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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
M61-22  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 100% (01:14) correct 0% (00:00) wrong based on 7 sessions

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Which of the following inequalities holds if $$3.24 < x < 5.36$$?

A. $$|x+4.3| < 1.06$$
B. $$|x-4.3| < 1.06$$
C. $$|x-2.1| < 0.53$$
D. $$|x+2.1| < 0.53$$
E. $$|x-2.1| < 1.06$$

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42 GPA: 3.82
Re M61-22  [#permalink]

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Official Solution:

Which of the following inequalities holds if $$3.24 < x < 5.36$$?

A. $$|x+4.3| < 1.06$$
B. $$|x-4.3| < 1.06$$
C. $$|x-2.1| < 0.53$$
D. $$|x+2.1| < 0.53$$
E. $$|x-2.1| < 1.06$$

The inequality $$|x - a| < b$$ is equivalent to the inequality $$a - b < x < a + b$$.

Note that a is the average of $$a – b$$ and $$a + b$$ and $$b$$ is half of the difference between $$a – b$$ and $$a + b$$, that is, $$b = \frac{(a + b ) – ( a – b )} {2}$$.

Thus, the inequality $$3.24 < x < 5.36$$ is equivalent to the inequality $$|x – 4.3 | < 1.06$$ since $$a = \frac{(3.24 + 5.36)}{2} = \frac{8.6}{2} = 4.3$$ and $$b = \frac{(5.36 – 3.24)}{2} = \frac{2.12}{2} = 1.06$$.

Answer: B
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Intern  B
Joined: 14 Jun 2018
Posts: 47
Location: India
Concentration: International Business, Marketing
Re: M61-22  [#permalink]

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hello,

can anyone please help in understanding the above concept of inequalities.

The inequality |x−a|<b|x−a|<b is equivalent to the inequality a−b < x <a+b.

also, How is this true: Note that a is the average of a–b and a+b and b is half of the difference between (a–b) and a+b, that is, b=(a+b)–(a–b)/2. Re: M61-22   [#permalink] 14 Sep 2018, 07:15
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# M61-22

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