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Inequalities and root

This topic has 1 expert reply and 0 member replies

Inequalities and root

Post Sat Sep 16, 2017 11:02 am
If √x is an integer, what is the value of √x?
(1) 11 (2) 2<√x<5
________________________________________________________________
A. EACH statement ALONE is sufficient.
B. Statements (1) and (2) TOGETHER are NOT sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
E. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

OA is d.

How best can we determine statement 2 is sufficient

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Top Reply
Post Sun Sep 17, 2017 7:52 am
Roland2rule wrote:
If √x is an integer, what is the value of √x?
(1) 11 < x < 17
(2) 2 <√x < 5
Target question: What is the value of √x?

Given: √x is an integer
This tells us that x is the SQUARE of an integer
So, some possible values of x include: 1, 4, 9, 16, 25, 36, 49, etc

Statement 1: 11 < x < 17
Since 16 is the only square of an integer that's between 11 and 17, we know that x = 16
If x = 16, then √x = 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 2 <√x < 5
This statement is NOT sufficient.
Since √x is an integer, then √x can equal EITHER 3 OR 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

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