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GMAT Practice exam 2 - Inequalities

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by GMATGuruNY » Sun Jun 05, 2016 6:26 am
Which of the following inequalities has a solution set that, when graphed on the number line is a single line segment of finite length?

1. x�> 1
2. x³ ≤ 27
3. x² ≥ 16
4. 2 ≤ |x| ≤ 5
5. 2 ≤ 3x+4 ≤ 6
The equation of a line generally doesn't include exponents or absolute value.
Thus, the most linear-looking answer choice is E:

Answer choice E: 2 ≤ 3x+4 ≤ 6
Subtract 4 from each part:
-2 ≤ 3x ≤ 2
Divide each part by 3:
-2/3 ≤ x ≤ 2/3.

-2/3 ≤ x ≤ 2/3 includes every value between -2/3 and 2/3, inclusive.
This range has two ENDPOINTS: -2/3 and 2/3.
Thus, when graphed on the number line, the solution set will yield a line segment with these two endpoints -- in other words, a line segment of FINITE LENGTH.

The correct answer is E.
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by [email protected] » Sun Jun 05, 2016 9:08 am
Hi lucas211,

There's a full discussion of this question here:

https://www.beatthegmat.com/value-of-x-t280194.html

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by Brent@GMATPrepNow » Sun Jun 05, 2016 10:23 am
Mitch's solution is great.
I'll only add that this is one of those questions that require us to check/test the answer choices. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top. For more on this strategy, see my article: https://www.gmatprepnow.com/articles/ha ... -questions

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by Matt@VeritasPrep » Tue Jun 07, 2016 10:59 pm
Another approach:

1:: Infinite
2:: Infinite
3:: Infinite
4:: Finite, but there are TWO lines here (2 ≤ x ≤ 5 and -2 ≥ x ≥ -5)

so by process of elimination, it must be E.
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