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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 

Rakesh speaks truth only in the morning and lies in the afternoon, whereas Sanjay speaks truth only in the afternoon and lies in the morning. A says that B is Rakesh. Is it morning or afternoon and who is A - Rakesh or Sanjay?
Consider the following 4 possible answers:
It is Morning and A is Rakesh.
It is Morning and A is Sanjay
It is Afternoon and A is Rakesh
It is Afternoon and A is Sanjay
Thus, it is Afternoon and A can be Sanjay or Rakesh

There is a grid of 20 squares by 10 squares. How many different rectangles are possible? Note that square is a rectangle.
Total number of rectangles = (Summation of row numbers) * (Summation of column numbers)
Here there are 20 rows and 10 columns or vice versa. Hence, total possible rectangles
= (20 + 19 + 18 + 17 + 16 + .... + 3 + 2 + 1) * (10 + 9 +8 + 7 + .... + 3 + 2 + 1)
= (210) * (55)
= 11550

A man took a certain number of apples to the bazaar and sold some of them. The next day, through the orchid of his apples, the number left over had been doubled, and he sold the same number as the previous day. On the third day the new remainder was tripled, and he sold the same number as before. On the fourth day the remainder was quadrupled, and his sales the same as before. On the fifth day what had been left over were quintupled, yet he sold exactly the same as on all the previous occasions and so disposed of her entire stock. What is the smallest number of apples he could have taken to market the first day, and how many did he sell daily? Note that the answer is not zero.
Let's assume that he had N apples on the first day and he sold X apples everyday. Putting down the given information in the table as follows:
 

Days

Apples at the start of the day

Apples Sold

Apples Remaining

Day 1

N

X

N – X

Day 2

2N-2X

X

2N-3X

Day 3

6N-9X

X

6N-10X

Day 4

24N-40X

X

24N-41X

Day 5

120N-205X

X

120N-206X

 
It is given that he disposed of his entire stock on the fifth day. But from the table above, the number of apples remaining are (120N-206X).Hence,
120N - 206X = 0
120N = 206X
60N = 103X
The smallest value of N and X must be 103 and 60 respectively. Hence, he took 103 apples to market on the first day and sold 60 apples everyday.

Vinod had twenty-one hens, all but eleven died, how many hens is Vinod left with?
Eleven

A man builds a house with all 4 sides facing south. A bear walks past the house. What color is the bear?
White: the house is built directly on the North Pole.

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