Square roots

[EasyTestIsEasy]

Hey, I am quite sure that I have read in an MGMAT guide, that square roots only have exactly one solution on the GMAT. I'm not quite sure if that was true on the CAT tests I took, though.

Consider the following question:

What is the value of x?

1) x^2 = 16

Would 1) alone be sufficient? If MGMAT is right, x should be 4 because the square root of 16 could only be 4. But if it's not true, it could be either 4 or -4 and therefore 1) would not be sufficient.

Hope you can help me!

[eagleeye]

Hi:

For any Data Sufficiency question, something is SUFFICIENT by itself only if it gives a unique value or answers a Yes/No question in a definite Yes/No.


Therefore 1) x^2 = 16 => x = +4 or -4; here, since x has two values, 1) is not sufficient.

[EasyTestIsEasy]

Hi:

For any Data Sufficiency question, something is SUFFICIENT by itself only if it gives a unique value or answers a Yes/No question in a definite Yes/No.


Therefore 1) x^2 = 16 => x = +4 or -4; here, since x has two values, 1) is not sufficient.

Thanks for your answer!

I am not sure if you really understood my question, though. I understand the concept of Data Sufficiency very well.
And I know that in proper mathematics, x^2= 16 has two solutions: 4 and -4

But, as stated above, I have read on a MGMAT guide (Number Properties, Chapter Roots), that on the GMAT, square roots have only one solution. In this case, x can only be 4 which makes 1) sufficient.

Also, are these two statements different?

1) x^2=16
2) x= squareroot of 16

[eagleeye]

Yes the two statements are in fact different.

x^2=16 means that x can be +4, -4 as you know already.
However x=sqrt(16) has only one answer which is 4.

so your MGMAT guide is right.

Another way of looking at it :

x^2 = 16 has two solutions x = - sqrt(16) and x = + sqrt(16). In both cases sqrt(16) gives us 4. However the +, - signs come from the power of x which is even.

Let me know if this helps

[EasyTestIsEasy]

Yes, that helps. Thank you very much.

[aneesh.kg]

More into square roots here:

https://www.beatthegmat.com/inequalities-t111308.html