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

Question

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.

MacFauz · Answer

Although each statement IS sufficient on its own,the statements are contradictory to each other... Are you sure the question is right?

KarishmaB · Answer

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.

shreyasvr · Answer

In reply to below:
 
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My view:

in statement 2, when they say 2 consecutive numbers, -1 and 0 can also be 2 consecutive numbers. So this statement alone is not sufficient to answer this question.

When the 2 consecutive numbers are -1,0 -- This results in value =1.
 0,1 -- This results in value <1.
 1,2 -- This results in value <1
 2,3 -- This results in value <1
 -1,-2-- This results in value >1

So the value is not giving us definitive answers. So,

Option A is the correct answer to this.

.

DSBlender · Answer

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

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

2. A and B are two consecutive numbers.

So:

Statement 1) AB = a negative number. Therefore, 0.5^(any negative number) will be 1/(0.5 ^ that number) which is always greater than 1. SUFFICIENT

Statement 2) A and B are two consecutive integers. Let's try three scenarios.

Scenario 1: Consecutive numbers -1 and -2. This means 0.5 will be raised to a positive number because AB will be positive. 0.5 raised to a positive number is less than 1. Okay, this answers the question. This answer is NOT greater than 1. 
Scenario 2: Consecutive numbers -1 and 0. This means 0.5 will be raised to 0, because AB will be 0. 0.5 raised to 0 is always 1. This answers the question. This answer is NOT greater than 1. 
Scenario 3: Consecutive numbers 1 and 2. This means 0.5 will be raised to 2, because AB will be 2. 0.5 raised to a positive number is less than 1. This answer is NOT greater than 1.

So, Statement 2) is also Sufficient. Correct answer must be D.

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

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