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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Which of the following inequalities holds if 3.24<x<5.36?  [#permalink]

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08 Feb 2018, 00:13
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[GMAT math practice question]

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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" examPAL Representative Joined: 07 Dec 2017 Posts: 1154 Re: Which of the following inequalities holds if 3.24<x<5.36? [#permalink] ### Show Tags 08 Feb 2018, 03:22 2 1 MathRevolution wrote: [GMAT math practice question] Which of the following inequalities holds if $$3.24<x<5.36$$? $$A. |x+4.3|<1.06$$ $$B. |x-4.3|<1.06$$ $$C. |x-2.1|<0.53$$ $$D. |x+2.1|<0.53$$ $$E. |x-2.1|<1.06$$ As the question ask about the range for which an inequality is true, we'll test the extreme values. This is a Logical approach. (A) If x = 3.24 then |x + 4.3| is larger than 7, so it is definitely larger than 1.06. Eliminated. (B) If x = 3.24 then |x - 4.3| is exactly 1.06 so x > 3.24, means |x - 4.3| < 1.06 Let's try the other extreme: If x = 5.36 then |x - 4.3| is exactly 1.06 so x < 5.36, means |x - 4.3| < 1.06 We have our answer! (B) is our answer. _________________ Retired Moderator Joined: 25 Feb 2013 Posts: 1130 Location: India GPA: 3.82 Re: Which of the following inequalities holds if 3.24<x<5.36? [#permalink] ### Show Tags 08 Feb 2018, 08:36 1 MathRevolution wrote: [GMAT math practice question] Which of the following inequalities holds if $$3.24<x<5.36$$? $$A. |x+4.3|<1.06$$ $$B. |x-4.3|<1.06$$ $$C. |x-2.1|<0.53$$ $$D. |x+2.1|<0.53$$ $$E. |x-2.1|<1.06$$ as $$x$$ is a positive number greater than $$3.24$$, so adding any positive number will further increase the value. Hence options A & D can be eliminated because adding positive number to $$x$$ will not yield a positive number lower than $$3.24$$ Option C & E have same LHS we have $$x>3.24$$ subtract $$2.1$$ from both sides to get $$x-2.1>3.24-2.1 => x-2.1>1.14$$ so $$|x-2.1|$$ can never be less than $$0.53$$ or $$1.06$$, hence eliminate option C & E Option B Math Expert Joined: 02 Aug 2009 Posts: 8296 Re: Which of the following inequalities holds if 3.24<x<5.36? [#permalink] ### Show Tags 08 Feb 2018, 09:01 MathRevolution wrote: [GMAT math practice question] Which of the following inequalities holds if $$3.24<x<5.36$$? $$A. |x+4.3|<1.06$$ $$B. |x-4.3|<1.06$$ $$C. |x-2.1|<0.53$$ $$D. |x+2.1|<0.53$$ $$E. |x-2.1|<1.06$$ Hi... Modulus does not mean anything except at B.. Others can be taken as normal equation.. One way will be to take 4 or 5 as the value.. Only B.. x-4.3 that is 5-4.3=0.7<1.6 stands The choices itself give you answer.. X is positive, so when you add something POSITIVE to it, the value has >that POSITIVE value.. So x+4.3<1.06 and X+2.1<0.53 can be discarded. In all choices, x-4.3 is the smallest as we are subtracting max amount of 4.3 from a positive value x.. So if any other choice matches, even x-4.3 will be true..but we can't have two Answers.. So ans x-4.3 _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8722 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following inequalities holds if 3.24<x<5.36? [#permalink] ### Show Tags 11 Feb 2018, 16:59 => 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 $$b = \frac{( 5.36 – 3.24 )}{2} =\frac{2.12}{2} = 1.06.$$ Therefore, B is the answer. 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$79 for 1 month Online Course"
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Re: Which of the following inequalities holds if 3.24<x<5.36?  [#permalink]

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08 Jun 2019, 21:44
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Re: Which of the following inequalities holds if 3.24<x<5.36?   [#permalink] 08 Jun 2019, 21:44
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