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If x^3 < 16x which of the following includes

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by vinni.k » Thu Jan 23, 2014 8:44 am
If x^3 < 16x which of the following includes at least some of the possible solutions for x, but no values that are not solutions?
A. |x| < 4
B. x < 4
C. x > 4
D. x < -4
E. x > 0

OA is D

I got the two ranges x<-4 and 0<x<4. But I am not able to understand the underlined part of the question. What does this mean at least some of the possible solutions for x, but no values that are not solutions

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by dimochka » Thu Jan 23, 2014 10:33 am
As there is no answer choice that will encompass all of the possible solutions for x, the question is asking you to pick the portion that will definitely include a range that is fully composed of possible solutions for x, but does not necessarily include every single answer for x.

So, for example, an answer of x<-5 would also work, as would 1<x<3. Let me know if this makes sense.
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by [email protected] » Thu Jan 23, 2014 1:06 pm
Hi vinni.k,

This question includes some language that is uncommon for the GMAT, but the phrase you mentioned means that you need to find an answer that includes SOME of the possible correct numbers but NO incorrect numbers.

With the given info x^3 < 16x, there are a couple of obvious incorrect numbers (x CANNOT = 0 and x CANNOT = 4) and some other incorrect numbers that we'll get to in a moment. With this info, we can eliminate some of the options, notably A (it includes 0), B (it includes 0) and E (it includes 4).

Between C and D, we have to do a bit more work to see which answer includes numbers that are incorrect.

With answer C, x could = 5, BUT x =5 doesn't fit the given inequality, so we can eliminate C.

Final Answer: D

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