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Official prep test on Inequalities

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by Brent@GMATPrepNow » Thu Nov 05, 2015 12:43 pm
Which inequality solution set, when graphed on the number line, is a single line segment of finite length?

A) x� ≥ 1
B) x³ ≤ 27
C) x² ≥ 16
D) 2 ≤ |x| ≤ 5
E) 2 ≤ 3x + 4 ≤ 6
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.beatthegmat.com/mba/2014/09/ ... -questions

E) 2 ≤ 3x + 4 ≤ 6
Subtract 4 from all sides to get: -2 ≤ 3x ≤ 2
Divide all sides by 3 to get: -2/3 ≤ x ≤ 2/3
So, x can have any value from -2/3 to 2/3
So, if we were to graph the possible values of x, the line segment would have a FINITE length.

Answer: E

Cheers,
Brent
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by manik11 » Thu Nov 05, 2015 1:38 pm
Brent@GMATPrepNow wrote:
Which inequality solution set, when graphed on the number line, is a single line segment of finite length?

A) x� ≥ 1
B) x³ ≤ 27
C) x² ≥ 16
D) 2 ≤ |x| ≤ 5
E) 2 ≤ 3x + 4 ≤ 6
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.beatthegmat.com/mba/2014/09/ ... -questions

E) 2 ≤ 3x + 4 ≤ 6
Subtract 4 from all sides to get: -2 ≤ 3x ≤ 2
Divide all sides by 3 to get: -2/3 ≤ x ≤ 2/3
So, x can have any value from -2/3 to 2/3
So, if we were to graph the possible values of x, the line segment would have a FINITE length.

Answer: E

Cheers,
Brent
Brent..Is D incorrect because we get two separate line segments with the absolute value of X while the prompt asks for a single line segment?

Thanks!
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by Brent@GMATPrepNow » Thu Nov 05, 2015 2:10 pm
manik11 wrote: Brent..Is D incorrect because we get two separate line segments with the absolute value of X while the prompt asks for a single line segment?

Thanks!
Yes, exactly.

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Brent
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