mathewhe/aqua_rat huggingface dataset:
Question: In a certain conservative mutual fund, 70 percent of the money is invested in bonds, and of that portion, 40 percent is invested in highly rated corporate bonds. If at least $1.4 million in this fund is invested in highly rated corporate bonds, what is the smallest possible total value for the mutual fund?
(A) $4 million
(B) $5 million
(C) $6 million
(D) $7 million
(E) $8 million
Rationale: Let x be the total money or value of the mutual fund.
Money in bonds=0.7x
Money in highly rated corporate bond= 0.4*0.7x=0.28x
0.28x > 1.4m
x > 1.4m/0.28 ; x > 140m/28 ; x>10 m/2 ;
so x > 5m
Smallest value is $ 5 million
ANSWER:B
Answer: (B) $5 million
Question: Workers at a campaign office have 2500 fliers to send out. If they send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day?
(A) 300
(B) 800
(C) 1500
(D) 1200
(E) 1900
Rationale: (1/5)*2500 = 500
Remaining = 2500-500 = 2000
(1/4) of remaining = (1/4)*2000 = 500
Remaining now = 2000-500 = 1500
Answer: Option C
Answer: (C) 1500
Question: If j < y < -1, which of the following is true?
(A) j/y > jy
(B) y/j > j+y
(C) y/j > jy
(D) y/j < j+y
(E) y/j > j/y
Rationale: Consider :
j= -3
y= -2
then put for every option. U'll get ans B.
Answer: (B) y/j > j+y
Question: 12, 34, 10, 11, 12, 5, 6 ,7, 13, 14, ?, ?
Logically, what two numbers should replace the question marks?
(A) 13 and 11
(B) 15 and 11
(C) 19 and 11
(D) 18 and 11
(E) 17 and 11
Rationale: B
15 and 11
1 + 2 + 3 + 4 = 10, then insert next two numbers 11, 12 and add digits
1 + 1 + 1 + 2 = 5.
Insert next two numbers 6, 7 and add digits 6 + 7 = 13. Insert next two numbers 14, 15 and add digits
1 + 4 + 1 + 5 = 11.
Answer: (B) 15 and 11
Question: If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 91 percent in some time period, which of the following could be the final mass of that element?
(A) 36 grams
(B) 28 grams
(C) 29 grams
(D) 31 grams
(E) 32 grams
Rationale: Let original mass be 100
The final mass of that element will be 9
So whatever option we have it will be divisible by 9
Check for the options the one that doesn't produce non terminating decimal is our answer
A. 36 grams
36/9 = 4
B. 28 grams
28/9 = 3.111.....
C. 29 grams
29/9 = 3.222.......
D. 31 grams
31/9 = 3.444.....
E. 32 grams
32/9 = 3.555..
Answer (A)
Answer: (A) 36 grams
Question: An article was sold after a discount of 20% and therewas a gain of 20%. If the profit madeon it was Rs.6 less thanthe discount offered on it, find its SP?
(A) Rs. 68
(B) Rs. 70
(C) Rs. 72
(D) Rs. 88
(E) Rs. 98
Rationale: Let CP = Rs. 100x
SP = Rs. 120x
MP = 120x/80 * 100 = Rs. 150x
D = Rs. 150x - Rs. 120x = Rs. 30x
D - P = 30x - 20x = Rs. 6, 10x = Rs. 6
120x = 120/10 * 6 = Rs. 72
C
Answer: (C) Rs. 72
Question: It would take one machine 6 hours to complete a large production order and another machine 5 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?
(A) A 11/30
(B) B 11/20
(C) C 30/11
(D) D 9/10
(E) E 4/10
Rationale: The rate of the first machine is 1/6 job per hour;
The rate of the second machine is 1/5 job per hour;
Thus, the combined rate of the machines is 1/6+1/5=11/30 job per hour, which means that it takes 1/(11/30)=30/11 hours both machines to do the job.
Answer: C.
Answer: (C) C 30/11
Question: The number of new words that can be formed by rearranging the letters of the word 'TOO' is?
(A) 1
(B) 5
(C) 11
(D) 4
(E) 2
Rationale: Number of words which can be formed
= 3! - 1 = 6- 1
= 5.
Answer:B
Answer: (B) 5
Question: How many multiples of 2 are there between 10 and 52, 10 and 52 inclusive?
(A) 27
(B) 25
(C) 24
(D) 21
(E) 22
Rationale: 2 multiples are ...10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,...,
the answer is =22
Answer is E
Answer: (E) 22
Question: Find the missing number in the given sequence : 2,4,6,8,10,?,14,?
(A) 11 & 15
(B) 12 & 16
(C) 13 & 15
(D) 12 & 18
(E) 11 & 17
Rationale: 2+2=4
4+2=6
6+2=8
8+2=10
10+2=12
12+2=14
14+2=16
ANSWER:B
Answer: (B) 12 & 16
Question: The sum of how many terms of the series 6 + 12 + 18 + 24 + … is 1800
(A) 16
(B) 22
(C) 24
(D) 18
(E) 26
Rationale: Let the number of terms be N.
Then, according to the formula,
=> 1800 = N/2[2A+(N-1)D] , where A = First-Term, D = Common-Difference.
=> 3600 = N[12 + (N-1)6]
=> 3600 =N[6 + 6N]
=> 6N^2 + 6N - 3600 = 0.
=> 6N^2 + 150N - 144n - 3600 = 0
=> 6N(N + 25)-144(N+25)
=> N = -25, 24
Hence, the number of terms is 24.
ANSWER:B
Answer: (B) 22
Question: A train 800 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 87 Kmph
(B) 97 Kmph
(C) 72 Kmph
(D) 144 Kmph
(E) 120 Kmph
Rationale: Length = Speed * time
Speed = L/T
S = 800/20
S = 40 M/Sec
Speed= 40 *18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 144 Kmph
Answer: D
Answer: (D) 144 Kmph
Question: A train 110 m long is running with a speed of 65 km/hr. In what time will it pass a man who is running at 7 km/hr in the direction opposite to that in which the train is going?
(A) 5
(B) 6
(C) 4
(D) 8.2
(E) 5.5
Rationale: Speed of train relative to man =65+7= 72 km/hr.
= 72 * 5/18 = 20 m/sec.
Time taken to pass the men = 110 * 1/20 = 5.5 sec.
Answer: Option E
Answer: (E) 5.5
Question: The price of a Bicycle was increased by 50 percent. The new price was then increased by 30 percent. A single increase of what percent is equivalent to these two successive increases?
(A) 80%
(B) 75%
(C) 95%
(D) 85%
(E) 70%
Rationale: consider base price - $100
25% increase = 1.50*100 = $150
another 40% increase on new price = 1.3* 150 = $195
so final price of radio - $195
therefore a 95% increase
correct option - C
Answer: (C) 95%
Question: How long does a train 110 m long running at a speed of 72 kmph take to cross a bridge 132 m in length?
(A) 9.8 sec
(B) 12.1 sec
(C) 12.42 sec
(D) 14.3 sec
(E) 24.3 sec
Rationale: 72 km/hr= 72*5/18 m/sec
= 20 m/sec
time= D/S = 110+132/20
= 242/20
= 12.1 sec
ANSWER:B
Answer: (B) 12.1 sec
Question: On the independence day, bananas were be equally distributed among the children in a school so that each child would get two bananas. On the particular day 420 children were absent and as a result each child got two extra bananas. Find the actual number of children in the school?
(A) 600
(B) 620
(C) 500
(D) 520
(E) 840
Rationale: Let the number of children in the school be x. Since each child gets 2 bananas, total number of bananas = 2x.
2x/(x - 420) = 2 + 2(extra)
=> 2x - 840 = x => x = 840.
ANSWER:E
Answer: (E) 840
Question: A man is 22 years older than his son. In two years, his age will be twice the age of his son. The present age of this son is
(A) 21 years
(B) 22 years
(C) 20 years
(D) 24 years
(E) 26 years
Rationale: Explanation:
Let's Son age is x, then Father age is x+22.
=> 2(x+2) = (x+22+2)
=> 2x+4 = x+24
=> x = 20 years
Option C
Answer: (C) 20 years
Question: If U = V/W, -1 < W < 0 and 4 < V, which of the following is correct?
(A) U > 4.
(B) 0 < U <4.
(C) -4 < U < 0.
(D) U < -4.
(E) U < -20.
Rationale: V is +veW is -ve
Eliminate AB
For min. value max. numerator and minimize dinominator
take V=4.1U=-0.9
U=4.1/-0.9
U<-4
Ans D
Answer: (D) U < -4.
Question: A train 100 meters long completely crosses a 300 meters long bridge in 45 seconds. What is the speed of the train is?
(A) 32 kmph
(B) 33 kmph
(C) 34 kmph
(D) 35 kmph
(E) 36 kmph
Rationale: A
32 kmph
S = (100 + 300)/45 = 400/45 * 18/5 = 32
Answer: (A) 32 kmph
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 4 children take to complete the work?
(A) 4
(B) 5
(C) 7
(D) 8
(E) 10
Rationale: 1 women's 1 day work = 1/70
1 child's 1 day work = 1/140
(5 women + 4 children)'s 1 day work
= (5/10 + 4/140) = 1/10
5 women and 4 children will complete the work in 10 days.
E
Answer: (E) 10
Question: Ayesha's father was30 years of age when she was born while her mother was 26 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
(A) 2 years
(B) 4 years
(C) 6 years
(D) 8 years
(E) 9 years
Rationale: Mother's age when Ayesha's brother was born = 26 years.
Father's age when Ayesha's brother was born = (30 + 4) years = 34 years.
Required difference = (34 - 26) years = 8 years. Answer: Option D
Answer: (D) 8 years
Question: Set T includes elements {8, 2, 11, x, 3, y} and has a mean of 7 and a median of 5.5. If x < y, then which of the following is the maximum possible value of x?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: First, reach to the point of getting the equation T : x + y = 18
It should take about 20 seconds.
Then Substitute the answer choices into the equation.
I don't know what the answer choices in this case are.
But I'm sure, you would be able to eliminate at least 2 or 3 answer choices. (about 10 seconds).
Say you are left with 2 answer choices. (If you are short on time, guess One of the two and you'll have a 50% probability of getting it right.)
The Median (of 6 numbers) = 5.5. See if the AVERAGE of any two numbers among (2,3,8,11) results in the median. In this case, it does for 3 and 8. (15 seconds).
Once you know that the numbers that contribute towards Median are 3 and 8, and not x or y, then given x < y, x≤3. (about 10 seconds)=D
Answer: (D) 3
Question: If x ¤ y = (x + y)^2 - (x - y)^2. Then √3 ¤ √3 =
(A) 0
(B) 5
(C) 12
(D) 15
(E) 20
Rationale: X = √3 and Y also =√3
Applying the function (√3+√3)^2 - (√3-√3)^2 = (2√3)^2 - 0 = 4 x 3 = 12.
Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√3 and y = √3 you get the answer 12.
Answer C
Answer: (C) 12
Question: A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $800. If each member of the club paid at least $53, then what is the greatest possible number of members in the club?
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: 800/53=15 plus remainder.
The answer is A.
Answer: (A) 15
Question: A rectangular field 30 m long and 20 m broad. How much deep it should be dug so that from the earth taken out, a platform can be formed which is 8 m long, 5.5 m broad and 1.5 m high where as the earth taken out is increase by 10/5?
(A) 12 cm
(B) 10 cm
(C) 18 cm
(D) 24 cm
(E) 26 cm
Rationale: 30 * 20 * x = (8 * 5.5 * 1.5)/2
ANSWER:B
Answer: (B) 10 cm
Question: What number is 60 more than two-fourth of itself?
(A) 180
(B) 225
(C) 288
(D) 324
(E) 336
Rationale: 2/4x+60= x
That means 60=2/4x
x= 60*3= 180
A is the answer
Answer: (A) 180
Question: The triplicate ratio of 1:6 is?
(A) 1:7
(B) 1:8
(C) 1:3
(D) 1:1
(E) 1:216
Rationale: 1^3: 6^3 = 1:216
Answer: E
Answer: (E) 1:216
Question: One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
(A) Rs. 30,000
(B) Rs. 50,000
(C) Rs. 60,000
(D) Rs. 90,000
(E) None
Rationale: EXPLANATION
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 – x) respectively. Then,
1/3x=1/2(150000-x)
=> x/3 + x/2 = 75000
=> 5x/6 = 75000
=> x= 75000 x 6 /5= 90000
Savings in Public Provident Fund = Rs. (150000 – 90000) = Rs. 60000
Answer C
Answer: (C) Rs. 60,000
Question: In Orange County one fourth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?
(A) 56.
(B) 42.
(C) 85.
(D) 145.
(E) 252.
Rationale: The number must be an integer and multiple of both 4 and 7.
Only option A fulfill this condition and hence is the answer.
Answer: (A) 56.
Question: Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?
(A) 18
(B) 77
(C) 66
(D) 55
(E) 31
Rationale: S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
Answer: A
Answer: (A) 18
Question: A man sitting in a train which is travelling at 15 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed?
(A) 52 kmph.
(B) 62 kmph.
(C) 97 kmph.
(D) 80 kmph.
(E) None
Rationale: Solution
Relative Speed	= (280 / 9)m/sec
= (280/9 x 18/5)
= 112 kmph.
Speed of the train	= (112 - 15)kmph
= 97 kmph.
Answer C
Answer: (C) 97 kmph.
Question: If (2)^n=(1/2)^2, what is the value of n?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: (2)^n = (1/2)^2
= (2)^-2
n = -2 (Answer = A)
Answer: (A) -2
Question: If a is an odd integer and b is an even integer, which of the following CANNOT be true?
(A) a + b is an odd integer.
(B) a is a factor of b.
(C) b is a factor of a.
(D) a^b is an odd integer.
(E) b^a is an even integer.
Rationale: a = Odd
b = Even
Checking Options:
A. a + b = odd+even = odd Hence It can be True
B. a is a factor of b. if a=3 and b=6 a may be factor of b Hence It can be True
C. b is a factor of a. and Even Number can NEVER be a factor of an ODD number Hence False hence CORRECT OPTION
D. a^b is an odd integer.
E. b^a is an even integer
Answer: Option C
Answer: (C) b is a factor of a.
Question: A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
(A) 20,000 square meters
(B) 10,000 square meters
(C) 30,000 square meters
(D) 40,000 square meters
(E) 50,000 square meters
Rationale: Let us first find the distance d jogged
distance = rate * time = (12 km / hr)* 30 minutes
= (12 km/hr)* 0.5 hr = 6 km
The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to
6 km / 10 = 0.6 km = 0.6* 1000 meters = 600 meters
Let L and W be the length and width of the field. The length is twice the width. Hence
L = 2 W
The perimeter is 600 meters and is given by
2 (L + W) = 600
Substitute L by 2 W
2 (2 W + W) = 600
Simplify and solve for W
4 W + 2 W = 600
6 W = 600
W = 100
Find L
L = 2 W = 200
Find the area A of the rectangle
A = L * W = 200 * 100 = 20,000 square meters correct answer A
Answer: (A) 20,000 square meters
Question: Integer X represents the product of all integers between 1 to 26 (inclusive). The smallest prime factor of (x+1) must be
(A) Between 1 to 10
(B) Between 11 to 15
(C) Between 15 to 20
(D) Between 20 to 26
(E) Greater than 26
Rationale: Answer = E = Greater than 26
This problem is asking smallest prime factor of (26!+1)
25! already have there prime factors 2,3,5,7,11,13.......... so on upto 23 (1 cannot be considered prime factor)
Just adding 1 to 26! will remove all the factors stated above;
so the smallest possible prime factor has to be greater than 26
Answer = E
Answer: (E) Greater than 26
Question: If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
(A) 27 2/23 %
(B) 33 1/3 %
(C) 30%
(D) 19%
(E) 18%
Rationale: Explanation:
100
150
------
150-------50
100-------? => 331/3%
ANSWER IS B
Answer: (B) 33 1/3 %
Question: A car travels first half distance between two places with a speed of 40 km/hr and rest of the half distance with a speed of 60 km/hr. The average speed of the car is:
(A) 48 km/hr
(B) 42km/hr
(C) 40 km/hr
(D) 35 km/hr
(E) None of these
Rationale: Explanation :
Let the total distance covered be S km.
The total time taken is:-
=>S/(2×40)+S/(2×60)=5S/240.
Hence, the average speed = S×240/5S.
=>48 km/hr.
Answer : A
Answer: (A) 48 km/hr
Question: If the time is currently 1:30 pm, what time will it be in exactly 645 hours?
(A) 9:30 am
(B) 10:30 am
(C) 11:30 am
(D) 12:30 pm
(E) 1:30 pm
Rationale: 645 = 26(24) + 21/24
The time will be 21 hours later than 1:30 pm which is 10:30 am.
The answer is B.
Answer: (B) 10:30 am
Question: Which of the following is satisfied with |x-4|+|x-3|<6?
(A) 1<x<5
(B) 2<x<5
(C) 0.5<x<6.5
(D) 0.5<x<4
(E) 3<x<4
Rationale: --> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<6 -> |x-4+x-3|<6 -> |2x-7|<6, -6<2x-7<6, 1<2x<13, 1/2<x<13/2 ->0.5<x<6.5
Therefore, the answer is C.
Answer: (C) 0.5<x<6.5
Question: A person spends 40% of his salary on food, 25% on house rent, 15% on entertainment and 5% on conveyance. If his savings at the end of the month is Rs. 1200, then his salary per month in rupees is:
(A) 4000
(B) 6000
(C) 8000
(D) 10000
(E) None of these
Rationale: Total expenditure = 40 + 25 + 15 + 5 = 85%
Saving = (100 - 85) = 15%
15/100 × Salary = 1200, Salary = 8000 Rs.
Answer:C.
Answer: (C) 8000
Question: The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum?
(A) Rs.17029
(B) Rs.17028
(C) Rs.17000
(D) Rs.17008
(E) Rs.17067
Rationale: The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year
So rate of the interest = (100 * 1530)/ (5100 * 1)
= 30% p.a.
So P = (100 * 10200)/ (30 * 2)
= Rs.17000
Answer:C
Answer: (C) Rs.17000
Question: How many different ways can you select a pilot and a co pilot if you have 40 people to choose from?
(A)  199
(B)  200
(C)  398
(D)  4950
(E)  1560
Rationale: You are not just choosing two from 40. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.
So the answer is in a sense (40C2) x 2 = 1560=E
Answer: (E)  1560
Question: In a garden, there are 10 rows and 16 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is
(A) 32 m
(B) 22 m
(C) 24 m
(D) 26 m
(E) 28 m
Rationale: Explanation:
Each row contains 16 plants.
There are 15 gapes between the two corner trees (15 x 2) metres and 1 metre on each side is left.
Therefore Length = (30 + 2) m = 32 m.
Answer: A
Answer: (A) 32 m
Question: Goldenrod and No Hope are in a horse race with 6 contestants. How many different Y arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
(A)  720
(B)  360
(C)  120
(D)  24
(E)  21
Rationale: no hope finishing before goldenrod= 1/2 of the times
therefore the different Y arrangements are 1/2* 6! = 360 = B
Answer: (B)  360
Question: P and Q started a business investing Rs. 85,000 and Rs. 25,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
(A) 17:6
(B) 17:0
(C) 17:4
(D) 17:2
(E) 17:5
Rationale: P:Q = 85000 : 25000
= 17:5.
Answer: E
Answer: (E) 17:5
Question: Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 25 percent in profit, and Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?
(A) 93%
(B) 97%
(C) 100%
(D) 107%
(E) 120%
Rationale: Assume Arthur had $100 and gave each of his children $20, then two years
A=20(1+0.5)(1+0.1)=33
B=20(1+0.5)(1+0.1)=33
C=20(1+0.5)(1-0.6)=12
D=20(1-0.4)(1+0.25)=33
E=0
Arthur's current money=A+B+C+D+E=93
ANSWER:A
Answer: (A) 93%
Question: A cube of edge 15 cm is imersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20 cm * 15 cm, find the rise in waer level.
(A) 11.25 cm.
(B) 12.25 cm
(C) 13.25 cm
(D) 14.25 cm
(E) None of these
Rationale: Sol. Increase in volume = Volume of the cube = (15 * 15 * 15) cm³.
∴ Rise in water level = [Volume/Area] = [15 * 15 * 15/20 * 15] cm = 11.25 cm.
Answer A
Answer: (A) 11.25 cm.
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 63 km/hr. What is the length of the platform?
(A) 240
(B) 288
(C) 277
(D) 226
(E) 280
Rationale: Speed = 63 * 5/18 = 17.5 m/sec.
Length of the train = 17.5 * 20 = 350 m.
Let the length of the platform be x m . Then,
(x + 350)/36 = 17.5 => x = 280 m.
Answer: E
Answer: (E) 280
Question: An accurate clock shows 8 o'clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 9 o'clock in the morning?
(A) 120°
(B) 60°
(C) 30°
(D) 90°
(E) 150°
Rationale: The angle traced by the hour hand in 12 hours is 360°, which is 30° per hour.
In 1 hour, the angle traced by the hour hand is 30°
The answer is C.
Answer: (C) 30°
Question: A train moves past a post and a platform 264 metre long in 8 seconds and 20 seconds respectively. What is the speed of the train?
(A) 79.2 km/hr
(B) 69 km/hr
(C) 74 km/hr
(D) 61 km/hr
(E) 55 km/hr
Rationale: lenghth and speed of the train x m and v m
train crosses the post in 8 sec
x=8v---1)
train crosses the platform in 20 sec
x+264=20v
(2)-(1)+>12v=264
v=264/12=22m/s
22 * 18/5 km/hr = 79.2km/hr
ANSWER A
Answer: (A) 79.2 km/hr
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
(A) 270 m
(B) 278 m
(C) 290 m
(D) 270 m
(E) 220 m
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 27 * 10 = 270 m.
The length of the faster train = 270 m.Answer: A
Answer: (A) 270 m
Question: In a certain match all the teams were to play with each other. If there are 10 teams, how many matches will have to be played?
(A) 40
(B) 45
(C) 60
(D) 90
(E) None of the above
Rationale: 10c2
=45
ANSWER:B
Answer: (B) 45
Question: 5220/? * 15 = 2175
(A) 34
(B) 36
(C) 33
(D) 42
(E) 24
Rationale: B
(5220/?) * 15 = 2175
? = (5220 * 15)/2175
=> ? = 36
Answer: (B) 36
Question: If x - 3 > 2 and x - 3 < 7, the value of x must be between which of the following pairs of numbers?
(A)  -3 and 10
(B)  -3 and 4
(C)  2 and 7
(D)  3 and 4
(E)  5 and 10
Rationale: Let’s isolate x in each inequality.
x - 3 > 2
x > 5
Next we simplify x – 3 < 7.
x – 3 < 7
x < 10
We know that x is greater than 5 and less than 10.
The answer is E.
Answer: (E)  5 and 10
Question: Two numbers N and 16 have LCM = 48 and GCF = 4. Find N.
(A) 35
(B) 56
(C) 76
(D) 87
(E) 12
Rationale: The product of two integers is equal to the product of their LCM and GCF. Hence.
16* N = 48 * 4
N = 48*4 / 16 = 12 correct answer E
Answer: (E) 12
Question: A man can row with a speed of 30 kmph in still water. If the stream flows at 10 kmph, then the speed in downstream is?
(A) 40
(B) 27
(C) 20
(D) 99
(E) 2
Rationale: M = 30
S = 10
DS = 30 + 10 = 40
Answer:A
Answer: (A) 40
Question: A trader purchases several articles at the rate of 13 for Rs. 10 and sells them at the rate of 10 for Rs. 13. What is his gain/loss?
(A) 68 %
(B) 69 %
(C) 66 %
(D) 63 %
(E) 29 %
Rationale: Explanation:
We have, C. P of 13 articles = Rs. 10
& S. P of 10 articles = Rs. 13
S. P of 13 articles = ?
= (13 * 13) / 10 = 16.9
Gain = [(16.9 – 10)/10] * 100 = 69 %
ANSWER: B
Answer: (B) 69 %
Question: Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 30 kg of fresh grapes?
(A) 3.75 kg
(B) 2.4 kg
(C) 2.5 kg
(D) 10 kg
(E) none of these
Rationale: The weight of non-water in 30 kg of fresh grapes (which is 100-90=10% of whole weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-20=80% of whole weight), so 30âˆ—0.1=xâˆ—0.8--> x=3.75
Answer: A
Answer: (A) 3.75 kg