Latest CAT Aptitude Question SOLUTION: You have 6561 balls. 1 is lighter than remaining. What is the minimum number of weighings required on a common balance to ensure that the odd ball is identified ? (a) 8 (b) 7 (c)

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(#M40010256) CAT question Keep an EYE

You have 6561 balls. 1 is lighter than remaining. What is the minimum number of weighings required on a common balance to ensure that the odd ball is identified ?

(a) 8 (b) 7 (c) 6 (d)5

Asked In CAT prashanthi (11 years ago)

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chaitanya sai kumar  (11 years ago)

For such questions power of 3 is used.

Let there be 3 balls, 1 out of them is heavy, minimum number of weighings to find the heavy ball is = 1

First take any 2 balls, if they are in balance => the 3rd ball is heavy.
if they are not in balance, we get the heavier ball.
Thus minimum number of weighings = 1

For 9 such balls, where 1 is heavy , it would be = 2 .
[ In the 1st weighing 3 balls on each side of balance. if they are in balance, another weighing with remaining 3 balls is required.
if they are not in balance, the heavier side having 3 balls is weighed again.]
Thus minimum number of weighings = 2

Similarly for 10-27 balls, minimum number of weighings = 3
28 - 81 balls, minimum number of weighings = 4
82 - 243 balls,minimum number of weighings = 5
244 - 729 balls, minimum number of weighings = 6
730 - 2187 balls, minimum number of weighings= 7
2188 - 6561 balls, minimum number of weighings = 8

Therefore, answer would be (a)8.

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Garima  (11 years ago)

8 weighings are reqd.
3^8 = 6561

Is this solution Helpfull? Yes | No (2)  

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