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]

17 Feb 2013, 20:58

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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]

17 Feb 2013, 21:53

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]

18 Feb 2013, 21:41

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] 18 Feb 2013, 21:41

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

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