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

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by Max@Math Revolution » Sun Jul 03, 2016 4:37 pm
If a and b are non-negative integers, ab=?
1) 9^a=3^b
2) 5^a=2^b

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by 800_or_bust » Sun Jul 03, 2016 4:48 pm
Max@Math Revolution wrote:If a and b are non-negative integers, ab=?
1) 9^a=3^b
2) 5^a=2^b

*An answer will be posted in 2 days
(1) Not sufficient. b = 2a, or b=a=0.
(2) Sufficient. b=a=0. There are no integer pairs of a and b that could make this equation true except for the case where both a & b are zero (and thus both sides of the equation simply evaluate as 1).

Answer: B
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by Max@Math Revolution » Tue Jul 05, 2016 8:07 pm
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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