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(1) The only perfect square in this range is 16. So √x can be +4 or -4. Not Sufficient. (2) The possible values for √x are 3 and 4. Not sufficient.

Combining (1) and (2), we get √x = 4. Ans C

Am I missing something?

Square root function cannot give negative result.

Any nonnegative real number has a unique non-negative square root called the principal square root and unless otherwise specified, the square root is generally taken to mean the principal square root.

When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root.

That is, \(\sqrt{25}=5\), NOT +5 or -5. In contrast, the equation \(x^2=25\) has TWO solutions, +5 and -5. Even roots have only non-negative value on the GMAT.

Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{-64} =-4\).
_________________

Thanks. i was bit confused with (2). sqrt(x) is an integer not x itself hence sqrt(x) can be 3 or 4 with x non-integer and integer respectively.
_________________

My dad once said to me: Son, nothing succeeds like success.

Re: If x is an integer, what is the value of x? (3) [#permalink]

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17 May 2011, 13:12

IEsailor wrote:

If √x is an integer, what is the value of √x? (1) 11<x<17 (2) 2<√x<5 ________________________________________________________________ A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.

\(\sqrt{x}\) is an integer means x is also an integer. (1) 11<x<17 x can be 12,13,14,15,16. But, only 16 will incur an integral root. Thus; x=16 and \(\sqrt{x}=4\) Sufficient.

(2) 2<\(\sqrt{x}\)<5 \(\sqrt{x}\) can be either 3 or 4. Not Sufficient.

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