MU-NLPC/Calc-aqua_rat huggingface dataset:
For any numbers a and b, a#b = ab(3 − b). If a and a#b both represent positive numbers, which of the following could be a value of b? Select:
A) −5
B) −2
C) 2
D) 4
E) 7

Solution: if a#b is positive then there are 2 cases   either ab &(3-b) both are negatives or both positives   let both are positives then for (3-b) to be positive b has to less than 3 (3-b>0--->3>b)   from options b can be -5,-2,or 2   but if we take negative value of b then ab will negative & hence a#b which is not possible.   also if we do both negative then (3-b) to be negative b has to be greater than 3 which from options are only 4&7   if we take any value then the term ab will positive leaving a#b negative.which is not possible   Hence b=2   ANSWER:2
Answer: C
A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Choose the correct choice
A) 150	B) 887	C) 167	D) 197	E) 161

Solution: Length of the train be ‘X’   X + 150/15 = X + 250/20   4X + 600 = 3X + 750   X = 150m   150nswer: 150
Answer: A
Select a card from pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both the cards being king ? Choose one
A) 1/111
B) 2/121
C) 1/221
D) 2/213
E) 3/412

Solution: Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways.   ∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221   1/221
Answer: C
Twelve coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?	Select:
A) 2^9
B) 2^11
C) 3 * 2^8
D) 3 * 2^9
E) 3 * 2^10

Solution: Fix the third coin as H. The remaining 11 coins have 2^11 outcomes.   2^11
Answer: B
The instructions state that Cheryl needs 4/19 square yards of one type of material and 2/13 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 4/26 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?  Answers
A) 4/19  B) 1/9  C) 2/3  D) 1 1/9  E) 2 1/9

Solution: Total bought = 4/19+2/13   left part 4/26--->2/13   so used part 4/19+2/13-2/13=4/19   4/19NSWER:4/19
Answer: A
In how many different number of ways 2 boys and 2 girls can sit on a bench?  Choose the correct choice from the following answers:	A) 720	B) 730	C) 740	D) 750	E) 24

Solution: npn = n!   4p4 =4 × 3 × 2 × 1 = 24   24
Answer: E
A takes twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 ays, can do the work alone in Pick one:	A) 10 days	B) 11 days	C) 15 days	D) 12 days	E) 18 days

Solution: work as x,x/2,x/3   ==(1/x+2/x+3/x)   =1/2==>6/x=1/2   ==>12   ANSWER 12 days
Answer: D
Two mixtures of A and B have A and B in the ratio 3:2 and 3:4. In what proportion should these two mixtures be mixed to get a new mixture in which the ration of A to B is 5:4?  Select.
A) 6:1  B) 5:4  C) 20:7  D) 10:9  E) 14:11

Solution: I got C but with a different, yet slightly longer approach, which I constantly use for proportion problems such as this one. Usually, this approach is very efficient when used with slightly difficult questions, but this problem is quite hard so I had to slightly tweak it. I will show you how I usually use the approach and later show you how to use it with this specific problem.   Example.   1 Liter of Solution A contains 45% alcohol, while 1 Liter of Solution B contains 20% alcohol. In what ratio must the two solutions be used to get a solution with 30% alcohol   Solution:   1.	45/100*[A/(A+B)]+20/100*[B/(A+B)] = 30/100   2.	Multiply 100 to both sides to arrive at 45A/(A+B) + 20B/(A+B) = 30   3.	Multiply (A+B) to both sides to arrive at 45A + 20B = 30A + 30B   4.	Distribute to arrive at 15A = 10B   5.	Thus the ratio is A/B = 10/15 = 2/3   Now using this same approach, we tackle Gopu106’s question. It is important to first think of X in the mixture as the alcohol in the problem above; hence, a mixture of X and Y in the ratio of 3:2 translates to X is 3/5 of the solution. Applying this concept to all three equations, we write:   1.	3/5*[A/(A+B)]+3/7*[B/(A+B)] = 5/9   2.	Now here is the tweak that must be made to continue with this approach. You must find the common denominator for all three numbers and organize the fractions accordingly. By finding the common denominator of 5,7,9 (or 315) we re-write the equations as follows   3.	189/315*[A/(A+B)]+135/315*[B/(A+B)] = 175/315   4.	Multiply 315 to both sides to arrive at 189A/(A+B) + 135B/(A+B) = 175   5.	Multiply (A+B) to both sides to arrive at 189A + 135B = 175A + 175B   6.	Distribute to arrive at 14A = 40B   7.	Thus the ratio is A/B = 40/14 = 20/7 or answer 20:7
Answer: C
Cream costs twice as much as skim milk. A certain brand of milk is 2/5 cream and 3/5 skim milk. What fraction of the cost of this brand is due to the cream?
Pick one: A) 2/7 B) 3/7 C) 4/7 D) 3/5 E) 2/5

Solution: Let x be the cost of the skim milk in the mixture.   The cost of the cream is (2/3)*x*2 = 4x/3.   The total cost is x+4x/3 = 7x/3 and the fraction due to the cream is (4x/3) / (7x/3) = 4/7   The answer is 4/7.
Answer: C
An art gallery has only paintings and sculptures. Currently, 1/3 of the pieces of art are displayed, and 1/6 of the pieces on display are sculptures. If 1/3 of the pieces not on display are paintings, and 1000 sculptures are not on display, how many pieces of art does the gallery have?  Choose the correct option
A) 360  B) 2250  C) 540  D) 640  E) 720

Solution: Too many words and redundant info there.   (i) 1/3 of the pieces of art are displayed, hence2/3 of the pieces of art are NOT displayed.   (ii) 1/6 of the pieces on display are sculptures, hence 5/6 of the pieces on display are paintings.   (iii) 1/3 of the pieces NOT on display are paintings, hence2/3 of the pieces NOT on display are sculptures.   1000 sculptures are not on display, so according to (iii) 2/3*{not on display} = 1000 --> {not on display} = 1500.   According to (i) 2/3*{total} = 1500 --> {total} = 2250.   Answer: 2250.
Answer: B
A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?  Pick one:  A) 10  B) 11  C) 23  D) 43  E) 66

Solution: 10   10   4 a 3 |   9 8 4 } ==> a + 8 = b ==> b - a = 8   13 b 7 |   10lso, 13 b7 is divisible by 11 (7 + 3) - (b + 1) = (9 - b)   (9 - b) = 0   b = 9   (b = 9 and a = 1) (a + b) = 10.
Answer: A
Riya covers journey from kavali to nellore by car at average speed of 50 Km/hr. She returns back by scooty with an average speed of 50 Km/hr. Find her average speed during the whole journey?  Choices:
A) 30Km/hr B) 50Km/hr C) 80Km/hr D) 90Km/hr E) 100km/hr

Solution: Explanation:   Average speed = 2 xy/x+y   = 2*50*50/100= 
2*50*50/100 = 50
50 Km/hr   Answer: Option 50Km/hr
Answer: B
The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 22.5 years. What is the age of the new member ?
Choose the correct choice from the following choices: A) 20 years B) 21 years C) 22 years D) 25 years E) 24 years

Solution: The average age of the 5 members is 20 years   => The sum of the ages of the 5 members is 20*5= 
20*5 = 100
100 years   Once the new member joins, the average age becomes 22.5 years.   Let the age of the new member be x.   Then (110+x)/6= 22.5   => x = 25 years   Answer 25 years
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 117 grams of water?  Choose the correct choice from the following.
A) 16  B) 104  C) 112  D) 128  E) 142

Solution: Since the ratio, by mass, of hydrogen to oxygen is 2:16, then oxygen is 16/(2+16)=8/9 of mass of water.   Therefore there are   117*8/9= 
  117*8/9 = 104
104 grams of oxygen in 117 grams of water.   Answer: 104.
Answer: B
Chunilal invests 65% in machinery 20% in raw material ands till has 1,305 cash with him. Find his total investment. Pick.
A) 6,500  B) 7,225  C) 8,500  D) 7,395  E) None of these

Solution: Let he had originally x.   Then 65% of x + 20 % of x + 1305 = x   0.65x + 0.2x + 1305 = x   ⇒ 0.15 x = 1305 ⇒ x = 8700   ∴ His total investment = 65% of 8700 + 20% of 8700   = 85% of 700 = 7395   Answer 7,395
Answer: D
The largest 4 digit number exactly divisible by 44 is?  Answers: A) 9988 B) 9939 C) 9944 D) 9954 E) 9960

Solution: Largest 4-digit number = 9999   44) 9999 (227   9988   Largest number : 9988   9988nswer : 9988
Answer: A
What is the remainder when the number 14^2 * 15^8 is divided by 5? Options:
A) 0 B) 1 C) 2 D) 4 E) 5

Solution: 14^2 has units digit 6   15^8 has units digit 5   Thus 14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero   0nswer: (0)
Answer: A
Find compound interest on $ 10000 at 15% per annum for 2 years 4 months, compounded annually.	Choose the correct choice from the following options.
A) 3886.25
B) 3286.25
C) 3186.25
D) 3386.25
E) 3586.25

Solution: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.   Amount = $ [10000 X (1+­(15/100))2 X (1+((1/3)*15)/100)]   =$ [10000 * (23/20) * (23/20) * (21/20)= 
10000 * (23/20) * (23/20) * (21/20) = 55_545/4 = around 13_886.25
$ 13886.25	.   :. C.I.= Rs. (13886.25 -10000) = $ 3886.25   3886.25nswer 3886.25.
Answer: A
The ratio between x and y is 8/5; x is increased by 10 and y is multiplied by 10 , what is the ratio between the new values of x and y?
Choose the correct choice
A) 8/5	B) 5/8	C) 1	D) 10	E) It Cannot Be Determined

Solution: Ratio = 8k/5k = 8/5, 16/10, etc.   x and y are decreased by 5 --> (8k + 10)/(5k * 10)   New ratio can be 18/50, 26/100, etc.   Answer: It Cannot Be Determined
Answer: E
The lenght of a room is 5.5 m and width is 4 m. Find the cost of paving the floor by slabs at the rate of Rs. 750 per sq. metre.	Select the correct option
A) s. 15,550  B) s. 15,600  C) s. 16,500  D) s. 17,600  E) s. 17,900

Solution: Area of the floor = (5.5 Ã— 4) m2 = 22 m2.   Cost of paving = Rs. (750 Ã— 22) = Rs. 16500   .   Answer: Option s. 16,500
Answer: C
How long does a train 100 m long running at the speed of 65 km/hr takes to cross a bridge 145 m length?	Options
A) 13.6 sec  B) 12.1 sec  C) 17.9 sec  D) 61.9 sec  E) 47.98 sec

Solution: Speed = 65 * 5/18 = 18 m/sec   Total distance covered = 100 + 145= 
100 + 145 = 245
245 m.   Required time= 245/18 = 13.6 sec.   13.6 secnswer:13.6 sec
Answer: A
The slant height of a cone is 12 cm and radius of the base is 4cm, find the curved surface of the cone.	Select.
A) 49 π cm2	B) 40 π cm2	C) 48 π cm2	D) 43 π cm2	E) 41 π cm2

Solution: Explanation:   π * 12 * 4 = 48   Answer: Option 48 π cm2
Answer: C
If P(A) = 4/5 and P (B) = 2/5, find P (A n B) if A and B are independent events.	Choose the correct choice from the following answers:	A) 7/25	B) 3/25	C) 8/25	D) 2/13	E) 3/17

Solution: P (A n B) = P(A) . P(B)   P (A n B) = 4/5 . 2/5   P (A n B) = 8/25.   8/25
Answer: C
Sum of three nos is 98. The ratio between 1 and 2 is 2:3. The ratio between 2 and 3 is 5:8 .
Find the second no? Choose one:  A) 10  B) 20  C) 30  D) 40  E) 50

Solution: x+y+z=98   x/y=2/3   x=2y/3   and   y/z=5/8   z=8y/5 subtitute this is x and z   2y/3+y+8y/5=98   y=30   ANSWER:30
Answer: C
Kaushalya can do a work in 20 days, while kaikeyi can do the same work in 25 days. They started the work jointly.Few days later Sumitra also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.700. What is the Share of Sumitra? Select the correct option:	A) Rs.130	B) Rs.185	C) Rs.70	D) can't be determined	E) None of these

Solution: Explanation:   Efficiency of kaushalya = 5%   Efficiency of kaikeyi = 4%   Thus, in 10 days working together they will complete only 90% of the work.   [(5 + 4) × 10] =90   Hence, the remaining work will surely done by sumitra, which is 10%.   Thus, sumitra will get 10% of Rs. 700, which is Rs.70   Answer: Rs.70
Answer: C
Three unbiased coins are tossed. What is the probability of getting 2 Heads and 2 Tail?
Choose the most appropriate option:
A) 5/8 B) 1/4 C) 3/8 D) 7/8 E) 1/8

Solution: Let, H --> Head , T --> Tail   Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}   Let E = event of getting 3 heads   Then E = {THH,HTH,HHT,THT,TTH}   P(E) = n(E)/n(S) =5/8   5/8nswer is 5/8
Answer: A
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?	Choose the correct choice.
A) 10 B) 12 C) 15 D) 13 E) 16

Solution: Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.   1/x + 1/(x - 5) = 1/(x - 9)   (2x - 5)(x - 9) = x(x - 5)   x2 - 18x + 45 = 0   (x- 15)(x - 3) = 0 => x = 15   ANSWER 15
Answer: C
A train passes a station platform in 36 seconds and a man standing on the platform in 23 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?	Pick one:
A) 877 m	B) 195 m	C) 167 m	D) 887 m	E) 265 m

Solution: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train   = (15 x 23)m = 345 m. Let the length of the platform be x meters. Then, (x + 345)/36 = 15   ==> x + 345 = 540 ==> x   = 195 m.   Answer: 195 m
Answer: B
A man purchased a watch for Rs.400 and sold it at a gain of 20% of the selling price. The selling price of the watch is: Choose the correct choice from the following options
A) 232  B) 480  C) 178  D) 277  E) 1981

Solution: Explanation:   Cost price = 400   Gain% = 20%   Gain = 400 × 2010020100 = 80   Cost price = 400 + 80= 
400 + 80 = 480
480   Answer: 480
Answer: B
A train passes a station platform in 40 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Choose the correct choice from the following answers
A) 180 m
B) 240 m
C) 260 m
D) 300 m
E) 380 m

Solution: Speed = 54 x 5/18 = 15 m/s   Length of the train = (15 x 20)m = 300 m.   Let the length of the platform be x metres.   Then, (x + 300)/40 = 15   --> x + 300 = 600   x = 300m.   Answer : 300 m.
Answer: D
A family consists of two grandparents, two parents and four grandchildren. The average age of the grandparents is 70 years, that of the parents is 40 years and that of the grandchildren is 6 years. What is the average age of family?	Select.
A) 8/4years  B) B)31  C) C)30  D) D)33  E) E)35

Solution: Required average   = (70 x 2 + 40 x 2 + 6 x 4 )/(2 + 2 + 4)   = (140 + 80 + 24)/8   = 244/8   = 30 8/4years.   8/4yearsnswer is 8/4years
Answer: A
Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one. Select the correct option.
A) 12 sec	B) 24 sec	C) 48 sec	D) 60 sec	E) 65 sec

Solution: Explanation:   Relative speed =	= (45 + 30) km/hr   =75 x	5/18 m/sec   =125/6 m/sec   We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.   So, distance covered = Length of the slower train.   Therefore, Distance covered = 500 m.   Required time =500 x	6/125 = 24 sec.   ANSWER IS 24 sec
Answer: B
A chair is bought for Rs.400/- and sold at Rs.500/- find gain or loss percentage Choose the correct choice from the following choices
A) 15% loss B) 20% gain C) 25% gain D) 30% gain E) 35% gain

Solution: Formula = (Selling price ~ 25% gainost price)/25% gainost price * 100   = (500 - 400)/400 = 25% gain   25% gain
Answer: C
A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets?  Choose one:
A) 289	B) 278	C) 211	D) 450	E) 476

Solution: 10 * 150= 
10 * 150 = 1_500
1500   3 * 100 + 5 * 150= 
3 * 100 + 5 * 150 = 1_050
1050   1500 – 1050= 450   Answer:450
Answer: D
If √(3 + ³√x) = 2, then x is equal to : Choices:
A) 1	B) 2	C) 4	D) 8	E) 12

Solution: On squaring both sides, we get:   3 + ³√x = 4 or ³√x = 1.   Cubing both sides, we get x = (1 x 1 x 1) = 1   1NSWER:1
Answer: A
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:	Choose the correct choice from the following answers:
A) 60 birds  B) 72 birds  C) 30 birds  D) 80 birds  E) 20 birds

Solution: Let the total number of shots be x. Then,   Shots fired by A =(5/8)x   Shots fired by B =(3/8)x   Killing shots by A =(1/3)of	(5/8)x=(5/24)x   Shots missed by B =(1/2) of (3/8)x	=(3/16)x   3x/16= 27 or x =(27 x 16)/3= 144.   Birds killed by A =(5x/24)	=(5/24*144)= 
(5/24*144) = 30
30.   Answer is 30 birds.
Answer: C
The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:
Choices.
A) 542  B) 540  C) 591  D) 567  E) 548

Solution: Required number = (L.C.M. of 12, 15, 20, 54) + 8   = 540 + 8= 
540 + 8 = 548
548.   Answer: Option 548
Answer: E
When y is divided by 288, the remainder is 45. What is the remainder when the same y is divided by 24? Pick:
A) 20	B) 21	C) 23	D) 25	E) 26

Solution: y = 288*a + 45 = (24*12)*a + 24 + 21   The answer is 21.
Answer: B
Which of the following is not a prime number ? Answers
A) 502
B) 503
C) 509
D) 521
E) 523

Solution: Clearly, 502 is not a prime number.   502nswer : 502
Answer: A
Best friends Sprite and Icey have are playing a game of marbles. They invite 10 of their friends to play with them. There are 36 marbles in the bag. If all 12 people are playing, how many marbles does each person get?
Choose the correct choice from the following answers:
A) 3  B) 4  C) 5  D) 6  E) 7

Solution: 3nswer= 3   36 / 12= 
36 / 12 = 3
3   3nswer= 3
Answer: A
Of the families in City X in 1904, 50 percent owned a personal computer. The number of families in City X owning a computer in 1908 was 30 percent greater than it was in 1904, and the total number of families in City X was 5 percent greater in 1908 than it was in 1904. what percent of the families in City X owned a personal computer in 1908?
Pick:
A) 61.90%	B) 52.20%	C) 56.20%	D) 70.45%	E) 74.41%

Solution: Say a 100 families existed in 1904 then the number of families owning a computer in 1904 - 50   Number of families owning computer in 1908 = 50 * 130/100= 
50 * 130/100 = 65
65   Number of families in 1908= 105   The percentage = 65/105 * 100 = 61.90%.   Option: 61.90%
Answer: A
A father was twelve times as old as his son twenty years back. Now he is twice as old as his son. What are their present ages?
Options:
A) Father 44 and Son 22
B) Father 35 and Son 23
C) Father 38 and Son 44
D) Father 55 and Son 22
E) None of these

Solution: Let present age of the Son = X.   Present age of the father = 2X.   Now according to question,   2X -20 = 12*(X-20)   2X - 20 = 12X -240   10X = 220   X = 22   Present age son = 22 years,   Present age father = 2*22= 
2*22 = 44
44.   Father 44 and Son 22NSWER : OPTION Father 44 and Son 22
Answer: A
The difference between a 4-digit number and the number formed by reversing its digit is not a multiple of
Choose the correct choice from the following answers.
A) 3  B) 27  C) 243  D) 81  E) 11

Solution: Another approach is to TEST a number.   Let's say the original number is 2031   So, the R11V11RS11D number is 1302   The DIFF11R11NC11 = 2031-1302= 
2031-1302 = 729
729   No check the answer choices   729 is a multiple of 3,27,81,243   11 is NOT a multiple of 729   Answer:11
Answer: E
John found that the average of 15 no.'s is 40. If 10 is added to each number then the mean of number is?	Choose the correct choice from the following choices:
A) 50
B) 55
C) 65
D) 72
E) 78

Solution: (x+x1+...x14)/15 = 40   50   Option 50
Answer: A
Of the 200 students at University XYZ majoring in one or more of the engineering disciplines, 110 are majoring in electrical and 150 are majoring in mechanical. If at least 30 of the students are not majoring in either electrical or mechanical, then the number of students majoring in both electrical and mechanical could be any number from
Choose the correct choice from the following options: A) 30 to 70 B) 70 to 100 C) 110 to 130 D) 130 to 150 E) 150 to 170

Solution: if there are 110 students majoring in electrical then there must be 90 person not majoring electrical at all, since both of the student not majoring electrical and mechanical is at least 30, so the number of the student who are not majoring electrical but majoring mechanical will be at least 60.   if there are 150 students majoring in mechanical there must be 50 students who are not majoring mechanical at all, since the number of the student who are not majoring electrical but majoring mechanical will be at least 60, hence the number of students both majoring mechanical and electrical will be at least 150   so there must be at least 150 students who major in both   see the answers option the only possible answer is 150 to 170 !
Answer: E
If the selling price of 100 articles is equal to the cost price of 63 articles, then the loss or gain percent is: Answers
A) 39%
B) 36%
C) 35%
D) 40%
E) 37%

Solution: Let C.P. of each article be Re. 1.   Then, C.P. of 100 articles = Rs. 100;   S.P. of 100 articles = Rs. 63.   Loss % = 37/100 * 100= 
37/100 * 100 = 37
37%   ANSW37%R:37%
Answer: E
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? Select:
A) 12 B) 25 C) 50 D) 10 E) 82

Solution: Explanation:   Due to stoppages, it covers 9 km less.   time taken to cover 9 km=(9/54*60)= 
(9/54*60) = 10
10 min   Answer 10
Answer: D
During the break of a football match, the coach will make 3 substitutions. If the team consists of 12 players among which there are 2 forwards, what is the probability that none of the forwards will be substituted?	Answers:
A) 21/55	B) 18/44	C) 28/55	D) 28/44	E) 36/55

Solution: Required probability = no. of favorable outcome/ total no. of outcomes   out of 12 players any 3 can be selected in 12C3 ways   after removing 2 forwards any 3 players can be selected from the remaining 9 players in 9C3 ways   thus required probability = 9C3/12C3 =21/55=21/55
Answer: A
529 is a perfect square. When x is added to the square root of 529, the result is also a perfect square. What is x?	Choose the correct choice from the following choices
A) 1 B) 2 C) 3 D) 4 E) 5

Solution: 529 is 23*23   here   A 23+1= 
23+1 = 24
24   B   23+2= 
  23+2 = 25
25   C   23+3= 
  23+3 = 26
26   D   23+4= 
  23+4 = 27
27   E   23+5= 
  23+5 = 28
28   so, B is the only addition that gives a perfect square. so x=3   then the answer is 2
Answer: B
Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 3 times his original investment. What is the value of n?	Choose the correct answer:
A) 50 years  B) 25 years  C) 12 years 6 months  D) 37 years 6 months  E) 40 years

Solution: Explanatory Answer   Let us say Braun invested $100.   Then, at the end of 'n' years he would have got back $300.   Therefore, the Simple Interest earned =300 - 100= 
300 - 100 = 200
$200.   We know that Simple Interest= (Principal * number of years * rate of interest) / 100   Substituting the values in the above equation we get 200 = (100 * n * 8) / 100   Or 8n = 200   Or n = 25 years.   correct choice is (25 years)
Answer: B
Which of the following can be a perimeter r of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100
Choices:
A) I only	B) III only	C) II and III only	D) I, II, and III	E) Not I, II, or III

Solution: Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.   But how do you use the above property to solve the question?   The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: r>0.   Answer is I, II, and III.
Answer: D