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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6390
GMAT 1: 760 Q51 V42
GPA: 3.82
If a and b are non-negative integers, ab=?  [#permalink]

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03 Jul 2016, 17:37
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Difficulty:

55% (hard)

Question Stats:

61% (01:28) correct 39% (01:40) wrong based on 131 sessions

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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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Joined: 22 Jun 2016
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Re: If a and b are non-negative integers, ab=?  [#permalink]

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03 Jul 2016, 21:39
1
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!

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6390
GMAT 1: 760 Q51 V42
GPA: 3.82
If a and b are non-negative integers, ab=?  [#permalink]

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05 Jul 2016, 21:06
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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21 Nov 2017, 23:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If a and b are non-negative integers, ab=? &nbs [#permalink] 21 Nov 2017, 23:31
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