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If a and b are non-negative integers, ab=?

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If a and b are non-negative integers, ab=? [#permalink]

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New post 03 Jul 2016, 16:37
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If a and b are non-negative integers, ab=?
1) 9^a=3^b
2) 5^a=2^b

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[Reveal] Spoiler: OA

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Re: If a and b are non-negative integers, ab=? [#permalink]

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New post 03 Jul 2016, 20:39
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Statement 1) 9^a=3^b

We get 3^2a = 3^b
So, 2a=b.

Insufficient!

2) 5^a=2^b

5^(anything>0) will be an odd number and 2^(anything > 0) will be an even number.

So, if 5^a=2^b, then a=b=0 ----> ab=0.

Sufficient!

Answer will be B.

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If a and b are non-negative integers, ab=? [#permalink]

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New post 05 Jul 2016, 20:06
From the original condition, there are 2 variables. Hence, there is a high chance that C is the correct answer. However, since this is an integer question, one of key questions, we should apply the common mistake type 4(A). From con 1), we get 2a=b. The answer is not unique and the condition is not sufficient. In case of con 2), we get a=b=0. The answer is unique and the condition is sufficient. Hence, the correct answer is B.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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Re: If a and b are non-negative integers, ab=? [#permalink]

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New post 21 Nov 2017, 22:31
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Re: If a and b are non-negative integers, ab=?   [#permalink] 21 Nov 2017, 22:31
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If a and b are non-negative integers, ab=?

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