Problem Solving

Hello

Please help with the problem below (reproduced as is : Manhattan Book 1 Chapter 6, Page 83 Q1)

If x^2 = 11 then x = Sq root 11. Indicate whether the statement is true or false.

As per my understanding we must consider both positive and negative values for the exponent but for the purpose of the exam negative square root is out of the scope of the exam. Still the answer states FALSE : if x^2 = 11 then x could be either + Sq root 11 or - Sq root 11.

Please help. Thanks

Hi melguy.

From what I can see you provided the answer to your own question without realizing it.

Your information indicates that the x in x² = 11 could be negative or positive, while √11 is always positive.

Doesn't that answer your question?

You're right that the GMAT won't allow "negative square roots", but let's be sure to clarify what those are.

-√11 is a negative square root, but the GMAT is fine with this number.

√(-11) is a "negative square root", but the GMAT is NOT fine with this number.

The crucial difference comes when the negative sign is INSIDE the square root. Any √(negative) is not recognized by the GMAT, and can be ignored, but -√(positive) is fine.

So in your question, x² = 11 DOES have two solutions that the GMAT will recognize: x = √11 and x = -√11. But x² = -11 has NO solutions that the GMAT will recognize, since its roots are x = √-11 and x = -√-11.

It's also worth mentioning that the GMAT only recognizes positive square roots when the square root term appears. So

x² = 121

has two roots, x = 11 and x = -11.

But x = √121 only has ONE root, x = 11. This seems so random, but the GMAT will be consistent about it, so any time a √ appears, you only need to consider the nonnegative roots. (In other words, if a DS question says "x = √121", you can say that x has one and only one solution, x = 11.)

Hi Marty

I actually thought -√11 and √(-11) meant the same thing. Hence the confusion.

CC Matt: Thanks a lot for clearing out the confusion!