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# If √(x-6)^2 = 6-x, then which of the following must be true?

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If √(x-6)^2 = 6-x, then which of the following must be true?  [#permalink]

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16 Mar 2020, 22:47
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Difficulty:

55% (hard)

Question Stats:

46% (01:27) correct 54% (01:04) wrong based on 24 sessions

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If $$√(x-6)^2 = 6-x$$, then which of the following must be true?

A) x = 6
B) x < 6
C) x ≤ 6
D) x ≥ 6
E) x = 0

Source: www.GMATinsight.com

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CEO
Status: GMATINSIGHT Tutor
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GMAT 1: 750 Q51 V41
WE: Education (Education)
If √(x-6)^2 = 6-x, then which of the following must be true?  [#permalink]

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16 Mar 2020, 23:08
PratapSingh wrote:
A

Posted from my mobile device

PratapSingh
Since x = 5 also satisfies the given expression hence, x=6 can not qualify for MUST BE TRUE

You may try again.

But welcome to Gmat Club
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Re: If √(x-6)^2 = 6-x, then which of the following must be true?  [#permalink]

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19 Mar 2020, 04:34
1
GMATinsight wrote:
If $$√(x-6)^2 = 6-x$$, then which of the following must be true?

A) x = 6
B) x < 6
C) x ≤ 6
D) x ≥ 6
E) x = 0

Source: www.GMATinsight.com

$$√(x-6)^2 = 6-x$$

√x-6)^2 = lx-6l

lx-6l=6-x
we get
x-6=6-x
2x=12 ; x=6
and
-x+6=6-x ; 0
so
0=x<=6
IMO C; x ≤ 6
Re: If √(x-6)^2 = 6-x, then which of the following must be true?   [#permalink] 19 Mar 2020, 04:34