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}>1Notice 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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