The tip on Page 14 of GMAT Club Math Book, highlighted in bold, states:

"Even roots have only a positive value on GMAT".

Where did the above statement originate?

Solving Question 191 in GMAT Review 13th Edition requires:

\(x - 1 = \sqrt{400}\)
\(x = -19\)

The two sources appear to contradict each other. If I look closer, GMAT Club Math Book also gives conditions such as,

"When the GMAT provides the square root sign..."

In Q.191, the sign is added while solving the problem, so is exempt from the tip. I tentatively suggest that printing conditional tips introduces a risk rather than remove one.

The question actually states:

If \((x-1)^2 = 400\), what is the value of \((x-5)\)?

Now I understand the general idea is to take a square root of both sides, but that action isn't the right way to proceed. The approach should be:

\((x-1)^2 = 400\)
=> \((x-1)^2 - 20^2 = 0\)
=> \((x-1-20)(x-1+20) = 0\)
=> \((x+19)(x-21) = 0\)

Hence the value of x can be -19 or 21. Now, using the same x-5 can be -24 and 16. Out of the two only -24 is under the answer choices. Hence the answer is [C]. GMAT always considers the positive value of a square root i.e\(\sqrt{x^2} = |x|\) always. Please refer to the below threads if you have further queries:

http://gmatclub.com/forum/confusion-on-square-roots-127807.html
http://gmatclub.com/forum/a-square-root-has-only-one-value-134601.html

Hope the above explanation helps!

Regards,
A

Thank you. I retract the word "requires" in my opening post.

How can you define which is the right way to proceed?

I always thought maths is maths: as long as it's done without error, there is no right or wrong approach. Using \(\sqrt{400} +1 = -19 or +21\) to derive the answer is the quickest and most direct approach (imho). I find that using roots is less prone to error because there are fewer steps and less to write down - but I doubt everyone is wired the same.

GMAT does not test approaches, only answers.

It seems to me the \(\sqrt{25} = +5\) is a house rule when writing questions, and I'm fine with any rules until those rules change without notice.

My friend, the reason that I mentioned that your method is not the correct way is that, when GMAT provides the square root sign for an even root, such as \sqrt{x} or \sqrt[4]{x}, then the only accepted answer is the positive root. In such a case \sqrt{400} would only be 20 and not {20,-20}. The solution to the equation \sqrt{x^2} = |x| i.e. the positive value only.

Now the method used by you is not wrong, but clearly the approach is not suited for GMAT-based questions. I am just echoing the concept which has been time and again elaborated very elegantly by several members in this community. If you do end up using the same concept over a different and rather complicated question, I would certainly wont want you to get it wrong just because of this. I'd request you to go through some of the reading material available at the forum, and some wonderful posts by Bunuel. I have mentioned some threads already in my previous post. I understand that end result is important, but the way we reach it is even more critical As it is said, The path walked is more important than the destination.- Corinthians 9:24 -

Regards,
A

hi ! everyone,
i am going to start GMAT so that will you please give me the links where I would find thousands Math practice questions?

Here you go!

http://gmatclub.com/forum/gmat-ps-question-directory-by-topic-difficulty-127957.html

You can find similar links for the DS and the verbal section as well. Have fun and best of luck!

Regards,
A