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# M61-22

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

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18 Jun 2018, 05:27
00:00

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. $$|x-2.1| < 1.06$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7372 GMAT 1: 760 Q51 V42 GPA: 3.82 Re M61-22 [#permalink] ### Show Tags 18 Jun 2018, 05:27 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
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Joined: 14 Jun 2018
Posts: 47
Location: India
Concentration: International Business, Marketing
Re: M61-22  [#permalink]

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14 Sep 2018, 07:15
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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