests scores are 4k, 5k, 6k, 7k, and 8k.
The sum of the test scores is 30k.
The average test score is 30k/5 = 66. Then k = 11.
The test scores are 44, 55, 66, 77, and 88.
The student passed 4 subjects.
The answer is D.
Answer: (D) 4
Question: A basket contains 7 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
(A) 1/5
(B) 2/7
(C) 2/9
(D) 3/5
(E) 4/11
Rationale: The total number of ways to choose 2 apples is 7C2 = 21
The number of ways that include the spoiled apple is 6C1 = 6
P(the spoiled apple is included) = 6/21 = 2/7
The answer is B.
Answer: (B) 2/7
Question: Find the number of elements in the power set of {1,2}
(A) 4
(B) 0
(C) 2
(D) 3
(E) 5
Rationale: Power set is the set of subsets of {1,2}
That is { {1,2}, {1}, {2}, f}
ANSWER:A
Answer: (A) 4
Question: A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 8 is
(A) 189
(B) 197
(C) 221
(D) 227
(E) 230
Rationale: In that case, the Sophie prime numbers greater than 8 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9
Product would be 1 x 3 x 7x9 =189 Answer should be A.
Answer: (A) 189
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 28 cm2
(B) 27 cm2
(C) 29 cm2
(D) 25 cm2
(E) 35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2
= 35 cm2
Answer: E
Answer: (E) 35 cm2
Question: A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 19 smaller photos. The couple has 5 large photos they could use for those three slots, and 21 smaller photos they could use for those 19 slots. Given these choices, how many different possible albums could they create?
(A) 2,100
(B) 4,200
(C) 5,040
(D) 20,520
(E) 84,000
Rationale: MAGOOSHOFFICIAL SOLUTION:
For the large photos, we need 5C3, which we calculated in the article:
5C3 = 10
For the smaller photos, we need 21C19, which by symmetry must equal 21C2, and we have a formula for that. In fact, in the article above, we already calculated that 21C2 = 210.
Now, by the FCP, we just multiply these: total number of possible albums = 10*210 = 2100.
Answer = A
Answer: (A) 2,100
Question: Two cars start from the same places in opposite directions. One is going towards north at 60 kmph and the other is going towards south 40kmph. What time will they take to be 100km apart?
(A) 1hr
(B) 2hrs
(C) 3hrs
(D) 4hrs
(E) 5hrs
Rationale: To be (60+40) km apart, they take 1 hour
To be 100 km apart, they take 1/100 *100 = 1 hr
Answer is A
Answer: (A) 1hr
Question: Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team Z, but each box of Team A’s has 60% fewer booklets than each box of Team Z’s. Which of the following could be the total number of booklets distributed by the two groups?
(A) 2,000
(B) 3,200
(C) 4,100
(D) 4,800
(E) 4,900
Rationale: Let x be the no of booklets in each box that team distributes. So, Team A has 60% fewer - 0.4x.
Let y be the no. of boxes distributed by team Z. So, Team A distributes 60% more - 1.6y
Total booklets distributed by team A = xy
Total booklets distributed by team Z=0.64xy
Total booklets distributed = xy+0.64xy=1.64xy
As no. of booklets can only be integer, plugging the answer choice equal to 1.64xy should give an integer.
Choice A - 1.64xy=2000; xy=2000/1.64 = doesn't provide an integer value.
Similarly all answer choices, except choice C, fail to provide an integer value.
Choice C = 4100/1.64= 2500 and is the correct answer.
Answer: (C) 4,100
Question: Which of the following can be expressed as a terminating decimal?
(A) 1/25 + 1/35
(B) 1/225 + 1/1,250
(C) 1/11,000 + 1/13,000
(D) 1/75 + 1/35
(E) 1/125 + 1/8
Rationale: In such questions, it is always easier to find an answer instead of eliminating choices. Let us start with the simplest ones first.
A. 1/25 + 1/35 = 12/175 = 12/25*1/7
1/7 does is not a terminating decimal.
E. 1/125 + 1/8 = 8 + 125/ 1000 = 133/1000
This is a terminating decimal and our answer.
Correct Option: E
Answer: (E) 1/125 + 1/8
Question: The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is
(A) 87
(B) 95
(C) 99
(D) 100
(E) 103
Rationale: If the value of all other except the largest is 55..
Largest will be 60*10-55*9=600-495=105..
However the top 5 are distinct and the smallest of these can be 55, so remaining THREE will be 1,2,&3 more so total combined value will be 1+2+3 or 6 more..
Therefore the largest will be 6 less than max possible..... 105-6=99
ANSWER:C
Answer: (C) 99
Question: Oranges are bought at 7 for Rs.3. At what rate per hundred must they be sold to gain 33%?
(A) 57
(B) 58
(C) 59
(D) 54
(E) 55
Rationale: 7 oranges bought for rs 3
1 orange cost =3/7
therefore for 100 oranges =100*(3/7)
gain =33%
300/7+(33/100)*300/7=rate per hundred he want to sell
ans :57
ANSWER:A
Answer: (A) 57
Question: The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 10%. if in july , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ?
(A) 45
(B) 40
(C) 35
(D) 47.61
(E) 30
Rationale: Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.2x
Price of coffee in July = 0.9x .
In July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50
1.2x(1/2) + 0.9x(1/2) = 50
=> x =47.61
D
Answer: (D) 47.61
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) 1/126
(B) 1/122
(C) 1/129
(D) 1/136
(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: The average of 12 result is 55. Average of the first 6 of them is 42 and that of the last 6 is 48. Find the 8th result?
(A) 35
(B) 564
(C) 526
(D) 48
(E) 50
Rationale: Sum of all the 12 results = 12 * 55 = 660
Sum of the first 6 of them = 6 * 42 = 252
Sum of the last 6 of them = 6 * 48 = 288
So, the 8th number = 600 + 252 - 288= 564.
B
Answer: (B) 564
Question: After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Explanation:
i) Let the ages of the five members at present be a, b, c, d & e years.
And the age of the new member be f years.
ii) So the new average of five members' age = (a + b + c + d + f)/5 ------- (1)
iii) Their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) & (e-3) years
So their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2)
==> a + b + c + d + e = 5x + 15
==> a + b + c + d = 5x + 15 - e ------ (3)
iv) Substituting this value of a + b + c + d = 5x + 15 - e in (1) above,
The new average is: (5x + 15 - e + f)/5
Equating this to the average age of x years, 3 yrs, ago as in (2) above,
(5x + 15 - e + f)/5 = x
==> (5x + 15 - e + f) = 5x
Solving e - f = 15 years.
Thus the difference of ages between replaced and new member = 15 years. Answer: D
Answer: (D) 15
Question: If x = a!, which of these following values of a is the least possible value (in this list) for which the last 8 digits of the integer x will all be zero?
(A) 21
(B) 29
(C) 37
(D) 41
(E) 80
Rationale: 2*5 will give one 0 at the end. We need 2^8*5^8 to get 8 zeroes at the end.
There are many 2's, so we need to find the first 8 appearances of 5.
These multiples of 5 are: 5, 10, 15, 20, 5*5, 30, 35...which gives us 8.
To have at least 8 zeroes at the end, a => 35.
The answer is C.
Answer: (C) 37
Question: Sreedhar and Sravan together can do a work in 25 days. With the help of Pavan, they completed the work in 8 days and earned Rs. 225. What is the share of Sravan, if Sreedhar alone can do the work in 75 days?
(A) $42
(B) $46
(C) $48
(D) $49
(E) $41
Rationale: C
$48
Sravan's one day's work = 1/25 - 1/75 = 2/75
Sravan worked for 8 days. So, his 8 days work = 8 * 2/75 = 16/75
Sravan completed 16/75th of total work.
So, his share is 16/75 * 225 = $48.
Answer: (C) $48
Question: If logx y =100 and log2 x =10, then the values of y is
(A) 2(10)
(B) 2 (100)
(C) 2 (1000)
(D) 2 (10000)
(E) None of these
Rationale: Solution
log2 x	= 10
x= 210
logx y	= 100
y= x100
=(210)100
y‹=›2(1000)
Answer D
Answer: (D) 2 (10000)
Question: P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?
(A) 9 days
(B) 9 (3/5) days
(C) 11 1/5 days
(D) 13 days
(E) 13 1/7
Rationale: Amount of work P can do in 1 day = 1/16
Amount of work Q can do in 1 day = 1/12
Amount of work P, Q and R can together do in 1 day = 1/4
Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48
=> Hence R can do the job on 48/5 days = 9 (3/5) days
B)
Answer: (B) 9 (3/5) days
Question: In how many ways can a committee consisting of 4 men and 5 women be formed from a group of 7 men and 7 women?
(A) 7C4 7C5
(B) 4C7 5C7
(C) 7C5 9C4
(D) 9C4 7C5
(E) NONE
Rationale: Group consisting of 7 men and 7 women
4 men can be selected from 7 men in 7C4 ways
5 women can be selected from 7 women in 7C5 ways
Therefore, Total number of ways= 7C4 7C5
ANSWER:A
Answer: (A) 7C4 7C5
Question: Each week, Harry is paid x dollars per hour for the first 24 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?
(A) 35
(B) 36
(C) 37
(D) 38
(E) 39
Rationale: 42x=24x+1.5x(H-24)
==> 42=24+1.5(H-24)
==> H-24 = 18/1.5=12=> H = 36
Answer is B
Answer: (B) 36
Question: At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/8 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
(A) 8 greater
(B) 17 fewer
(C) 28 fewer
(D) 36 fewer
(E) 44 fewer
Rationale: Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/8* 480 =60
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 60-68 =-8>>> therfore answer is 8 greater
A
Answer: (A) 8 greater
Question: To produce an annual income of Rs. 800 from a 8% stock at 90, What is the amount of stock needed?
(A) 10000
(B) 11000
(C) 12000
(D) 13000
(E) 14000
Rationale: Since face value is not given, take it as Rs.100.
As it is an 8% stock, income (dividend) per stock = Rs.8
ie, For an income of Rs.8,amount of stock needed = Rs.100
For an income of Rs.800, amount of stock needed = 100×800/8=10000
Answer is A.
Answer: (A) 10000
Question: In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?
(A) 66 kg
(B) 67 kg
(C) 68 kg
(D) 69 kg
(E) None of these
Rationale: Explanation:
Let Arun’s weight by X kg.
According to Arun, 65 < X < 72
According to Arun’s brother, 60 < X < 70.
According to Arun’s mother, X <= 68
The values satisfying all the above conditions are 66, 67 and 68.
Required average = [66+67+68/3]=[201/3]=67kg
Answer B
Answer: (B) 67 kg