Advanced GMAT Quant ebook

[ricardocs84]

Hello:

Just wondering if the solution of the problem: Try-It#3-4, on the ebook version of The Advanced GMAT Quant Guide (page 58) is correct.

Is x=1?

(1)x^2=1/x^2
(2)x^2=1/x

Statement (1): Clearly insufficient (x could be 1 or -1)

But statement (2) could also be this algebraic equation:

x^3=1 so => x^3 - 1= 0

Thus

(x-1)(x^2+x+1)=0

So x=1 and the solution of the quadratic equation doesn't have real numbers solution (appliying the discriminant formulae).

In this case the the statement (2) may not be sufficient, and the answer will be (E), instead of (B).

Please confirm what I missing,

Thanks in advance,

[RonPurewal]

all gmat problems, everywhere, all the time, are limited to real numbers only. (this condition is stated in the official guide, as well as in the introductory material to the math section of the real test.)

you should disregard "complex numbers" and "imaginary numbers" entirely. in fact, you should just go ahead and pretend that you've never heard of those things before.

[ricardocs84]

Ok Ron thanks for your response, but in this case, if this algebraic formula (a^3- b^3)= (a-b)(a^2+ab+b^2) is applied to the statement (2) x^2=1/x, this expression is obtained: (x-1)(x^2+x+1)=0, wherein the non-real numbers are from the second part [ (x^2+x+1)].

So in this particular case if the problem is tackled with the algebraic formula above mentioned, what is the best approach to follow?:

1. Is safe to conclude that X^3=1 is X=1 (getting the cubic root of both parts) , because with the other method one will arrive to a dead end?

2. Or this part (x^2+x+1) of the equation should be ignored and the answer will be equating (x-1) to zero?

I will appreciate your feedback and what I'm overlooking,

Sorry for the annoyance,

[tim]

yes. ignore the quadratic because it yields complex number solutions, as Ron said..