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Data Sufficiency (DS) | If A is an integer, what is the value of A?

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If A is an integer, what is the value of A = ?

S1:
1, 000, 000 < (23)^A < 10,000,000

(10)^6 < (23)^A < (10)^7

A positive integer (23) raised to an exponent must be between two positive integers as per statement 1. Thus, exponent A must be a positive integer.

assume (in an alternate universe) (23)^k is equal to the next lowest power of the lower boundary:

Assume (23)^k = (10)^5 = 100,000

If we were to increase the power by +1, the next consecutive integer, we would
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