Hi Anik89,

For a number to be perfectly divisible by another number, the number in the denominator needs to cancel out completely with whatever number is present in the numerator. For e.g. 8/2 = 4, here 2 gets cancelled out leaving a denominator of 1.

Factorizing 24 we get 2^3 * 3. We need to cancel out the three 2's and one 3 with the numerator, so the numerator needs to have a minimum of three 2's and one 3. The numerator here is n^3, so the

minimum possible value of n such that n^3 is perfectly divisible by 24 is

n = 2 * 3. Notice that if n = 2 * 3, n^3 gives us 2^3 * 3^3 which cancels out the denominator of 24 (2^3 * 3).

Since the

minimum possible value of n is 6, the number that will

ALWAYS divide n out of the five answer choice is 6.

The best way to solve questions similar to this is to always find out the minimum value of the variable in the numerator which cancels out the denominator completely.

Hope this helps!

CrackVerbal Academics Team

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