mathewhe/aqua_rat huggingface dataset:
Question: When tossed, a certain six-sided die has an equal probability of landing on any of the six sides. If the die is tossed 3 times, what is the probability that it will land on the same side each time?
(A) 1/6
(B) 1/12
(C) 1/36
(D) 1/72
(E) 1/216
Rationale: On the first toss, the die will land on one of the sides.
On the second toss, the probability of landing on the same side is 1/6.
On the third toss, the probability of landing on the same side is 1/6.
P(same side three times)=1/6*1/6=1/36.
The answer is C.
Answer: (C) 1/36
Question: In a certain sequence of 10 numbers, each number after the first is 1 more than the previous number. If the first number is −5, how many of the numbers in the sequence are positive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: Non - Negative ( zero to positive infinity )
Solution to the question :
-5,-4,-3,-2,-1,0 , 1,2,3,4
Hence ans is 4 ..option E
Answer: (E) Four
Question: A cube of edge 16cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of vessel are 20cm * 15cm , find the rise in water level?
(A) 6cm
(B) 8.25cm
(C) 13.65cm
(D) 15.12cm
(E) 20.62cm
Rationale: Increase in volume = volume of the cube = 16*16*16 cm^3
Rise in water level = volume / area = 16*16*16/20*15 = 13.65cm
Answer is C
Answer: (C) 13.65cm
Question: Walking at 8KMPH From Point Q to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point Q to Railway station?
(A) A)9KM
(B) B)6.66KM
(C) C)7.25KM
(D) D)12.40KM
(E) E)13KM
Rationale: Since time differences given are in minutes so let's convert speed in Km per minute
8 kmph = 8/60 km per minute = (2/15) km per minute
10 kmph = 10/60 km per minute = (1/6) km per minute
Let, Time of train to depart from station = t minutes
Distance between Point Q and Railway Station = Speed*Time = (2/15)*(t+5)
Distance between Point Q and Railway Station = Speed*Time = (1/6)*(t-5)
i.e. (2/15)*(t+5) = (1/6)*(t-5)
i.e. 12t+60 = 15t - 75
i.e. 3t = 135
i.e. t = 45 minutes
i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km
Answer: Option B
Answer: (B) B)6.66KM
Question: 1/3 +1/2 - 5/6 + 1/5 + 1/4 - 9/20 -5/6=
(A) 0
(B) 2/15
(C) 2/5
(D) 9/20
(E) 5/6
Rationale: We need to determine the result of 1/3 + 1/2 - 5/6 + 1/5 + 1/4 - 9/20
Let’s add the given fractions in two groups. In the group of the first three fractions, notice that1/3 and 1/2 share a common denominator of 6 with 5/6.
1/2 + 1/3 = 3/6 + 2/6 = 5/6
Thus, 5/6 – 5/6 = 0
Looking at the 2nd group of the fractions (1/5, 1/4, and 9/20), notice that1/5 and 1/4 share a common denominator of 20 with 9/20.
1/5 + 1/4 = 4/20 + 5/20 = 9/20
Thus, 9/20 – 9/20 = 0.
Thus, the result of 1/3 + 1/2 – 5/6 + 1/5 + 1/4 – 9/20 is 5/6.
Answer: E
Answer: (E) 5/6
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
(A) 1/2
(B) 1/2
(C) 8/15
(D) 9/20
(E) 9/24
Rationale: Explanation :
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) = n(E)/n(S) = 9/20
Answer : D
Answer: (D) 9/20
Question: A box contains nine bulbs out of which 3 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
(A) 125/167
(B) 125/186
(C) 83/84
(D) 125/186
(E) 125/128
Rationale: Required probability
= 1 - 1/84
= 83/84
Answer: C
Answer: (C) 83/84
Question: If you roll a fair-sided die twice, what is the probability of getting a (3,3 ) double?
(A) 1/2!
(B) 1/4!
(C) 1/3!
(D) 1/5!
(E) 1/6!
Rationale: total no. in two dice (1,1) ,(2,2) .....(6,)
Total number of events= 6*6
Total events of getting same pair(3, 3) = 6
Probability= 6/6*6= 1/6=1/3!
C
Answer: (C) 1/3!
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions
(A) 700
(B) 704
(C) 704
(D) 706
(E) 707
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4 = 70400 cm = 704 m
Answer: Option B
Answer: (B) 704
Question: How many times are the hands of a clock at right angle in a day?
(A) 22
(B) 11
(C) 33
(D) 55
(E) 44
Rationale: In 12 hours, hands of a clock are at right angles 22 times.
In 24 hours, hands of a clock are at right angles 44 times.
Answer is E.
Answer: (E) 44
Question: Howmany three digits odd numbers can be formed using the digits 4,5,6,7,8,9 (repetition of digits not allowed)
(A) 60
(B) 75
(C) 65
(D) 55
(E) 45
Rationale: There are 3 ways of filling the unit place of the number. The remaining ten's and 100's place canbe filled in 5ways and
4 ways respectively. Required number of numbers =3x5x4=60. Ans: A
Answer: (A) 60
Question: If the quantity 6^2+ 6^4 + 6^6 is written as (a + b)(a – b), in which both a and b are integers, which of the following could be the value of b?
(A) 52
(B) 15
(C) 36
(D) 22
(E) 25
Rationale: (a+b)(a-b) = a^2 - b^2
6^2+ 6^4 + 6^6 = 6^2 (1+6^2+6^4)
if the above expression is solved even then every term of the expression will remain a multiple of 6^2 which is out of parenthesis
hence, b must be a multiple of 6^2 i.e. 36
Answer: option C
Answer: (C) 36
Question: What does RBI regulate through Open Market Operation Transactions?
(A) Flow of Foreign Direct Investment
(B) What does RBI regulate through Open Market Operation Transactions?
(C) Borrowing powers of the banks
(D) Liquidity in economy
(E) . Inflation
Rationale: Explanation:
Outright purchase and Repurchase agreement are the two traditional type of OMO's used by RBI.
ANSWER: D
Answer: (D) Liquidity in economy
Question: A company has 12 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?
(A) 475
(B) 480
(C) 485
(D) 490
(E) 495
Rationale: 12C4=495
The answer is E.
Answer: (E) 495
Question: A candidate got 25% of the votes polled and he lost to his rival by 4000 votes. How many votes were cast?
(A) 7500
(B) 2028
(C) 2775
(D) 5496
(E) 8000
Rationale: 25%-----------L
75%-----------W
------------------
50%----------4000
100%---------? => 8000
Answer: E
Answer: (E) 8000
Question: Which of the following correctly lists the data sets in order of least to greatest standard deviation?
I. 12, 13, 15, 12, 14, 14
II. 32, 32, 32, 32, 32, 32
III. 37, 48, 59, 40, 41, 42
(A) I, II, III
(B) I, III, II
(C) II, I, III
(D) II, III, I
(E) III, II, I
Rationale: (D) To answer a question such as this, you DO NOT need to know how to calculate standard deviation. You simply need to understand how to compare standard deviations of different sets. The more spread out the numbers are, the greater the standard deviation will be. Even one or two numbers that are much larger or smaller than the others will cause the standard deviation to rise drastically.
correct order from least to greatest standard deviation is II, I. III
C
Answer: (C) II, I, III
Question: A train 210 metres long is moving at a speed of 25 kmph. It will cross a man coming from the opposite direction at a speed of 2 km per hour in :
(A) 28 sec
(B) 32 sec
(C) 36 sec
(D) 38 sec
(E) 40 sec
Rationale: Relative speed = (25+2) km/hr = 27 km/hr
= (27×5/18) m/sec = 15/2 m/sec.
Time taken by the train to pass the man =(210×2/15) sec=28 sec
ANSWER :A
Answer: (A) 28 sec
Question: A jogger running at 9 km/hr along side a railway track is 150 m ahead of the engine of a 100 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 88
(B) 27
(C) 36
(D) 80
(E) 25
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 150 + 100 = 250 m.
Time taken = 250/10 = 25 sec.
Answer: E
Answer: (E) 25
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) 24:8
Rationale: Explanation:
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: Option D
Answer: (D) 19 : 5
Question: A pipe can fill a cistern in 7 minutes whereas the cistern when fill can be emptied by a leak in 14 minutes. When both pipes are opened, find when the cistern will be full?
(A) 17
(B) 16
(C) 70
(D) 14
(E) 12
Rationale: 1/7 - 1/14 = 1/14
14 minutes
Answer: D
Answer: (D) 14
Question: Due to an increase in 30% in the price of eggs, 3 eggs less are available for Rs. 7.80. Find the present rate of eggs per dozen.
(A) Rs. 9.36
(B) Rs. 10.36
(C) Rs. 11.36
(D) Rs. 12.36
(E) Rs. 14.36
Rationale: Explanation:
Let the original price per egg be Rs x
Then increased price will be,
(130/100)x
=>7.80/x- 7.80/ 130/100x =3
=>x=0.6
Actual price was Rs 0.6,
Present price per dozen will be
Rs.(12*130/100*0.6)=Rs.9.36
(130100x)=>7.80xâˆ’7.80130100x=3=>7.80xâˆ’780130x=3=>390x=234=>x=0.6Actual price was Rs 0.6Present price per dozen will beRs.(12âˆ—130100âˆ—0.6)=Rs.9.36
ANSWER IS A
Answer: (A) Rs. 9.36
Question: If the average (arithmetic mean) of three consecutive integers is 21, then the product of the greatest and least integer is
(A) 443
(B) 442
(C) 440
(D) 444
(E) 441
Rationale: n = smallest number
n+2 = largest number
(n + n + 2)/2 = 21
=> (2n+2)/2 = 21
=> n + 1 = 21
=> n = 20
So Product of n and n+2 = (20)(22)
= 440
Answer - C
Answer: (C) 440
Question: In expressing a length 81.469 km as nearly as possible with three significant digits, find the percentage error?
(A) 0.075%
(B) 0.156%
(C) 0.034%
(D) 0.038%
(E) 0.152%
Rationale: Error = 81.5-81.469 = 0.031
Required percentage = (0.031/81.469)*100 = 0.038%
Answer is D
Answer: (D) 0.038%
Question: In how many ways can the letters of the word BUTTER be arranged in a row so that the vowels appear in alphabetic order?
(A) 380
(B) 420
(C) 360
(D) 400
(E) 320
Rationale: two letters can be arranged in 2! ways.
only one combination EU is required.
6 letters can be arranged in 6! ways.
thus 6!/ 2! * 1 = 360
C
Answer: (C) 360
Question: If there are 4 seats and two students, in how many ways can they be seated?
(A) 12
(B) 6
(C) 8
(D) 16
(E) 10
Rationale: No. of ways of choosing 2 chairs out of 4 chairs on which two students will sit = 4C2 = 6
No. of ways of 2 people sitting on selected chairs = 2!
Total ways of making 2 people sit on 2 of 4 chairs = 4C2*2! = 6*2 = 12
ANSWER:A
Answer: (A) 12
Question: The greatest number that divides 3560 and 3450 leaving remainder 4 and 6 respectively is:
(A) 23
(B) 25
(C) 26
(D) 28
(E) 30
Rationale: explanation:
3560-4=3556 ,3450-6=3444
Highest number that can divide 3556 and 3444 is HCF of numbers
HCF of 3556 and 3444 =28
Answer :D
Answer: (D) 28
Question: If '+' denotes ÷ , '–' denotes ×, ‘×’ denotes – and ‘÷’ denotes +, then
35 + 7 – 5 ¸5 × 6 = ?
(A) 22
(B) 26
(C) 24
(D) 28
(E) 29
Rationale: C
24
35÷ 7 × 5 + 5 – 6
= 5 × 5 + 5 – 6
25 + 5 – 6
30 – 6 = 24
Answer: (C) 24
Question: A train 410 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40 sec
(B) 50 sec
(C) 44 sec
(D) 49 sec
(E) 60 sec
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 410 + 140 = 550 m
Required time = 550 * 2/25 = 44 sec
Answer:C
Answer: (C) 44 sec
Question: The average age of 9 men increases by 4 years when two women are included in place of two men of ages 36 and 32 years. Find the average age of the women?
(A) 78
(B) 26
(C) 52
(D) 54
(E) 56
Rationale: Explanation:
36 + 32 + 9 * 4 = 104/2 = 52
Answer: C
Answer: (C) 52
Question: Excluding stoppages, the speed of a bus is 52 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 7 min
(B) 6 min
(C) 9 min
(D) 8 min
(E) 11 min
Rationale: Due to stoppages, it covers 7 km less.
Time taken to cover 7 km =(7/52)x60 = 8 min
answer : D
Answer: (D) 8 min
Question: A garrison of 1850 men has provisions for 28 days. At the end of 12 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement?
(A) 1850
(B) 2960
(C) 3000
(D) 1110
(E) 1712
Rationale: 1850 ---- 28
1850 ---- 16
x ----- 10
x*10 = 1850*16
x = 2960
1850
-------
1110
Answer: D
Answer: (D) 1110
Question: The Hat Company makes hats of different colors, some plain and some with printing. For a particular order of hats, 2 out of every 3 hats are blue. If 1 out of every 3 blue hats has printing, and there are 200 blue hats with printing in the shipment, how many hats total are there in the shipment?
(A) 200
(B) 900
(C) 1,000
(D) 5,000
(E) 520
Rationale: Proportions: Let H = hats, and Hb = blue hats, and Hbp = blue hats with printing.
200Hbp/xHb = 1Hbp/3Hb
xHb = 600Hb
600Hb/yH = 2Hb/3H
yH = 900H
Answer: B
Answer: (B) 900
Question: Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 30km/hr, then find the area of square field.
(A) 125
(B) 225
(C) 325
(D) 425
(E) None of these
Rationale: Explanation :
D = 30*3/2 = 45 km. So side of square is 22.5km, so area – 506.25km^2
Answer – E
Answer: (E) None of these
Question: A cistern 6m long and 5 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
(A) 49 m2
(B) 50 m2
(C) 53.5 m2
(D) 55 m2
(E) 57.5 m2
Rationale: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (5 x 1.25 + 6 x 1.25) + 6 x 5] m2
= 57.5 m2.
Answer: Option E
Answer: (E) 57.5 m2
Question: A rectangular cube has a volume of 7 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
Choices
(A) 24
(B) 48
(C) 56
(D) 80
(E) 100
Rationale: Lets say the sides of the rectangular cube are x, y and z. Problem states volume is 7.
i.e,
x*y*z = 7 .
If every side is increased twice as before. then new volume is
2x*2y*2z = 8*(x*y*z) = 8*7 = 56.
Answer is C
Answer: (C) 56
Question: If d=1/(2^3*5^9) is expressed as a terminating decimal, how many nonzero digits will d have?
(A) One
(B) Two
(C) Three
(D) Seven
(E) Ten
Rationale: Another way to do it is :
We know x^a*y^a=(X*Y)^a
given = 1/(2^3*5^9)
= Multiply and divide by 2^4
=2^6/(2^3*2^6*5^9)
=2^6/10^9
=> non zero digits are 64 => Ans B
Answer: (B) Two
Question: If the side of a square is increased by 55%, its area is increased by?
(A) 140%
(B) 145%
(C) 150%
(D) 160%
(E) none of these
Rationale: Since Side x Side = Area
Therefore, net% change in area
= ( x + y + xy/100) %
= [55 + 55 + (55 x 55)/100]% or 140.25%
Therefore, area is increased by 140.25%
ANSWER:A
Answer: (A) 140%
Question: The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 15 consecutive integers that start with (m + 2)?
(A) m + 4
(B) n + 6
(C) n + 7
(D) m + 5
(E) n + 4
Rationale: The average of consecutive numbers is the middle number.
Then n = m+2.
The average of 15 consecutive numbers starting from n is n+7.
The answer is C.
Answer: (C) n + 7
Question: A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,055. How much did she invest at 5%?
(A) $500
(B) $600
(C) $700
(D) $900
(E) $950
Rationale: et x be the portion invested at 5% and
Let (1-x) be the rest which is invested at 6%
The question states that the return after 1 year is (1055/1000)-1 = 0.055 = 5.5%
We want to find the dollar amount invested in X
Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)
0.05x+0.06(1-x)= 0.055
(0.05)x +0.06 - (0.06)x = 0.055
-0.01x = -0.005
x= -0.005/-0.01 = 5/10 = 50%
So X = 50% of the 1000 which is 500
ANSWER:A
Answer: (A) $500
Question: What is the perimeter of a square field whose diagonal is 8âˆš2?
(A) 64 m
(B) 32 m
(C) 30 m
(D) 16 m
(E) 18 m
Rationale: Explanation:
aâˆš2=bâˆš2 ->a=8
4a = 32 m
ANSWER IS B
Answer: (B) 32 m
Question: The product of the squares of two positive integers is 1600. How many pairs of positive integers satisfy this condition?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Ans: E - 4 pairs
(xˆ2)(yˆ2) = 1600 [square root both sides]
xy = 40
40 = 1x40, 4x10, 40x1, 10x4, 5x8, 8x5, 20x2, 2x20
Cancel the repeats
This leaves us with exactly 4 options.
Hence, E
Answer: (E) 4
Question: The sum of first five prime numbers is:
(A) 28
(B) 29
(C) 24
(D) 22
(E) 43
Rationale: A
28
Required sum = (2 + 3 + 5 + 7 + 11) = 28.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
Answer: (A) 28
Question: Find the fourth proportional to 5.1, 3.6 and 2.3?
(A) 2.62
(B) 1.22
(C) 3.12
(D) 2.62
(E) 1.62
Rationale: Explanation:
Formula = Fourth propotional = (b × c)/a
A = 5.1 , B = 3.6 and C = 2.3
(3.6 × 2.3)/5.1 = 1.62
Answer: Option E
Answer: (E) 1.62
Question: In a workshop there are 4 kinds of beds, 3 kinds of closets, 3 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
(A) A)168.
(B) B)80.
(C) C)56.
(D) D)48.
(E) E)120.
Rationale: ways to select one shelf = 3
ways to select one bed = 4
ways to select one of the following: a chair or a closet = 7+3 = 10
ways to select all of them together = 3*4*10 = 120
Answer : E
Answer: (E) E)120.
Question: ((1^7m)/(5^7m))((1^18)/(4^18)) = 1/(2(10)^35)
What is m?
(A) 17
(B) 5
(C) 34
(D) 35
(E) 36
Rationale: ((1^7m)/(5^7m))((1^18)/(4^18)) = 1/(2(10)^35)
((1/5)^7m ) * ((1/2)^36) = 1/ (2 * (2*5)^35))
2^36 will cancel out,since 1 can be written as 1^35 ,So (1/5)^7m= (1/5)^35
((1/5)^7m ) * ((1/2)^36) = 1/[(2^36)*(5^35)]
So, m=5
ANswer B
Answer: (B) 5
Question: If b < 2 and 4x - 8b = 0, which of the following must be true?
(A) x > -3
(B) x < 5
(C) x = 4
(D) x < 4
(E) D. x > 3
Rationale: 4x - 8b = 0
Therefore, 4x = 8b
As, b<2
4x < 8(2)
i.e x < 4
Answer : D
Answer: (D) x < 4
Question: David is a trail runner who decides to take a day off work to run up and down a local mountain. He runs uphill at an average speed of 3 miles per hour and returns along the same route at an average speed of 8 miles per hour. Of the following, which is the closest to his average speed, in miles per hour, for the trip up and down the mountain?
(A)  4.3
(B)  5.8
(C)  6.0
(D)  6.3
(E)  6.5
Rationale: to calculate average of 2 speeds a and b when distance is constant
Formula - 2ab/(a+b)
Here David's uphill speed = 3 mph
David's downhill speed = 8 mph
2*3*8/(3+8) = 48/11 = 4.3
Correct answer - A
Answer: (A)  4.3
Question: A boat goes 100 km downstream in 10 hours, and 90 km upstream in 15 hours. The speed of the stream is?
(A) 5km/h
(B) 4km/h
(C) 2km/h
(D) (1/2) km/h
(E) E)None
Rationale: 100 --- 10 DS = 10
? ---- 1
90 ---- 15 US = 6
? ----- 1 S = (10 - 6)/2
= 2 kmph
ANSWER:C
Answer: (C) 2km/h
Question: Rovert traveled a distance of 30 km, covering the first 10 km in x minutes, the next 10 km in y minutes and the last 10 km in z minutes. If he totally took 3y minutes to cover the whole distance, then which of the following cannot be true? Assume x , y and z are different.
(A) z=3x
(B) x=3z
(C) y=2x
(D) x=2y
(E) y=3x
Rationale: Rovert Travelled for x,y and for z min.
Total Time : x + y + z
Which is equal to : 3y
Equating both sides we get
x+y+z = 3y
=> x+z =2y ........ Eqn 1
Looking out at options
D Says x =2y
Using it in Eqn 1
2y + z = 2y
=> Z = 0 mins, Which I guess is not possible.
The Ans isD
Answer: (D) x=2y
Question: (1/2) of a number is 3 more than the (1/6) of the same number?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 5
Rationale: let number is=x;
by question-------
x/2=(x/6)+3
x/2-x/6=3
x=9
ANSWER:D
Answer: (D) 9
Question: One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 20 cm2. Find the lengths of all sides.
(A) 10 and 3
(B) 7 and 10
(C) 11 and 8
(D) 3 and 10
(E) 10 and 10
Rationale: Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 20 cm2 more than the first area. Therefore
A1+20=A2
x(x−3)+20=(x+1)(x−2)
x2−3x+20=x2+x−2x−2
2x=22
x=11. So, the sides of the rectangle are 11 cm and (11−3)=8 cm long.
So answer is C.
Answer: (C) 11 and 8
Question: What will be the remainder when 17^200 is divided by 18 ?
(A) 3
(B) 8
(C) 5
(D) 1
(E) 7
Rationale: When n is even,(x^n-a^n) is completely divisible by (x-a).
(17^200-1^200)is completely divisible by (17+1),
(17^200-1) is completely divisible by 18.
On dividing 17^200 by 18,we get 1 as remainder.
Answer is D
Answer: (D) 1
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 108 grams of water?
(A)  16
(B)  96
(C)  112
(D)  128
(E)  142
Rationale: Solution:
We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 108 grams of water.
2x + 16x = 108
18x = 108
x = 6
Since x is 6, we know that there are 16 x 6 = 96 grams of oxygen in 108 grams of water.
Answer B.
Answer: (B)  96
Question: In a staircase, there ar 10 steps. A child is attempting to climb the staircase. Each time she can either make 1 step or 2 steps. In how many different ways can she climb the staricase?
(A) 23
(B) 277
(C) 18
(D) 178
(E) 181
Rationale: Use fibonnacci series, with starting two terms as 1, 2. So next terms are 3, 5, 8, 13, 21, 34, 55, 89
Answer:B
Answer: (B) 277
Question: If 1.5 cm of a pencil is purple, 0.5 cm of the remaining is black and the remaining 2 cm is blue, what is the total length of the pencil?
(A) 5 cm
(B) 3 cm
(C) 1 cm
(D) 4 cm
(E) 2 cm
Rationale: Purple is 1.5 cmBlack is 0.5 cmBlue is 2 cm1.5+0.5+2=4 cmAnswer is D) 4 cm
Answer: (D) 4 cm
Question: Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes?
(A) 28
(B) 25
(C) 27
(D) 23
(E) 21
Rationale: Let the pipe B be closed after x minutes.
30/16 - x/24 = 1 => x/24 = 30/16 - 1 = 14/16
=> x = 14/16 * 24 = 21.
Answer: E
Answer: (E) 21
Question: A certain sum becomes four times itself at simple interest in eight years. In how many years does it become ten times itself?
(A) 24
(B) 55
(C) 77
(D) 99
(E) 01
Rationale: Let the sum be Rs. x, then it becomes Rs. 4x in eight years Rs. 3x is the interest on x for eight years.
R = (100 * 3x)/(x * 8) = 300/8 %
If the sum becomes ten times itself, then interest is 9x.
The required time period = (100 * 9x)/(x * 300/8) = (100 * 9x * 8)/(x * 300) = 24 years.Answer: A
Answer: (A) 24
Question: The sume of the ages of 5 children born at the intervals of 3 years each is 50 years.What is the age of the youngest child ?
(A) 4 years
(B) 8 years
(C) 10 years
(D) None of these
(E) 11 years
Rationale: Solution
Let the ages of the children be x,(x + 3),(x + 6)(x + 9) and (x + 12) years.
Then,x + (x + 3)+(x + 6)+(x + 9)+(x + 12) =50 ⇔ 5x = 20 ⇔ x =4.
∴ Age of the youngest child =x=4 years. Answer A
Answer: (A) 4 years