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

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VP
Joined: 19 Oct 2018
Posts: 1075
Location: India
Find the number of solutions of following equation-: ||x|-6|=2^x  [#permalink]

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04 Sep 2019, 05:29
1
12
00:00

Difficulty:

95% (hard)

Question Stats:

12% (01:52) correct 88% (01:58) wrong based on 102 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
Senior Manager
Joined: 30 Sep 2017
Posts: 405
Concentration: Technology, Entrepreneurship
GMAT 1: 720 Q49 V40
GPA: 3.8
WE: Engineering (Real Estate)
Re: Find the number of solutions of following equation-: ||x|-6|=2^x  [#permalink]

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04 Sep 2019, 18:25
7
2
Nice question.

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

+1 kudo is appreciated

Posted from my mobile device
Attachments

IMG_20190905_092154.jpg [ 411.68 KiB | Viewed 1278 times ]

##### General Discussion
Manager
Joined: 17 Jul 2017
Posts: 199
Re: Find the number of solutions of following equation-: ||x|-6|=2^x  [#permalink]

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04 Sep 2019, 07:51
1
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.
Attachments

IMG20190904201317 (1).jpg [ 3.72 MiB | Viewed 1404 times ]

Senior Manager
Joined: 30 Sep 2017
Posts: 405
Concentration: Technology, Entrepreneurship
GMAT 1: 720 Q49 V40
GPA: 3.8
WE: Engineering (Real Estate)
Find the number of solutions of following equation-: ||x|-6|=2^x  [#permalink]

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04 Sep 2019, 21:02
1
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
Manager
Joined: 17 Jul 2017
Posts: 199
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

+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: 53
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

+1 kudo is appreciated

Posted from my mobile device

Can you explain the fourth graph breifly
Intern
Joined: 28 Aug 2019
Posts: 5
Re: Find the number of solutions of following equation-: ||x|-6|=2^x  [#permalink]

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14 Sep 2019, 05:54
1
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

Posted from my mobile device
Re: Find the number of solutions of following equation-: ||x|-6|=2^x   [#permalink] 14 Sep 2019, 05:54
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