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

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

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

Vinni

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Source: Beat The GMAT — Problem Solving | Thu Jan 23, 2014 8:44 am

dimochka: Senior | Next Rank: 100 Posts; Posts: 48; Joined: Mon May 23, 2011 9:18 amFollowed by: 4 members; Location: NYC; Thanked: 17 times; GMAT Score:770

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.

Please feel free to private message me with any questions; I don't check the forums regularly, whereas PMs go straight to my email.

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

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

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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