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If |x - 5| = 2|x - 8|, then what is the value of x?

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Manager
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If |x - 5| = 2|x - 8|, then what is the value of x?  [#permalink]

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New post 25 Mar 2019, 09:41
1
2
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

30% (02:44) correct 70% (02:26) wrong based on 43 sessions

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If |x - 5| = 2|x - 8|, then what is the value of x?

I. |x^2 – 100| > 50

II. |x^2 – 49| =0
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If |x - 5| = 2|x - 8|, then what is the value of x?  [#permalink]

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New post 25 Mar 2019, 11:23
1
The answer should be B(Statement 2 alone is sufficient), as X can have the value of 7, which satisfies the given equation.
1st statement is not sufficient as X could be anything.

Soln:- |X^2-49|=0
- Either X would be -7 or +7 which satisfy the above statement. By placing -7 for X in the problem, we are not getting any correct result, but by putting X=+7, the result would be |7-5|=2|7-8| => |2| = 2|-1| => 2=2*1 which makes both LHS and RHS equal.

Kindly let me know, if my answer and approach is correct.Thanks in advance!
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Re: If |x - 5| = 2|x - 8|, then what is the value of x?  [#permalink]

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New post 30 Mar 2019, 10:16
mangamma wrote:
If |x - 5| = 2|x - 8|, then what is the value of x?

I. |x^2 – 100| > 50

II. |x^2 – 49| =0


solve for
|x - 5| = 2|x - 8l
we get
x-5=-2x+16
x= 7
or
|x - 5| = 2|x - 8
x=11
#1
|x^2 – 100| > 50
possible at x= 7
sufficient
#2
|x^2 – 49| =0
sufficeint at x= 7
IMO D
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Re: If |x - 5| = 2|x - 8|, then what is the value of x?  [#permalink]

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Re: If |x - 5| = 2|x - 8|, then what is the value of x?  [#permalink]

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New post 30 Mar 2019, 10:53
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Joined: 11 Feb 2013
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WE: Analyst (Commercial Banking)
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Re: If |x - 5| = 2|x - 8|, then what is the value of x?  [#permalink]

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New post 30 Mar 2019, 10:57
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Re: If |x - 5| = 2|x - 8|, then what is the value of x?   [#permalink] 30 Mar 2019, 10:57
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If |x - 5| = 2|x - 8|, then what is the value of x?

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