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Math Expert V
Joined: 02 Sep 2009
Posts: 61358
If a, b are positive integers, what is the value of b?  [#permalink]

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Question Stats: 94% (00:59) correct 6% (01:21) wrong based on 17 sessions

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If a, b are positive integers, what is the value of b?

(1) $$2^a7^b=1,372$$

(2) $$a=2$$

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Joined: 11 May 2019
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Re: If a, b are positive integers, what is the value of b?  [#permalink]

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Statement 1 alone is sufficient
2^2 7^3 = 1372
a=2; b=3

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Math Revolution GMAT Instructor V
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Re: If a, b are positive integers, what is the value of b?  [#permalink]

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Bunuel wrote:
If a, b are positive integers, what is the value of b?

(1) $$2^a7^b=1,372$$

(2) $$a=2$$

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

Condition 1)
Since $$2^a \cdot 7^b = 1372 = 2^2 \cdot 7^3$$, we have $$a = 2$$ and $$b = 3$$.

Since condition 1) yields a unique solution, it is sufficient.

Condition 2)

Since there is no information about the variable $$a$$ in condition 2), condition 2) is not sufficient obviously.

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Re: If a, b are positive integers, what is the value of b?  [#permalink]

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(1) 2^a * 7^b = 1372 = 2^2 * 7^3
Therefore, a=2, b = 3
Sufficient

(2) a=2, but value of b cannot be calculated. Insufficient

A is correct Re: If a, b are positive integers, what is the value of b?   [#permalink] 27 Jan 2020, 20:05
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# If a, b are positive integers, what is the value of b?  