Find the number of solutions of following equation-: ||x|-6|=2^x : Problem Solving (PS)

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Find the number of solutions of following equation-: ||x|-6|=2^x

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Joined: 19 Oct 2018

Posts: 1293

Location: India

Find the number of solutions of following equation-: ||x|-6|=2^x [#permalink]

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04 Sep 2019, 05:29

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Difficulty:

95% (hard)

Question Stats:

11% (01:52) correct

89% (01:58) wrong

based on 109 sessions

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Find the number of solutions of following equation-:
\(||x|-6|=2^x\)

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

Spoiler: OA

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Director

Joined: 30 Sep 2017

Posts: 581

GMAT 1: 720 Q49 V40 Verified score

GPA: 3.8

Re: Find the number of solutions of following equation-: ||x|-6|=2^x [#permalink]

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04 Sep 2019, 18:25

Nice question.

I think graphical solution is fastest and most painless to solve this. Check my solution

Answer is (D)
+1 kudo is appreciated

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Manager

Joined: 17 Jul 2017

Posts: 216

Re: Find the number of solutions of following equation-: ||x|-6|=2^x [#permalink]

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04 Sep 2019, 07:51

nick1816 wrote:

Find the number of solutions of following equation-:
\(||x|-6|=2^x\)

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

only x=2 satisfies so answer should be B i think

PFA the image

I am not clear on how to check for fractions in these equations.
nick1816 can u please help

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Manager

Joined: 17 Jul 2017

Posts: 216

Re: Find the number of solutions of following equation-: ||x|-6|=2^x [#permalink]

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04 Sep 2019, 20:30

chondro48 wrote:

Nice question.

I think graphical solution is fastest and most painless to solve this. Check my solution

Answer is (D)
+1 kudo is appreciated

Posted from my mobile device

can u explain the last graph ,how did u find intersecting point of 2^x nd other graph

Manager

Joined: 20 Jul 2019

Posts: 55

Re: Find the number of solutions of following equation-: ||x|-6|=2^x [#permalink]

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04 Sep 2019, 20:51

chondro48 wrote:

Nice question.

I think graphical solution is fastest and most painless to solve this. Check my solution

Answer is (D)
+1 kudo is appreciated

Posted from my mobile device

Can you explain the fourth graph breifly

Director

Joined: 30 Sep 2017

Posts: 581

GMAT 1: 720 Q49 V40 Verified score

GPA: 3.8

Find the number of solutions of following equation-: ||x|-6|=2^x [#permalink]

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04 Sep 2019, 21:02

vanam52923 wrote:

can u explain the last graph ,how did u find intersecting point of 2^x nd other graph

Hi Peddi and vanam52923

That's the characteristic of line y=2^x that the line increases exponentially --if X goes further to the right-- and decreases slowly --if Z goes to the left--, but Y is never negative and not even touches 0. Therefore, the line y=2^x will eventually intersect TWICE with the absolute line (points A and B) on negative X range.

Draw both lines on you sketch and you may understand better what I mean above

Intern

Joined: 28 Aug 2019

Posts: 9

WE: Business Development (Computer Software)

Re: Find the number of solutions of following equation-: ||x|-6|=2^x [#permalink]

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14 Sep 2019, 05:54

This one is completely over my head I tend to use more sophisticated and simple approaches (the methodical apporach) Can I have your take on this one? Bunuel

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