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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 

Stranded on a deserted island, Harry Puttar is left with only a 40 litres container of milk. To conserve his milk he decides that on the first day he will drink one litre of milk and then refill the container back up with water. On the 2nd day he will drink 2 litres and refill the container. On the 3rd day he will drink 3 litres and so on... By the time all the milk is gone, how much water has he drunk?
It is given that the man has 40 litres container of milk. Also, he will drink 1 litre on the first day and refill the container with water, will drink 2 litres on the second day and refill the container, will drink 3 litres on the third day and refill the container, and so on till 40th day. Thus at the end of 40 days, he must have drunk (1 + 2 + 3 + 4 + ..... +38 + 39 + 40) = 820 litres of liquid.
Out of those 820 litres, 40 litres is the milk which he had initially. Hence, he must have drunk 780 litres of water.

You have six 8's and you may use any of the (+, -, /, ×, .) as many times as you like. How many arithmetical expressions which use the six 8's to form 1000 are possible?

There are 3 such expressions.

 (888/.888) = 1000

(8/.8) × (8/.8) × (8/.8) = 1000

 (888-88)/.8 = 1000

What is the four-digit number in which the first digit is 1/4 of the second, the third is the sum of the first and second, and the last is two times the second?
It is given that the first digit is 1/4 of the second. There are 2 such possibilities.
1 and 4
2 and 8
Now, the third digit is the sum of the first and second digits.
1 + 4 = 5
2 + 8 = 10
It is clear that option 2 is not possible. So we are left with only one options. Also, the last digit is two times the second. Hence, the answer is 1458.

A 3 digit number is such that its tens digit is equal to the product of the other two digits which are prime. Also, the difference between its reverse and itself is 99. What is the sum of the three digits?
It is given that the two digits of the required number are prime numbers i.e. 2, 3, 5 or 7. Note that 1 is neither prime nor composite. Also, the third digit is the multiplication of the first two digits. Thus, hundreds digit and units digit must be either 2 or 3 i.e. 2_2, 2_3, 3_2 or 3_3 which means that there are four possible numbers - 242, 263, 362 and 393.
Now, it is also given that - the difference between its reverse and it is 99. So 263 and 362 satisfy this condition. Hence, the sum of the three digits is 11 in each case.

One side of the bottom layer of a triangular pyramid has 11 balls. How many are there in the whole pyramid? Note that the pyramid is equilateral and solid.
As there are 11 balls along one side, it means that there are 11 layers of balls. The top most layer has 1 ball. The second layer has 3 (1+2) balls. The third layer has 6 (1+2+3) balls. The fourth layer has 10 (1+2+3+4) balls. The fifth layer has 15 (1+2+3+4+5) balls. Similarly, there are 21, 28, 36, 45, 55 and 66 balls in the remaining layers.
Hence, the total number of balls is = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 = 286 balls

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