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If ab≠0, is |a^b|=a^b?

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by Max@Math Revolution » Fri Jul 01, 2016 1:28 am
If ab≠0, is |a^b|=a^b?
1) |a|=a
2) |b|=b

*An answer will be posted in 2 days.
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Source: — Data Sufficiency |
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by 800_or_bust » Fri Jul 01, 2016 8:36 am
Max@Math Revolution wrote:If ab≠0, is |a^b|=a^b?
1) |a|=a
2) |b|=b

*An answer will be posted in 2 days.
(1) Sufficient. This implies that a is greater than or equal to zero. Since a is greater than or equal to zero, a raised to any power is also going to be greater than or equal to zero. The absolute value of a number that is greater than or equal to zero is equal to that number.

(2) Not sufficient. This implies that b is greater than or equal to zero. However, if b is an odd positive integer and a is negative, then this statement is false. If a is positive, or b is an even positive integer, then the statement is true. Since we cannot reach a definitive answer, this is insufficient.

Answer: A
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by Max@Math Revolution » Sun Jul 03, 2016 4:29 pm
If we modify the original condition and the question, the question becomes |a^b|=a^b? --> a^b≥0? --> a≥0?. Hence, the correct answer is A.

- 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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