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M61-22

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Math Revolution GMAT Instructor
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M61-22  [#permalink]

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New post 18 Jun 2018, 04:27
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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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Re M61-22  [#permalink]

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New post 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 \(b = \frac{(5.36 – 3.24)}{2} = \frac{2.12}{2} = 1.06\).


Answer: B
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Re: M61-22  [#permalink]

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