In reply to below:
VeritasKarishma wrote:
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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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.
.