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

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

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New post 27 Jan 2020, 01:51
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A
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94% (00:59) correct 6% (01:21) wrong based on 17 sessions

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

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New post 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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New post 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) \(a=2\)



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.

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

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