If x and y are integers, is 3^x(0.5)^y< 1 ? (1) y=2 x. (2) x=8.

Correct Answer is : Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

Either statement BY ITSELF is sufficient to answer the question.

Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

GMAT Quantitative Reasoning Practice Test 6

Question : 79 of 100

Marks: +1, -0

x

and

y

are integers, is

3^x(0.5)^y< 1

?
(1)

y=2 x

.
(2)

x=8

Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
Either statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

Validate

Solution:

Use statement (1) to write the expression:

3^x(0.5)^{2 x}=(0.75)^x

the value of this expression can be either smaller or larger than 1 , if

x

was only a positive integer the answer would be distinct.
Use statement (2) alone to write the expression:

3^8(0.5)^y

this expression is either bigger or smaller than 1 . Use both statements together:

(0.75)^8< 1

. Therefore, both statements are needed to answer the question.

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