What is the value of x? (1) |x| = 4. (2) x^2 = 16.

Question

What is the value of x?

(1) |x| = 4.

(2) x^2 = 16.

I want to know how B is not sufficient here. Isn't it a general rule that square root of any number is always positive?

Bunuel · Accepted Answer

What is the value of x?

(1) |x| = 4 --> x = 4 or x = -4. Not sufficient.

(2) x^2 = 16 --> the same here: x = 4 or x = -4. Not sufficient.

(1)+(2) Same two values from both: x = 4 or x = -4. Not sufficient.

Answer: E.

As for your question: when the GMAT provides the square root sign for an even root, such as  \sqrt{x}  or  \sqrt {x} , then the only accepted answer is the positive root.

That is,  \sqrt{16}=4 , NOT +4 or -4.  Even roots have only a positive value on the GMAT.

In contrast, the equation  x^2=16  has TWO solutions, +4 and -4.

Hope it's clear.

ashikaverma13 · Answer

I think I understood but one more thing. So if, the statement B had said x =  \sqrt{16}  then it would have been sufficient?

but what is the difference if I, on my own am taking a square root of the statement B. That is my confusion. If I take square root of the entire statement B then won't it be:

\sqrt{x^2}  =  \sqrt{16}  which, therefore, will lead to x =4?

unless I am doing something wrong by taking square root of the entire statement.

Skywalker18 · Answer

1.  \sqrt{16} =4 
The square root of a negative number is not a real number and is not tested on the GMAT.

2. x^2 = 16 
=> x = 4 or -4 
In this case , we have an exponent . If we square the number 4 , we get 16 . If we square the number - 4 , we get 16 .
Therefore, both numbers are possible values for x, because both make the equation true.

3.  \sqrt{x^2}  =  \sqrt{16}

Now squaring both sides, we get
x^2 = 16
the above is same as case 2 , thus x can have 2 values -> 4 and - 4

Cbirole · Answer

1. Value of X can be +4 or -4
2. Value of X can be +4 or -4 as 4^2=16 and (-4)^2=16
 Both are giving 2 different values and hence none is sufficient . Answer: E

AkshdeepS · Answer

(1) |x| = 4.

(2) x^2 = 16.

st 1: |x| means x = - 4 or x = 4 as "|x|" shows the distance of "x" from "0" on the number line is "4". And distance is always >= 0

So st 1 is insufficient

st 2: x^2 = 16

Value of exponent over the number shows the number of roots so, here "x" can take 2 values -4 & +4

So insufficient.

combining 1 & 2 do not give us any single value so (E)

gmatmo · Answer

isn't the root of x^2 = the absolute value of x therefore i thought you need to combine the ac...

Bunuel · Answer

Yes,  \sqrt{x^2}=|x| . Could not understand what you mean after that.

gmatmo · Answer

my question is because Root x^2 ->|x|-> |x| = 4 
whats wrong with this assumption.

Bunuel · Answer

Nothing wrong. The next step would be |x| = 4 --> x = 4 or x = -4. The same as we have in the solution above.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the value of x? (1) |x| = 4. (2) x^2 = 16.

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

What is the value of x? (1) |x| = 4. (2) x^2 = 16.

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