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If g(x) = 3x + x^(1/2)...

by StephanieX378 Fri Sep 08, 2017 5:12 pm


This is MGMAT Guide #2, 6th edition, Algebra, regarding Question 7 of the Chapter 12 problem set (page 179). (Please note I'm using "^(1/2)" instead of the root sign in reproducing this question - can't figure out how to type a root sign!)

"If g(x) = 3x + x^(1/2), what is the value of g(d^2 + 6d + 9)?"

The solution on page 182 says "3d^2 + 19d + 30 OR 3d^2 + 17d + 24."

I understand how to arrive at the first solution, but the explanation for the second solution reads:

g(d^2 + 6d + 9) = 3(d^2 + 6d + 9) + (d^2 + 6d + 9)^(1/2)
= 3d^2 + 18d + 27 + ((d+3)^2)^(1/2)
= 3d^2 + 18d + 27 - (d+3)
= 3d^2 + 17d + 24

However, back on page 71, we covered that "If a given equation contains a square root symbol on the GMAT, only use the positive root." This second possible solution above seems to use the negative root of ((d+3)^2)^(1/2). (Again, noting that the problem uses a square root symbol, not the "raised to the one-half" way I'm noting it here. What am I missing here? Shouldn't we have only considered the positive root?

Thanks in advance!
Sage Pearce-Higgins
ManhattanGMAT Staff
Posts: 233
Joined: Thu Apr 03, 2014 4:04 am

Re: If g(x) = 3x + x^(1/2)...

by Sage Pearce-Higgins Tue Sep 12, 2017 10:00 am

First of all, this isn't an actual GMAT problem, so there's no guarantee that we'll keep precisely within the exam format.

Second, don't misread the injunction on p71 as meaning "only consider positive square roots" - considering a negative square root is one of the recurring traps on the GMAT. We meant, that if a given equation has a square root symbol, then only consider the positive root. In the case of this problem, we made the equation by substituting (d^2 + 6d + 9) into the function, and therefore we should consider both square roots.

Actually, you should take issue with this problem for asking for a "value", when we can only get an algebraic expression.