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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # M61-22  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6499 GMAT 1: 760 Q51 V42 GPA: 3.82 M61-22 [#permalink] ### Show Tags 18 Jun 2018, 04:27 00:00 Difficulty: (N/A) Question Stats: 100% (01:10) correct 0% (00:00) wrong based on 3 sessions ### HideShow timer Statistics 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. $$|x-2.1| < 1.06$$ _________________ 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$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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18 Jun 2018, 04:27
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 $$b = \frac{(5.36 – 3.24)}{2} = \frac{2.12}{2} = 1.06$$.

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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.
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Intern
Joined: 14 Jun 2018
Posts: 47
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14 Sep 2018, 06:15
hello,

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 &nbs [#permalink] 14 Sep 2018, 06:15
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# M61-22

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