If √m is an integer, what is the value of √m?

Question

(1) 13 ≤ m ≤ 16
(2) 3 ≤ √m ≤ 4

GMATinsight · Answer

Given:  √m = Integer

Question : what is the value of √m?

Statement 1 : 13 ≤ m ≤ 16

i.e.  √13 ≤ √m ≤ √16

i.e.  3.6 ≤ √m ≤ 4

Only possible integer value of  √m = 4 
i.e. m = 16
SUFFICIENT

Statement 2 :  3 ≤ √m ≤ 4

i.e. m may be 9 or 16 and  √m  may be 3 or 4 hence

NOT SUFFICIENT

Answer: Option A

EgmatQuantExpert · Answer

Solution

Given:  
 • √m is an integer

To find:  
 • The value of √m

Analysing Statement 1  
From the information given in statement 1, 13 ≤ m ≤ 16.

• As √m is an integer, m must be a perfect square. 
In the given range 13 ≤ m ≤ 16, only one perfect square exists, which is 16.

Therefore, we can find unique value of √m.

Hence, statement 1 is sufficient.

Analysing Statement 2  
From the information given in statement 2, 3 ≤ √m ≤ 4.
 • From this statement, we can say √m can be either 3 or 4.

Hence, statement 2 is not sufficient.

The correct answer is option A.

Answer: A

mitrakaushi · Answer

But root m could be both +4 and -4. We wont get a unique solution. Why is A sufficient?

sheen22 · Answer

I have the same confusion.  Bunuel , Could you please clarify ?

Bunuel · Answer

\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 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 .

sheen22 · Answer

Thank you so much for the response, Bunuel! It was really helpful.

If √m is an integer, what is the value of √m?

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