If sqrt(x) is an integer, what is the value of sqrt(x)?

Question

If  \sqrt{x}  is an integer, what is the value of  \sqrt{x} ?

(1)  11 < x < 17

(2)  2 < \sqrt{x} < 5

BrentGMATPrepNow · Answer

Given :  \sqrt{x}  is an integer  
This information tells us that x must be a perfect square 
So, some possible values of x include   0, 1, 4, 9, 16, 25, ... .

Target question :    What is the value of  \sqrt{x} ?

Statement 1 :  11 < x < 17    
Since there's only one  perfect square  among the integers from 12 to 16 inclusive, we can be certain that x =  16 , which means the answer to the target question is   \sqrt{x}= \sqrt{16}= 4  
Statement 1 is SUFFICIENT

Statement 2 :  2 < \sqrt{x} < 5  
If we square all three values in the inequality we get:  4 < x < 25 
Since we already know that x is a  perfect square , we can see that there are TWO possible values of x in the given range. 
Let's consider both possible values of x:
 Case a :  x = 9 . In this case, the answer to the target question is   \sqrt{x}= \sqrt{9}= 3  
 Case b :  x = 16 . In this case, the answer to the target question is   \sqrt{x}= \sqrt{16}= 4  
Since we can’t answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

masip63 · Answer

Hi !

why are you not considering +-4 as possible solution of sqrt(16) ?

Thanks

Bunuel · Answer

When we have the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:

\sqrt{9} = 3 , NOT +3 or -3;
 \sqrt {16} = 2 , NOT +2 or -2.

\sqrt{...}  is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign ( \sqrt{...} ) always means non-negative square root.

https://gmatclub.com/forum/download/file.php?id=39502 
 The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
 When the GMAT (and generally in math) provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root.  That is:

\sqrt{9} = 3 , NOT +3 or -3;
 \sqrt {16} = 2 , NOT +2 or -2;

Notice that in contrast, the equation  x^2 = 9  has TWO solutions, +3 and -3. Because  x^2 = 9  means that  x =-\sqrt{9}=-3  or  x=\sqrt{9}=3 .

If sqrt(x) is an integer, what is the value of sqrt(x)?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If sqrt(x) is an integer, what is the value of sqrt(x)?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards