What is the value of q ? (1) q = 9^(1/2) (2) |q| = 3

Question

What is the value of q ?

(1)  q = \sqrt{9}

(2) |q| = 3

Archit3110 · Answer

f

from 1: q= 3
sufficient

from 2; q can be + 0r -ve 3

Answer A

priyanknema · Answer

q cannot be -3 from point 1?

Bunuel · Answer

No.

\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 .

akkkk1 · Answer

Hi Bunuel,

Does this still hold true?

Bunuel · Answer

Do you think the rules of mathematics changed overnight?

akkkk1 · Answer

Nope, just wanted to clarify what the GMAT meant. Have seen it used in the other way in many places.

Bunuel · Answer

GMAT does not have its own math.

What is the value of q ? (1) q = 9^(1/2) (2) |q| = 3

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