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# How many solutions has the equation ||x-3|-2|=1?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5593
GMAT 1: 800 Q59 V59
GPA: 3.82
How many solutions has the equation ||x-3|-2|=1? [#permalink]

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22 Jan 2018, 01:04
2
2
00:00

Difficulty:

55% (hard)

Question Stats:

58% (00:51) correct 42% (00:53) wrong based on 138 sessions

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[GMAT math practice question]

How many solutions has the equation ||x-3|-2|=1?

A. 0
B. 1
C. 2
D. 3
E. 4

_________________

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" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" PS Forum Moderator Joined: 25 Feb 2013 Posts: 1142 Location: India GPA: 3.82 How many solutions has the equation ||x-3|-2|=1? [#permalink] ### Show Tags 22 Jan 2018, 09:55 MathRevolution wrote: [GMAT math practice question] How many solutions has the equation ||x-3|-2|=1? A. 0 B. 1 C. 2 D. 3 E. 4 $$||x-3|-2|=1$$ $$=>|x-3|-2=1$$ or $$|x-3|-2=-1$$ $$=>|x-3|=3$$ or $$|x-3|=1$$ $$=>x-3=3$$ or $$x-3=-3$$ or $$x-3=1$$ or $$x-3=-1$$ therefore $$x=6$$ or $$0$$ or $$4$$ or $$2$$. hence $$4$$ solutions Option E Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2570 Re: How many solutions has the equation ||x-3|-2|=1? [#permalink] ### Show Tags 23 Jan 2018, 08:58 MathRevolution wrote: [GMAT math practice question] How many solutions has the equation ||x-3|-2|=1? A. 0 B. 1 C. 2 D. 3 E. 4 We see that |x-3| - 2 could be 1 or -1 since both |1| and |-1| are equal to 1. 1) If |x - 3| - 2 = 1, then |x - 3| = 3. So x - 3 could be 3 or -3. i) If x - 3 = 3, then x = 6. ii) If x - 3 = -3, then x = 0. 2) If |x - 3| - 2 = -1, then |x - 3| = 1. So x - 3 could be 1 or -1. i) If x - 3 = 1, then x = 4. ii) If x - 3 = -1, then x = 2. We see that the equation has 4 solutions. Answer: E _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5593 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: How many solutions has the equation ||x-3|-2|=1? [#permalink] ### Show Tags 24 Jan 2018, 01:31 => $$||x-3|-2|=1$$ $$⇔|x-3|-2=±1$$ $$⇔|x-3|=2±1$$ $$⇔|x-3|=1 or |x-3|=3$$ $$⇔x-3=±1 or x-3=±3$$ $$⇔x=3±1$$ or $$x=3±3$$ $$⇔x=2, x = 4, x = 0$$ or $$x = 6$$ Thus, the equation has four solutions. Therefore, the answer is E. Answer: E _________________ 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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Re: How many solutions has the equation ||x-3|-2|=1?   [#permalink] 24 Jan 2018, 01:31
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