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

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

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27 Jan 2020, 01:51
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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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Re: If a, b are positive integers, what is the value of b?  [#permalink]

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27 Jan 2020, 02:12
Statement 1 alone is sufficient
2^2 7^3 = 1372
a=2; b=3

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

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27 Jan 2020, 19:58
Bunuel wrote:
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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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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27 Jan 2020, 20:05
(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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