11. Two bikers Rohan and Ajay are practicing with two different sports bike; Yamaha and Honda, on the circular racing track, for the bike racing tournament to be held next month. Both Rohan and Ajay start from the same point on the circular track. Rohan completes one round of the track in 1 min and Ajay takes 2 min to complete a round. While Rohan maintains speed for all the rounds, Ajay halves his speed after the completion of each round. How many times Rohan and Ajay will meet between 4th round and 7th round of Sunil (4th and 7th round is excluded)? Assume that the speed of Sunil remains steady throughout each round and changes only after the completion of that round.
Answer:
Explanation:Time taken by Ajay for 1st round = 2 min 2nd round = 4minutes
3rd round = 8 minutes 4th round = 16 minutes 5th round = 32 minutes
6th round = 64 min Rohan tales one minute for every round.
He meets 31 times in 5th and 63 times in 6th round Total meet = 31 + 63 = 94.
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12. The pacelength P is the distance between the rear of two consecutive footprints. For men, the formula, n/P = 144 gives an approximate relationship between n and P where, n = number of steps per minute and P = pacelength in meters. Bernard knows his pacelength is 164cm. The formula applies to Bernard's walking. Calculate Bernard's walking speed kmph.
Answer:
Explanation:n/P = 144 gives an approximate relationship between n and P where, n = number of steps per minute and P = pacelength in meters. Bernard knows his pacelength is 164cm.
Number of steps in one minute = 144*1.64
Distance travelled in 1 minute = 144*1.64*1.64 metres Distance travelled in one hr = 144*1.64*1.64*60/1000 km = 23.24 km approx
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13. Arun was all bent on building a new house. He carefully got the blue print of his house designed by his friend Ashwin, a civil engineer. He wanted to build a room of dimension 27 by 48 ft and lay tiles in this room. Each tile was of dimension 2 by 3 ft. How many such tiles should Arun buy?
Answer:
Explanation:27*48/2*3=216
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14. Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is
Answer:
Explanation:There are 4 such points. One point is the incenter of the triangle.3 is the excenters with respect to each angle of the triangle. In the picture given below, I is the incenter and JA, JB, JC are excenters.
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15. After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1 letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?
Answer:
Explanation:If one letter is in wrong envelope, one other letter must also be in wrong envelope. So zero is the probability that exactly 1 letter is inserted in an improper envelope.
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16. The Tatas have decided to launch their new brand "Aria" in the SUV segment. Mr.Mehra decided to take a test drive before deciding on Aria. During the test drive he found that Aria could cover 500 m in 20 seconds. Aria is known for its uniform acceleration. Can you find out the acceleration?
Answer:
Explanation:As we know, Speed=Distance/Time
I.e. Speed=500/20=2.5
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17. A circular dartboard of radius 1 foot is at a distance of 20 feet from you. You throw a dart at it and it hits the dartboard at some point Q in the circle. What is the probability that Q is closer to the centre of the circle than the periphery?
Answer:
Explanation:0.25.
Total area of board = Pi*1^2= Pi Preferred are =Pi (1/2)^2= Pi/4
So prob = (pi/4)/pi =1/4= 0.25
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18. Six friends decide to share a big cake. Since all of them like the cake, they begin quarrelling as to who gets to first cut and has a piece of the cake. One friend suggests that they blindfold a friend and then choose from a well shuffled set of cards numbered from one to six. You check and find that this method works as it should be simulating a fair throw of a die. You check by performing multiple simultaneous trials of picking the cards blindfolding and throwing a die. You note that the number shown by the method of picking up a card and throwing a real world die, sums up to a number between 2 and 12. Which total would be likely to appear more often 8, 9 or 10?
Answer:
Explanation:The best solution will be 7, and there will be total 6 cases for this choice (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)but this one is not in the choices so out of the 4 choices given 8 will be the best choice. For this choice there are 5 methods (2,6), (3,5), (4,4), (5,3), (6,2)
Similarly for 9 there are 4 choices (3,6), (4,5), (5,4),
(6,3) for 10 there are 3 choices (4,6), (5,5), (4,6)
Answer is 8.
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19. If Tarun buys only pens costing Rs. 13 each or only pencils costing Rs. 5 each, he is left with Rs. 2 in each case. Which of the following cannot be the amount available with him?
Answer:
Explanation:Given that: When the person buys either only pens, each costing Rs.13 OR he buys only pencils, each costing Rs.5, he will have remaining 2 rupees. (i.e. when the amount he has is divided by 13 or 5, the remainder is 2 ).
Looking at the options, the only number that does not satisfy the given condition is 577. (577 when divided by 13 do not give remainder 2).
OR
The number must be divisible by 13 or 5 exactly, leaving (minus) the remainder 2.
Only 575 is not divisible by 13 exactly.
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20. A sheet of paper has statements numbered from 1 to 40. For each value of n from 1 to 40, statement n says "At least n of the statements on this sheet are true." Which statements are true and which are false?
Answer:
Explanation:"The first 13 statements are true and the rest are false." is the correct answer.
All others do not satisfy the rule and contradict itself.
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