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# Which of the following is true if -3<x<9?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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Which of the following is true if -3<x<9?  [#permalink]

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15 Nov 2017, 01:54
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Difficulty:

5% (low)

Question Stats:

88% (01:03) correct 12% (01:16) wrong based on 175 sessions

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[GMAT math practice question]

Which of the following is true $$if -3<x<9$$?

A. $$|x-3|<4$$
B. $$|x-3|<5$$
C. $$|x-3|<6$$
D. $$|x-3|>4$$
E. $$|x-3|>5$$

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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" Retired Moderator Joined: 25 Feb 2013 Posts: 1196 Location: India GPA: 3.82 Which of the following is true if -3<x<9? [#permalink] ### Show Tags 15 Nov 2017, 01:59 2 MathRevolution wrote: [GMAT math practice question] Which of the following is true $$if -3<x<9$$? A. $$|x-3|<4$$ B. $$|x-3|<5$$ C. $$|x-3|<6$$ D. $$|x-3|>4$$ E. $$|x-3|>5$$ $$-3<x<9$$, add both sides of the inequality $$-3$$ $$=> -6<x-3<6$$ or $$|x-3|<6$$ Option C Senior SC Moderator Joined: 22 May 2016 Posts: 3080 Which of the following is true if -3<x<9? [#permalink] ### Show Tags 15 Nov 2017, 10:09 MathRevolution wrote: [GMAT math practice question] Which of the following is true $$if -3<x<9$$? A. $$|x-3|<4$$ B. $$|x-3|<5$$ C. $$|x-3|<6$$ D. $$|x-3|>4$$ E. $$|x-3|>5$$ 1) Find the distance between, then the midpoint of, the endpoints: $$9 -(-3) = 12$$ $$\frac{12}{2}$$= 6 = midpoint 2) Change the inequality so it relates to 6 and -6. Subtract 3 from each side: (-3 - 3) < x < (9 - 3) -6 < x < 6 3) The -3 becomes part of the absolute value expression: -6 < |x - 3| < 6, or |x - 3| < 6 The last step just takes the two cases created by the absolute value inequality |x - 3| < 6, and combines them. That is, -6 < |x - 3| < 6 says "the absolute value of something is less than 6 (and absolute value is nonnegative)," so change it to |x - 3| < 6 To check: The two cases for |x - 3| < 6 are LHS: x - 3 > - 6 RHS: x - 3 < 6 Combined: -6 < x - 3 < 6 -3 < x < 9 = original. Correct Answer C _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Tell me, what is it you plan to do with your one wild and precious life? -- Mary Oliver Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7612 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following is true if -3<x<9? [#permalink] ### Show Tags 17 Nov 2017, 01:22 => |x-a|<b ⟺ -b < x – a < b ⟺ a - b < x < a + b So, a is the midpoint of the end points a – b and a + b, and b is half the distance between the end points a – b and a + b. The midpoint of -3 and 9 is $$\frac{[(-3)+9]}{2} = \frac{6}{2} = 3$$. So, $$a = 3$$. Since the distance between -3 and 9 is 12, $$b = \frac{12}{2} = 6$$. Thus, |x-3| < 6. Therefore, the answer is C. Answer: C _________________ 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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Which of the following is true if -3<x<9?  [#permalink]

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09 Mar 2018, 05:53
MathRevolution wrote:
[GMAT math practice question]

Which of the following is true $$if -3<x<9$$?

A. $$|x-3|<4$$
B. $$|x-3|<5$$
C. $$|x-3|<6$$
D. $$|x-3|>4$$
E. $$|x-3|>5$$

You can use estimate here:

Add the ranges given and divide by 2 i.e., (9 + 3)/ 2 = 6

Only answer choice which has 6 at RHS is (C).

This method will work if we have all different number at RHS of inequality, but you can certainly narrow down your choices by this method.

Regular method is to Use POE and eliminate every answer choices.
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Which of the following is true if -3<x<9?   [#permalink] 09 Mar 2018, 05:53
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