MU-NLPC/Calc-aqua_rat huggingface dataset:
The cost of the paint is rs.40.00 per kg. if 1kg of paint covers 20sq.ft, how much will it cost to paint outside of a cube having 10 feet each side
Choose the correct choice from the following choices
A) Rs.1200	B) Rs.672	C) Rs.546	D) Rs.876	E) None of these

Solution: Explanation:   surface area of a cube= 6 x 10^2 = 600s q.ft   quantity of paint required=(600/20)= 
(600/20) = 30
30 kg   cost of painting= 40 x 30 = Rs.1200   Rs.1200nswer: Rs.1200
Answer: A
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?
Answers.
A) 1/6 B) 1/12 C) 1/36 D) 1/72 E) 1/216

Solution: 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 1/36.
Answer: C
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?	Choose the correct choice from the following answers
A) None  B) One  C) Two  D) Three  E) Four

Solution: 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 Four
Answer: E
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?	Choose the most appropriate option:	A) 6cm	B) 8.25cm	C) 13.65cm	D) 15.12cm	E) 20.62cm

Solution: 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 13.65cm
Answer: C
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?
Choose the most appropriate option.
A) A)9KM	B) B)6.66KM	C) C)7.25KM	D) D)12.40KM	E) E)13KM

Solution: 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 6.66KM
Answer: B
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? Choose the correct option.
A) 1/2	B) 1/2	C) 8/15	D) 9/20	E) 9/24

Solution: 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 : 9/20
Answer: D
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. Choose the correct choice from the following answers.
A) 125/167	B) 125/186	C) 83/84	D) 125/186	E) 125/128

Solution: Required probability   = 1 - 1/84   = 83/84   Answer: 83/84
Answer: C
If you roll a fair-sided die twice, what is the probability of getting a (3,3 ) double?  Choose the correct choice from the following answers:
A) 1/2!  B) 1/4!  C) 1/3!  D) 1/5!  E) 1/6!

Solution: 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!   1/3!
Answer: C
The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions	Pick:
A) 700 B) 704 C) 704 D) 706 E) 707

Solution: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.   = 500 * 2 * 22/7 * 22.4= 
500 * 2 * 22/7 * 22.4 = 70_400
70400 cm= 704 m   Answer: Option 704
Answer: B
How many times are the hands of a clock at right angle in a day?	Choose the correct choice from the following answers.
A) 22
B) 11
C) 33
D) 55
E) 44

Solution: 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 44.
Answer: E
Howmany three digits odd numbers can be formed using the digits 4,5,6,7,8,9 (repetition of digits not allowed)	Choices.
A) 60 B) 75 C) 65 D) 55 E) 45

Solution: 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. 60ns: 60
Answer: A
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? Choose the correct answer:  A) 52  B) 15  C) 36  D) 22  E) 25

Solution: (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 36
Answer: C
What does RBI regulate through Open Market Operation Transactions?	Choose one:  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

Solution: Explanation:   Outright purchase and Repurchase agreement are the two traditional type of OMO's used by RBI.   ANSWER: Liquidity in economy
Answer: D
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? Choose the correct choice from the following answers:	A) 475	B) 480	C) 485	D) 490	E) 495

Solution: 12C4=495   The answer is 495.
Answer: E
A candidate got 25% of the votes polled and he lost to his rival by 4000 votes. How many votes were cast?
Options:  A) 7500  B) 2028  C) 2775  D) 5496  E) 8000

Solution: 25%-----------L   75%-----------W   ------------------   50%----------4000   100%---------? => 8000   Answer: 8000
Answer: E
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	Pick
A) I, II, III B) I, III, II C) II, I, III D) II, III, I E) III, II, I

Solution: (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   II, I, III
Answer: C
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 : Choose the most appropriate option:
A) 28 sec
B) 32 sec
C) 36 sec
D) 38 sec
E) 40 sec

Solution: 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   28 secNSWER :28 sec
Answer: A
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? Choose one:
A) 88	B) 27	C) 36	D) 80	E) 25

Solution: Speed of train relative to jogger = 45 - 9= 
45 - 9 = 36
36 km/hr.= 36 * 5/18= 
36 * 5/18 = 10
10 m/sec.   Distance to be covered= 150 + 100= 
150 + 100 = 250
250 m.   Time taken= 250/10= 
250/10 = 25
25 sec.   Answer: 25
Answer: E
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?  Choose the correct choice from the following answers
A) 16 : 5  B) 14 : 5  C) 16 : 7  D) 19 : 5  E) 24:8

Solution: 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= 
19/4 = 19/4 = around 4.75
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 19 : 5
Answer: D
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?	Select:
A) 17
B) 16
C) 70
D) 14
E) 12

Solution: 1/7 - 1/14 = 1/14   14 minutes   Answer: 14
Answer: D
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.  Choose the correct choice from the following.
A) Rs. 9.36
B) Rs. 10.36
C) Rs. 11.36
D) Rs. 12.36
E) Rs. 14.36

Solution: 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   Rs. 9.36ctual 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=0.6Rs. 9.36ctual price was Rs 0.6Present price per dozen will beRs.(12âˆ—130100âˆ—0.6)=Rs.9.36   Rs. 9.36NSWER IS Rs. 9.36
Answer: A
If the average (arithmetic mean) of three consecutive integers is 21, then the product of the greatest and least integer is  Choose the correct answer
A) 443 B) 442 C) 440 D) 444 E) 441

Solution: 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 - 440
Answer: C
In expressing a length 81.469 km as nearly as possible with three significant digits, find the percentage error?
Select the correct option
A) 0.075%	B) 0.156%	C) 0.034%	D) 0.038%	E) 0.152%

Solution: Error = 81.5-81.469= 
81.5-81.469 = 0.031
0.031   Required percentage= (0.031/81.469)*100 = 0.038%   Answer is 0.038%
Answer: D
In how many ways can the letters of the word BUTTER be arranged in a row so that the vowels appear in alphabetic order?
Choices:	A) 380	B) 420	C) 360	D) 400	E) 320

Solution: 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   360
Answer: C
If there are 4 seats and two students, in how many ways can they be seated?  Pick one
A) 12 B) 6 C) 8 D) 16 E) 10

Solution: 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= 
6*2 = 12
12   12NSWER:12
Answer: A
The greatest number that divides 3560 and 3450 leaving remainder 4 and 6 respectively is: Choose the correct choice
A) 23	B) 25	C) 26	D) 28	E) 30

Solution: explanation:   3560-4= 
3560-4 = 3_556
3556 ,3450-6=3444   Highest number that can divide 3556 and 3444 is HCF of numbers   HCF of 3556 and 3444 =28   Answer :28
Answer: D
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? Options.
A) 40 sec	B) 50 sec	C) 44 sec	D) 49 sec	E) 60 sec

Solution: Speed = 45 * 5/18 = 25/2 m/sec   Total distance covered = 410 + 140= 
410 + 140 = 550
550 m   Required time= 550 * 2/25= 
550 * 2/25 = 44
44 sec   Answer:44 sec
Answer: C
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?
Choose the correct option:
A) 78 B) 26 C) 52 D) 54 E) 56

Solution: Explanation:   36 + 32 + 9 * 4= 
36 + 32 + 9 * 4 = 104
104/2= 
104/2 = 52
52   Answer: 52
Answer: C
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?	Choose the correct choice from the following:
A) 7 min
B) 6 min
C) 9 min
D) 8 min
E) 11 min

Solution: Due to stoppages, it covers 7 km less.   Time taken to cover 7 km =(7/52)x60 = 8 min   answer : 8 min
Answer: D
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?
Answers:
A) 1850 B) 2960 C) 3000 D) 1110 E) 1712

Solution: 1850 ---- 28   1850 ---- 16   x ----- 10   x*10 = 1850*16   x = 2960   1850   -------   1110   Answer: 1110
Answer: D
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? Choose the correct choice from the following choices
A) 200  B) 900  C) 1,000  D) 5,000  E) 520

Solution: 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: 900
Answer: B
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.  Choose one.
A) 125  B) 225  C) 325  D) 425  E) None of these

Solution: Explanation :   D = 30*3/2= 
30*3/2 = 45
45 km. So side of square is 22.5km, so area – 506.25km^2   Answer – None of these
Answer: E
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:	Select:
A) 49 m2
B) 50 m2
C) 53.5 m2
D) 55 m2
E) 57.5 m2

Solution: 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 57.5 m2
Answer: E
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 Choose the correct choice from the following answers: A) 24 B) 48 C) 56 D) 80 E) 100

Solution: 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)  2 *2 *2= 
 2 *2 *2 = 8
8*(x*y*z)= 8*7= 
8*7 = 56
56.   Answer is 56
Answer: C
If d=1/(2^3*5^9) is expressed as a terminating decimal, how many nonzero digits will d have?  Pick one
A) One	B) Two	C) Three	D) Seven	E) Ten

Solution: 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 Two
Answer: B
If the side of a square is increased by 55%, its area is increased by?  Select:
A) 140% B) 145% C) 150% D) 160% E) none of these

Solution: Since Side x Side = 140%rea   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%   140%NSWER:140%
Answer: A
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)?
Choices.
A) m + 4  B) n + 6  C) n + 7  D) m + 5  E) n + 4

Solution: 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 n + 7.
Answer: C
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%? Choose the most appropriate option:
A) $500  B) $600  C) $700  D) $900  E) $950

Solution: 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= 
(1055/1000)-1 = 11/200 = around 0.055
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   $500NSWER:$500
Answer: A
What is the perimeter of a square field whose diagonal is 8âˆš2?	Select the correct option: A) 64 m B) 32 m C) 30 m D) 16 m E) 18 m

Solution: Explanation:   aâˆš2=bâˆš2 ->a=8   4a = 32 m   ANSWER IS 32 m
Answer: B
The product of the squares of two positive integers is 1600. How many pairs of positive integers satisfy this condition?  Choices.
A) 0  B) 1  C) 2  D) 3  E) 4

Solution: 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, 4
Answer: E
The sum of first five prime numbers is: Select the correct option.
A) 28 B) 29 C) 24 D) 22 E) 43

Solution: A   28   Required sum = (2 + 3 + 5 + 7 + 11)= 
(2 + 3 + 5 + 7 + 11) = 28
28.   Note: 1 is not a prime number.   Definition: 28 prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
Answer: A
Find the fourth proportional to 5.1, 3.6 and 2.3?	Select the correct option:
A) 2.62
B) 1.22
C) 3.12
D) 2.62
E) 1.62

Solution: 1.62xplanation:   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 1.62
Answer: E
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?  Select the correct option:
A) A)168.  B) B)80.  C) C)56.  D) D)48.  E) E)120.

Solution: 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= 
7+3 = 10
10   ways to select all of them together= 3*4*10= 
3*4*10 = 120
120   Answer : 120.
Answer: E
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?	Pick one:
A) 4.3  B) 5.8  C) 6.0  D) 6.3  E) 6.5

Solution: 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 - 4.3
Answer: A
A boat goes 100 km downstream in 10 hours, and 90 km upstream in 15 hours. The speed of the stream is? Choose the correct choice from the following answers
A) 5km/h	B) 4km/h	C) 2km/h	D) (1/2) km/h	E) E)None

Solution: 100 --- 10 DS = 10   ? ---- 1   90 ---- 15 US = 6   ? ----- 1 S = (10 - 6)/2= 
(10 - 6)/2 = 2
2 kmph   ANSWER:2km/h
Answer: C
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.  Choose the correct answer:  A) z=3x  B) x=3z  C) y=2x  D) x=2y  E) y=3x

Solution: 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 isx=2y
Answer: D
(1/2) of a number is 3 more than the (1/6) of the same number?	Choose the correct choice from the following options
A) 6  B) 7  C) 8  D) 9  E) 5

Solution: let number is=x;   by question-------   x/2=(x/6)+3   x/2-x/6=3   x=9   ANSWER:9
Answer: D
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.
Choose one
A) 10 and 3	B) 7 and 10	C) 11 and 8	D) 3 and 10	E) 10 and 10

Solution: 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 11 and 8.
Answer: C
What will be the remainder when 17^200 is divided by 18 ? Select the correct option:
A) 3	B) 8	C) 5	D) 1	E) 7

Solution: 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 1
Answer: D
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?  Choose the correct choice from the following answers:	A) 16	B) 96	C) 112	D) 128	E) 142

Solution: 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 96.
Answer: B
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?	Choose the most appropriate option.
A) 23  B) 277  C) 18  D) 178  E) 181

Solution: Use fibonnacci series, with starting two terms as 1, 2. So next terms are 3, 5, 8, 13, 21, 34, 55, 89   Answer:277
Answer: B
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?  Choices.
A) 5 cm  B) 3 cm  C) 1 cm  D) 4 cm  E) 2 cm

Solution: Purple is 1.5 cmBlack is 0.5 cmBlue is 2 cm 1.5+0.5+2= 
 1.5+0.5+2 = 4
4 cmAnswer is 4 cm) 4 cm
Answer: D
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?
Choose one
A) 28  B) 25  C) 27  D) 23  E) 21

Solution: 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= 
14/16 * 24 = 21
21.   Answer: 21
Answer: E
A certain sum becomes four times itself at simple interest in eight years. In how many years does it become ten times itself?  Choose the correct option: A) 24 B) 55 C) 77 D) 99 E) 01

Solution: 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.24nswer: 24
Answer: A
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 ?	Choose the correct choice:
A) 4 years
B) 8 years
C) 10 years
D) None of these
E) 11 years

Solution: 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. 4 yearsnswer 4 years
Answer: A