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A and B are integers, is (0.5)^(AB) > 1?

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A and B are integers, is (0.5)^(AB) > 1? [#permalink] New post 17 Feb 2013, 19:58
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A and B are integers, is \((0.5)^{AB}>1\) ?

(1) A is positive integer and B is negative integer.

(2) A and B are two consecutive numbers.
[Reveal] Spoiler: OA

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Re: A and B are integers, is (0.5)^(AB) > 1? [#permalink] New post 17 Feb 2013, 20:53
Although each statement IS sufficient on its own,the statements are contradictory to each other... Are you sure the question is right?
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Re: A and B are integers, is (0.5)^(AB) > 1? [#permalink] New post 18 Feb 2013, 20:41
Expert's post
daviesj wrote:
A and B are integers, is \((0.5)^{AB}>1\) ?

1. A is positive integer and B is negative integer.

2. A and B are two consecutive numbers.


Is \((\frac{1}{2})^{AB}>1\)

Notice that when you raise 1/2 to a positive integer power, the value keeps going down.
(1/2)^2 = 1/4;
(1/2)^3 = 1/8;
(1/2)^4 = 1/16 etc

On the other hand, when you raise 1/2 to a negative integer power, you get a value greater than 1 in all cases
(1/2)^(-1) = 2
(1/2)^(-2) = 4
and so on...

When you raise (1/2) to 0, you get 1.

1. A is positive integer and B is negative integer.
This means that AB is a negative integer.
So (1/2)^AB will be greater than 1 in all cases. Answer is Yes. Sufficient.

2. A and B are two consecutive numbers.
The product of two consecutive integers will be either a positive integer or 0. In either case, (1/2)^AB will not be greater than 1. Answer is No. Sufficient.

Notice that the answer obtained from the two statements in definitive in each case but contradictory (statement 1 says yes, 2 says no). This does not happen in actual GMAT questions.
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Re: A and B are integers, is (0.5)^(AB) > 1? [#permalink] New post 24 Mar 2015, 20:01
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Re: A and B are integers, is (0.5)^(AB) > 1?   [#permalink] 24 Mar 2015, 20:01
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