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Tickle Your Grey Cells

Puzzle corner is a dedicated section for honing analytical, mathematical and reasoning skills. In this section every week you will find five Puzzles. Theses mind twisters have been carefully selected after a thorough research and provide right inputs for tickling your grey cells. Solving puzzles is considered very good exercise so as to remain mentally active. Puzzle solving enhances memory and processing speed.

Puzzle is one of the most popular category in competitive examinations. All the major Indian MBA entrance exams like CAT, MAT, XAT and SNAP have direct questions or questions based on similar logics in written test. Besides MBA exams, competitive exams like GRE, GMAT, Bank PO, SSC & other government exams include puzzle questions. Most of the companies while recruiting through campus includes Puzzles in the written tests or at interview stage. Hence those who are preparing for campus placement tests this section is a must.

Week of the Year 

For her Birthday, Madhuri Dutt bought some T-shirts. If she gives 6 T-shirts to each friend, one friend will get only 4 T-shirts. Also, if she gives 4 T-shirts to each friend, she will have 30 T-shirts remaining. How many T-shirts she got on her Birthday, and how many friends are there?
Let's assume that there are total T T-shirts and F friends.
According to first case, if she gives 6 T-shirts to each friend, one friend will get only 4 T-shirts.
6*(F - 1) + 4 = T
Similarly, if she gives 4 T-shirts to each friend, she will have 30 T-shirts remaining.
4*F + 30= T
Solving above 2 equations, F = 16 and T = 94. Hence, Madhuri got 94 T-shirts and 16 friends.

Punkhuri and Chiriya met each other after a long time. In the course of their conversation, Punkhuri asked Chiriya her age. She replied, "If you reverse my husband's age, you will get my age and he is older than me. Also, the sum of our ages is 11 times the difference of our age." Can you help out Punkhuri in finding Chiriya's age?
Assume that Chiriya's age is 10X+Y years. Hence, her hubby's age is (10Y + X) years.
It is given that difference between their ages is 1/11th of the sum of their age.
Hence, (11)[(10Y + X) - (10X + Y)] = [(10Y + X) + (10X + Y)]
(9Y - 9X) = (1/11)(11X + 11Y)
9Y - 9X = X + Y
8Y = 10X
4Y = 5X
Hence, the possible values are X=4, Y=5 and Chiriya's age is 45 years.

A fish had a tail as long as its head plus a quarter the length of its body. Its body was three-quarters of its total length. Its head was 4 inches long. What was the length of the fish?
It is obvious that the length of the fish is the summation of lengths of the head, the body and the tail. Hence, Fish (F) = Head (H) + Body (B) + Tail (T)
But it is given that the length of the head is 4 inches i.e. H = 4. The body is three-quarters of its total length i.e. B = (3/4)*F.
And the tail is its head plus a quarter the length of its body i.e.
T = H + B/4.
Thus, the equation is
F = H + B + T
F = 4 + (3/4)*F + H + B/4
F = 4 + (3/4)*F + 4 + (1/4)*(3/4)*F
F = 8 + (15/16)*F
(1/16)*F = 8
F = 128 inches
Thus, the fish is 128 inches long.

A man drove his Innova car all the way from Shimla to Delhi only to discover at the end of the trip that he had a punctured tyre from the very start. Yet his Innova car was not at all affected by it? How is this possible?
Punctured tyre must be a spare tyre.

In a temple, there were three beggars. A pilgrim came to the temple with few coins. The pujari of the temple gave him a magic bag in which coins get doubled each time you put that coins into it. He put all the coins he had in that bag and the coins got doubled. He took out all the coins and gave few to the first beggar and then again put the remaining coins back in the bag. The coins got doubled again; he took out all the coins again and gave few coins to the second beggar. He then again put the remaining coins in the bag and the coins got doubled again. He took out all the coins and gave few coins to third beggar. There were no coins left with him when he gave coins to third beggar and he gave equal number of coins to each beggar. What is the minimum number of coins the pilgrim had initially? How many coins did he gave to each beggar?
Assume that the pilgrim had X coins initially and he gave Y coins to each beggar.
 
 
From the above figure, there are (8X - 7Y) coins left with pilgrim after giving coins to third beggar. But it is given that there were no coins left with him at the end. It means that (8X - 7Y) = 0, so we get 8X = 7Y.
The minimum values of X and Y are 7 and 8 respectively to satisfy above equation. Hence, the pilgrim had 7 coins and he gave 8 coins to each beggar. In general, the pilgrim had 7N coins initially and he gave 8N coins to each beggar, where N = 1, 2, 3, 4, .....

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