If m and n are integers greater than 1, is m^n>500?

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

If a question states “greater than”, then we should find the minimum value because all data are greater than the minimum. Considering condition 1), the minimum value is \(m^n=2^9=512>500\), so the answer is ‘yes’ and condition 1) is sufficient.

Condition 2)
If \(m = 2, n = 100\), then \(2^{100} > 500\) and the answer is ‘yes’.
If \(m = 2, n = 5\), then \(2^5 = 32 < 500\) and the answer is ‘no’.
Thus, condition 2) is not sufficient, since we don’t have a unique solution.

Therefore, A is the answer.

Answer: A

Statement One Alone:

n>8

We see that n is at least 9, and m is at least 2. Since 2^9 = 512 > 500, then m^n will certainly be greater than 500.

Statement one alone is sufficient.

Statement Two Alone

n>2m

We can’t determine whether m^n > 500 by knowing only that n > 2m. For example, if m = 2 and n = 5, then m^n = 2^5 = 32 is not greater than 500. On the other hand, if m = 3 and n = 7, then m^n = 3^7 = 2187 is greater than 500.

Statement two alone is not sufficient.

Answer: A

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Given that \(m\) and \(n\) are integers greater than 1 and we need to find is \(m^n>500\)?

Note that m and n are integers greater than 1
=> minimum value of m and n will be 2.

STAT 1: \(n>8\)
n > 8 => min value of n is 9
and minimum value of m = 2
=> Minimum value of \(m^n\) = \(2^9\) = 512 > 500
=> \(m^n>500\) ALWAYS
=> SUFFICIENT

STAT 2: \(n>2m\)
Minimum value of m = 2
=> n > 2*2 => n > 4
=> Minimum value of n is 5
=> Min value of n = 5
Min value of \(m^n\) = \(2^5\) = 32 < 500
There are some cases in which \(m^n\) < 500 and in some \(m^n\) > 500
NOT SUFFICIENT

So, Answer will be A
Hope it helps!

Watch the following video to learn the Basics of Exponents