If -x- andlt; 20 and -x andndash; 8- andgt; -x + 4-, which of the following expresses the allowable range for x?a)andndash;12 andlt; x andlt; 12b)andndash;20 andlt; x andlt; 2c)andndash;20 andlt; x andlt; andndash;12 and 12 andlt; x andlt; 20d)andndash;20 andlt; x andlt; andndash;8 and 4 andlt; x andlt; 20e)andndash;20 andlt; x andlt; andndash;4 and 8 andlt; x andlt; 20Correct answer is option 'B'. Can you explain this answer?

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GMAT Exam > GMAT Questions > If |x| < 20 and |x – 8| > |x + 4|...

If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses the allowable range for x?

a)
–12 < x < 12
b)
–20 < x < 2
c)
–20 < x < –12 and 12 < x < 20
d)
–20 < x < –8 and 4 < x < 20
e)
–20 < x < –4 and 8 < x < 20

Correct answer is option 'B'. Can you explain this answer?

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If |x| < 20 and |x – 8| > |x + 4|, which of the following ...

Some folks might think this involves a sophisticated calculation, but much of this can be done with simple spatial analysis. Look at the second inequality, the more complicated one: |x – 8| > |x + 4|. All this says is that we are looking for points such that the distance to x = 8 is greater than the distance from x = –4; in other words, we want all the points that are closer to x = –4 and farther from x = 8.

The midpoint between x = –4 and x = 8 is the point x = 2. This point is not included because it’s equidistant from both points, but everything to the left of this point on the number line is closer to x = –4 than it is to x = 8. That entire complicated inequality simplifies to x < 2.

Combine that with the first inequality, |x| < 20, which in the negative realm means that x must be greater than –20. Thus, the allowed region is –20 < x < 2.

Answer = (B)

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If |x| < 20 and |x – 8| > |x + 4|, which of the following expresses the allowable range for x?a)–12 < x < 12b)–20 < x < 2c)–20 < x < –12 and 12 < x < 20d)–20 < x < –8 and 4 < x < 20e)–20 < x < –4 and 8 < x < 20Correct answer is option 'B'. Can you explain this answer?

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