MU-NLPC/Calc-aqua_rat huggingface dataset:
Two Guys A and B leave point A and point B simultaneously and travel towards Point B and Point A on the same route at their respective constant speeds. They meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively. How long will B take to cover the entire journey between Point B and point A? Choose the correct choice from the following options.
A) 65
B) 90
C) 70
D) 75
E) 80

Solution: Let x per minute be the speed of A and y per minute be the speed of B.   After meeting at a point, A travels for 32 mins and B travels for 50 mins. So distance covered by each of them post point of crossing   A= 32x and B=50y   The distance covered by A and B before they cross each would be distance covered by B and A post crossing respectively.   Therefore distance covered by B before he meets A= 32x   Time taken by B cover 32x distance= 32x/y mins   Therefore total time taken by B= 32x/y + 50 mins ................. I   We need to find value of x in terms of y to arrive at final answer.   Total distance= 32x+50y   Combined speed of A and B= x+y   Therefore time taken before A and B meet en-route= (32x+50y)/(x+y)   Time taken by B reach destination after meeting A= 50 mins   Total travel time for B= [(32x+50y)/(x+y)]+50 mins ...................II   Equate I and II   32x/y+50= [(32x+50y)/(x+y)]+50   (32x+50y)/y=(82x+100y)/(x+y)   32x^2+50xy+32xy+50y^2=82xy+100y^2   32x^2+82xy-82xy+50y^2-100y^2=0   32x^2-50y^2=0   32x^2=50y^2   16x^2=25y^2   Taking square root.. (since x and y denote speed, square root can't be negative)   4x=5y   y=4x/5 ............ III   substitute in I   =32x/(4x/5) + 50   =32x*5/4x + 50   =40+50= 
40+50 = 90
90 mins   90
Answer: B
A trader marks his books 20% more than the cost price. If he allows 20% discount, then find his gain or loss percent? Pick one
A) 2% profit	B) 2% loss	C) 4% loss	D) No profit No loss	E) None of these

Solution: 4% loss   Let 4% lossP of an book = $100   MP= $120   Discount = 20%   SP = M[(100 - d%)/100] = 120(80/100) = $96   4% losslearly, the trader gets 4% loss.
Answer: C
A 6-liter solution is 20% alcohol. How many liters of pure alcohol must be added to produce a solution that is 50% alcohol?
Choose the correct choice from the following options
A) 2.4	B) 2.7	C) 3.0	D) 3.3	E) 3.6

Solution: Let x be the amount of pure alcohol required.   0.2(6) + x = 0.5(x+6)   0.5x = 3 - 1.2   x = 3.6 liters   The answer is 3.6.
Answer: E
What is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 50? Pick one
A) 10 B) 25 C) 50 D) 75 E) 100

Solution: Surprisingly no one answered this easy one.   property of a set of consecutive integerz.   mean=median=(first element+last element)/2 = (second element+last but one element)/2 =(third element+ third last element)/2 Etc. Etc.   So mean=median=50/2= 
50/2 = 25
25   Answer is 25
Answer: B
In the annual Cultural Programme of indra prastha there was this Math Quiz going on.yudhisthir faced this last question that will bring the champion's trophy. What will be thesolution for the given problem?The function f is defined is defined asf(2x+3)= (x-3)(x+4)What is f(29)? Choose the correct option.
A) 200
B) 230
C) 140
D) 170
E) None of these

Solution: Explanation :   f(2x+3)= (x-3)(x+4)put x=13f(2*13+3)=(13-3)*(13+4)=10*17f(29)=170   Answer : 170
Answer: D
The cost of an article was Rs.75. The cost was first increased by 20% and later on it was reduced by 20%. The present cost of the article is:	Choose the correct answer.
A) Rs. 72
B) Rs. 60
C) Rs. 75
D) Rs. 76
E) None

Solution: Solution: Initial Cost = Rs. 75   After 20% increase in the cost, it becomes,   (75+ 20% of 75) = Rs. 90   Now, Cost is decreased by 20%, So cost will become,   (90 - 20% of 90) = Rs. 72.   So, present cost is Rs. 72.   Mind Calculation Method: 75-----20%↑--→90-----20%↓-----→72.   Rs. 72nswer: Option Rs. 72
Answer: A
The probability of having a girl is identical to the probability of having a boy. In a family with two children, what is the probability that all the children are of the same gender?
Choose the correct choice from the following answers:	A) 1/2	B) 1/16	C) 1/9	D) 1/4	E) 1/25

Solution: There are two cases. All boys and all girls.   case 1. all boys.   1/2*1/2= 1/4   case 2 .all girls.   1/2*1/2=1/4   We will add the cases to get 1/2
Answer: A
The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? Choose the correct choice from the following answers:
A) 16 2/3%  B) 16 2/8%  C) 16 2/5%  D) 16 2/1%  E) 16 1/3%

Solution: 15 CP = 18 SP   18 --- 3 CP loss   100 --- ? => 16 2/3% loss.16 2/3%nswer: 16 2/3%
Answer: A
A(8, w^2) is the (x, y) coordinate of point located on the parabola Y = X^2 + 17. What is the value of w?  Choose the correct choice from the following choices:	A) 3.	B) 4.	C) 5.	D) 6.	E) 9.

Solution: y=x^2 +17   w^2=8^2+17   w^2=81   W=9   Answer 9.
Answer: E
Paul sold an item for Rs.3600/- and incurred a loss of 40%. At what price should he have sold the item to have gained a profit of 40%?  Choose the correct option
A) 8000  B) 8200  C) 8400  D) 8600  E) 8800

Solution: Explanation:   40% loss means SP = 60% of CP   :. CP = Rs.3600x100/60 = Rs.6000.   The SP for a gain of 40% = 6000+40% of 6000 = 6000+2400= 
6000+2400 = 8_400
Rs8400.   Answer: Option 8400
Answer: C
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?	Select
A) 4/8
B) 9/2
C) 7/6
D) 9
E) 2/21

Solution: Explanation:   Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = Â³Câ‚‚/Â¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 1/35   Probability that both are yellow = Â²Câ‚‚/Â¹âµCâ‚‚ = (2 * 1)/(15 * 14) = 1/105   Probability that one blue and other is yellow = (Â³Câ‚ * Â²Câ‚)/Â¹âµCâ‚‚ = (2 * 3 * 2)/(15 * 14) = 2/35   Required probability = 1/35 + 1/105 + 2/35   = 3/35 + 1/105 = 1/35(3 + 1/3)   = 10/(3 * 35) = 2/21   Answer: 2/21
Answer: E
There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 40 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City? Options.
A) 90.
B) 80.
C) 60.
D) 40.
E) 25.

Solution: STREET-60.AT DOMESTI60.-60.at   70 130   (40gray+30other) 70gray+60other   Answer:60.
Answer: C
One-tenth of the students at a nursery school are 4 years old or older. If 20 students have not yet reached their third birthday, and a total of 25 students are not between 3 years old and 4 years old, how many children are in the nursery school?	Pick one
A) 51  B) 20  C) 40  D) 50  E) 55

Solution: x/10 students are > 4 yrs   20 students are < 3 yrs   x/10+ 20 = 25   x/10 = 5   x = 50   Answer: 50
Answer: D
The product of all the prime numbers less than or equal to19 is closest to which of the following powers of 10 ?	Choose the correct choice:  A) 10^9  B) 10^8  C) 10^6  D) 10^7  E) 10^5

Solution: P = 2*3*5*7*11*13*17*19   = 21 * (11 * 19) (13*17) *10   ~ 21 * (10 * 20) (10 *20) * 10   ~ 8210 ^5   ~ 10^ 7   Answer : 10^7
Answer: D
A shopkeeper sells 400 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth? Options.
A) Rs. 45 B) Rs. 40 C) Rs. 35 D) Rs. 50 E) None of these

Solution: SP per metre = 18000/400 = Rs. 45 Loss per metre = Rs. 5 CP per metre = 45 + 5 = Rs. 50   ANSWER:Rs. 50
Answer: D
Exactly one of the following numbers cannot be written as a3 + b3 where a and b are integers.
Which number is it?
Choices:
A) 700056	B) 707713	C) 7000639	D) 7077283	E) 7077915

Solution: If a is an integer, then a3 gives remainder 0, 1, or 6 when divided by 7 (just consider the   remainders of 03, 13, 23, 33, 43, 53, and 63 when divided by 7). Then a3 + b3 gives remainder   0, 1, 2, 5, or 6 when divided by 7. Well, 7077283 gives remainder 3 when divided by 7. (The   remaining numbers can be represented as a sum of two cubes of integers, 700056 = 403 + 863,   707713 = 143 + 893, 7000639 = 323 + 1913, and 7077915 = 33 + 1923.)   correct answer 7077283
Answer: D
A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was $1480?	Choose the correct choice from the following answers:
A) $100  B) $150  C) $125  D) $134  E) $243

Solution: $100   $100   3x 4x 5x   6 9 4   18x + 36x + 20x = 1480   74x = 1480 => x = 20   5x = 100 Rs.
Answer: A
A side of beef lost 35 percent of its weight in processing. If the side of beef weighed 545 pounds after processing, how many pounds did it weigh before processing?	Choose the correct choice from the following
A) 191 B) 355 C) 737 D) 838 E) 1,560

Solution: Let weight of side of beef before processing = x   (65/100)*x = 545   => x = (545 * 100)/65 = 838   Answer 838
Answer: D
How many of the positive factors of 26 , 16 and how many common factors are there in numbers?	Choose the most appropriate option:	A) 1	B) 2	C) 3	D) 4	E) 5

Solution: factors of 26 - 1, 2, 13 and 26   factors of 16 - 1 , 2, 4, 8 and 16   Comparing both, we have three common factors of 45,16-2   Answer : 2
Answer: B
Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill cistern. How much time will be taken by A to fill the cistern separately?
Choose the correct choice from the following options:
A) 7	B) 8	C) 6	D) 54	E) 3

Solution: Let the cistern be filled by pipe A alone in x hours.   Then, pipe B will fill it in (x + 6) hours.   1/x + 1/(x + 6) = 1/4   x2 - 2x - 24 = 0   (x - 6)(x + 4) = 0 => x = 6.   Answer:6
Answer: C
The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the younger child insists of standing by his dog?
Choose the correct option.
A) 12  B) 24  C) 30  D) 48  E) 120

Solution: We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that C2 and D are always together.   Consider F and M to be one unit, then we would have total of four units: {F}, {M}, {C1}, {C2D}. The number of arrangements of these four units is 4!, but C2 and D within their unit can be arranged in 2 ways: {C2D} or {DC2}, so total number of arrangements is 4!*2=48.   Answer: 48
Answer: D
If 2^2n + 2^2n + 2^2n + 2^2n = 4^18, then n = Choose the correct choice
A) 3  B) 6  C) 17  D) 23  E) 24

Solution: 2^2n + 2^2n + 2^2n + 2^2n = 4^18   => 4 x 2^2n = 4^24 = 2^36   => 2^2 x 2^2n = 2^36   => 2^(2n+2) = 2^36   => 2n+2 = 36=> n =17   So. Answer will be 17.
Answer: C
If x = 3^27 and x^x = 3^k, what is k?	Options.
A) 3^9	B) 3^12	C) 3^27	D) 3^30	E) 3^33

Solution: Solution:   We know that x=3^27   which implies x^x = (3^27)^(3^27) = 3^(27 * 3^27) [because (x^y)^z = x^(y*z))]   so 3^(3^3 * 3^27) = 3^(3^(3+27)) [because x^a * x^b = x^(a+b)]   therefore x^x = 3^(3^30)   Given that x^x=3^k   so 3^(3^30) = 3^k   Since the base is same the exponent will also be same   therefore k = 3^30   Answer: 3^30
Answer: D
Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word BANANA could be arranged to create a six-letter code?  Choose the correct choice:
A) 6!	B) 6! − (3! + 2!)	C) 6! − (3! × 2!)	D) 6!/(3! + 2!)	E) 6!/(3! × 2!)

Solution: Number of letters in word 'BANANA' = 6.   The letters 'A' and 'N' appear 3 times and 2 times respectively in the word 'BANANA'.   Therefore the mathematical solution for number of ways that the letters of the word BANANA can be arranged to create six-letter code   = 6!/(3!*2!)   Answer: 6!/(3! × 2!)
Answer: E
A car takes 6 hours to cover a distance of 144 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?  Answers.
A) 50 Kmph B) 60 Kmph C) 65 Kmph D) 16 Kmph E) None

Solution: Time = 6   16 Kmphistence = 144   3/2 of 6 hours = 6 * 3/2= 
6 * 3/2 = 9
9 Hours   Required speed= 144/9= 
144/9 = 16
16 Kmph   16 Kmph)
Answer: D
A pair of prime numbers that can be expressed in the form {p, (p + 6)} is deﬁned as a pair of “sexy primes.” A “sexy triplet” is a group of three primes that can be expressed in the form {p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT  Options
A) 11
B) 13
C) 17
D) 19
E) 23

Solution: {x-6, x, x+6} all must be primes. Substitute options for x to check whether this will hold true. If x=19, then x+6=25, which is not a prime.   Answer: 19
Answer: D
Listed below are the mean temperatures measured in the Tokharian desert in a certain month. What is the median temperature W in that particular month?
Mean Temp (C°) No. of days
29 --------------------> 5
30 --------------------> 11
31 --------------------> 8
32 --------------------> 6 Choices.
A) 29 B) 30 C) 30.5 D) 31 E) 32

Solution: to find out median===>they must be arranged in ascending order.   29 29 29...(5 times)30 30 30 30.....(11 times)31 31 31.....(8 times)32 32 32 .....(6 times)   total days=5+11+8+6= 
5+11+8+6 = 30
30   therefore 30 numbers ...median W will be==>mean of 15 and 16 th place temperature===>(30+30)/2= 
(30+30)/2 = 30
30   hence 30
Answer: B
A & B start a business jointly. A invests Rs 16000 for 8 month & B remains in a business for 4 months. Out of total profit, B claims 2/7 of the profit . How much money was contributed by B ?
Choose the correct answer:
A) 11200	B) 12000	C) 12400	D) 12800	E) None of these

Solution: Explanation :   B's share = 2/7 of the profit   => A : B = 5 : 2   (We can easily find out A:B as given above by doing quick mental calculations   and it will be excellent if you can do as much as mental calculations possible.   Just for explanation, see below steps to systematically find out A : B   Let the total profit = x   B's share = 2x/7   A's share = x – 2x/7 = 5x/7   A:B = 5x/7 : 2x/7 = 5:2)   Let the money contributed by B = b   Then A:B = 16000*8 : b*4 = 5:2   => (16000*8)/4b = 5/2   => b = (16000*8*2)/ (4*5) = 800*8*2= 
800*8*2 = 12_800
12800. Answer : Option 12800
Answer: D
Mr. Thomas invested an amount of 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be 3508, what was the amount invested in Scheme B?
Answers:
A) 6400  B) 6500  C) 7200  D) 7500  E) None of these

Solution: Let the sum invested in Scheme A be x and that in Scheme B be (13900 – x).   Then, (x×14×2/100)+[(13900−x)×11×2/100]=3508   ⇒ 28x – 22x = 350800 – (13900 × 22) ⇒ 6x = 45000   ⇒ x = 7500.   So, sum invested in Scheme B = (13900 – 7500) = 6400.   6400nswer 6400
Answer: A
A motorist knows eight different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?	Choose the correct choice from the following choices: A) 4 B) 8 C) 12 D) 24 E) 48

Solution: 48xplanation:   Total number of routes from Bristol to Carlisle = (8 x 3 x 2) = 48   Answer: 48
Answer: E
A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 900 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?	Choose the correct option
A) 2880. B) 4860. C) 5780. D) 5760. E) 6480.

Solution: 6480.fficiency per machine = 900 watt/hr   6480.fficiency due to increase in wind speed = 900*120% => 1080 watt/hr   Production by each machine in 2 hours is  1080*2= 
 1080*2 = 2_160
> 2160 watt   Production by 3 machines=> 2160 watt * 3 = 6480 watt   Answer will be (6480.)
Answer: E
The radius of a circle is increased by 1%. Find how much % does its area increases?  Options
A) 2.07%  B) 2.71%  C) 2.09%  D) 2.01%  E) 1.01%

Solution: r = 100 r = 101   r2 = 10000 r2 = 10201   10000 ---- 201   100 ---- ? => 2.01%   Answer:2.01%
Answer: D
Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 90% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above? Options.
A)  5%  B)  10%  C)  15%  D)  55%  E)  30%

Solution: Total = n(A) + n(B) - n(Exactly 2 products) -2 (AnBnC) + Neither.   Neither is zero.   Hence 100 = 90 + 50 + 35 - n (Exactly 2 products) - 2*10   100 = 155 - n (Exactly 2 products) => n (Exactly 2 products) = 55.   Answer:  55%
Answer: D
When 2 no.'s divided by 17, leave remainders 13 and 11 respectively. If the sum of those 2 no.'s is divided by 17, the remainder will be	Choose the correct choice from the following options:
A) 3	B) 4	C) 7	D) 10	E) 12

Solution: (7)   Required remainder = remainder by (13 +11)/17 = 7
Answer: C
In the xy-plane the point (-2 -3) is the centre of a circle, the point (-2, 2) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle r is an integer then r=	Choose the most appropriate option: A) 6 B) 5.5 C) 4 D) 3 E) 2

Solution: Can be solved without much calculations.   You are given that (-2,-3) is the center of the circle. Point (4,-3) lies inside the circle ---> the radius is lesser than distance of (-2,-3) from (4,-3) ---> lesser than 6 units but the radius will also be greater than the distance of (-2,-3) from (-2,2) ----> greater than 5 units.   Thus the radius is >5 but <6 and as it is an integer, the only possible value of radius = 5. 5units.   5.5 is the correct answer.
Answer: B
A certain lab experiments with white and brown mice only. In one experiment, 2/3 of the mice are white. If there are 11 brown mice in the experiment, how many mice in total are in the experiment?  Select the correct option
A) 39	B) 33	C) 26	D) 21	E) 10

Solution: Let total number of mice = M   Number of white mice = 2/3 M   Number of brown mice = 1/3 M = 11   => M = 33   Answer 33
Answer: B
A room of 6m 44cm long and 3m 00cm broad is to be paved with square tiles. Find the least number of square tiles required to cover the floor.
Choose the correct choice from the following options: A) 12076 B) 12070 C) 12077 D) 12075 E) 12074

Solution: Explanation:   area of the room = 644 * 300sq cm   size of largest square tile = H.C.F of 644cm and 300cm= 4cm   area of 1 tile = 4*4 sq cm   no. of tiles required = (644*300) / (4 * 4)= 
(644*300) / (4 * 4) = 12_075
12075   Answer: 12075) 12075
Answer: D
In a Function, every person shakes hand with every other person. If there was a total of 28 handshakes in the function, how many persons were present in the Function?	Pick one
A) 8 B) 7 C) 2 D) 6 E) 5

Solution: Suppose there are nn persons present in a function and every person shakes hand with every other person. Then, total number of handshakes   = nC2=n(n−1)/2   n(n−1)=28×2n(n−1)=56   n=8   8NSWER 8 8
Answer: A
Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.1,80,000 earned at the end of 3 years from the start of the business in 1999?  Choices:
A) Rs.60,000
B) Rs.50,000
C) Rs.70,000
D) Rs.75,000
E) none

Solution: Solution   Sekar:Rajeev:Jatin=	(25000×12+35000×12+45000×12):(35000×24) : (35000×12)   = 1260000 : 840000 : 420000   = 3 : 2 : 1.   Rajeev's share	=Rs.(180000×2/6)   = Rs.60000.   Rs.60,000nswer Rs.60,000
Answer: A
When the positive integer y is divided by 9, the remainder is 5. What is the remainder when 3y is divided by 9?
Choose the correct choice from the following answers
A) 0
B) 1
C) 3
D) 4
E) 6

Solution: Lets take the number as y   when y is divided by 9 the remainder is 5 hence y can be written as   y=9k +5   Multiplying by 3 will give   3y = 27k + 15   we can also write   3y = 27k + 9 + 6   Now 27k and 9 are divisible by 9 leaving the remainder as 6 hence 6 is the answer.
Answer: E
the price of a maruti car rises by 30% while the sales of the car came down by 20%. what is the percent change in the total revenue?  Select: A) -4 B) 4 C) -2 D) 0 E) none of these

Solution: Assume that price is 100 and sales are also 100. Total revenue is 100*100= 
100*100 = 10_000
10000(100%). Now price increased by 30%. So new price is 130. Similarly new sales are 80. Now revenue is  130*80= 
 130*80 = 10_400
10400(104%)= So total change is 4%   ANSWER:4
Answer: B
The difference between C.I. and S.I. on an amount of $20,000 for 2 years is $72. What is the rate of interest per annum?  Choices:
A) 5%	B) 6%	C) 7%	D) 8%	E) 9%

Solution: $72 is the interest on the first year of interest.   Let x be the interest rate.   The interest after the first year is 20000*x.   The interest on the first year's interest is 20000*x*x   20000*x^2 = 72   x = 0.06   The answer is 6%.
Answer: B
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 30 years now, the son's age 2 years back was:  Pick one:  A) 14 years  B) 19 years  C) 13 years  D) 38 years  E) 39years

Solution: Let the son's present age be x years. Then, (30 - x) = x   2x = 30   x = 15   Son's age 5 years back (15- 2)= 
(15- 2) = 13
13 years.   Answer: 13 years
Answer: C
Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 35 km/hr. For how many minutes does the bus stop per hour?	Answers:
A) 22	B) 88	C) 24	D) 20	E) 99

Solution: In 1hr, the bus covers 60 km without stoppages and 35 km with stoppages.   Stoppage time = time take to travel (60 - 35) km i.e 25 km at 60 km/hr.   stoppage time = 25/60 hrs = 24 min.   Answer: 24
Answer: C
There are 20 Kids in a classroom. 12 Kids are wearing socks and 8 are wearing Shoes. 6 Kids are wearing both.
How many are Bare Feet ? Choose the correct choice from the following options.
A) 1
B) 2
C) 4
D) 5
E) 6

Solution: 12 kids wear socks   8 kids wear shoes   6 wear both.   12 â€“ 6 = 6 (wear only socks)   8 â€“ 6 = 2 (wear only shoes)   6 (wear both)   hence, 20 -14 = 6   6 kids are with bare feet.   6
Answer: E
A train 220 m long is running with a speed of 59 kmph. In what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going?
Options
A) 15 seconds B) 10 seconds C) 11 seconds D) 12 seconds E) 14 seconds

Solution: Relative speed=66kmph or 330/18m/s   Time taken to pass the man:   Length of the train/relative speed     220*18/330= 
  220*18/330 = 12
12 seconds   ANSWER:12 seconds
Answer: D
A table is bought for Rs.400/- and sold at Rs.600/- find gain or loss percentage Choose the correct answer:  A) 15%loss  B) 10%gain  C) 30%gain  D) 20%loss  E) 50% gain

Solution: Formula = (Selling price ~ Cost price)/Cost price * 100   = (600 - 400)/400 = 50% gain   50% gain
Answer: E
a, b, c are three distinct integers from 2 to 10 (both inclusive). Exactly one of ab, bc and ca is odd. abc is a multiple of 4. The arithmetic mean of a and b is an integer and so is the arithmetic mean of a, b and c. How many such triplets are possible (unordered triplets)?
Pick.
A) 8	B) 6	C) 2	D) 4	E) 0

Solution: DETAILED SOLUTION   Exactly one of ab, bc and ca is odd => Two are odd and one is even   abc is a multiple of 4 => the even number is a multiple of 4   The arithmetic mean of a and b is an integer => a and b are odd   and so is the arithmetic mean of a, b and c. => a+ b + c is a multiple of 3   c can be 4 or 8.   c = 4; a, b can be 3, 5 or 5, 9   c = 8; a, b can be 3, 7 or 7, 9   Four triplets are possible.   Correct Answer : 4
Answer: D