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# What is the value of |4−|3−x||? (1) |x−4|=6 (2) |6−x|=4

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What is the value of |4−|3−x||? (1) |x−4|=6 (2) |6−x|=4  [#permalink]

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28 Apr 2017, 03:00
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95% (hard)

Question Stats:

37% (01:51) correct 63% (01:57) wrong based on 113 sessions

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What is the value of |4−|3−x||?

(1) |x−4|=6
(2) |6−x|=4

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Re: What is the value of |4−|3−x||? (1) |x−4|=6 (2) |6−x|=4  [#permalink]

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Updated on: 28 Apr 2017, 06:32
What is the value of |4−|3−x||?

(1) |x−4|=6
x can take values 10 and -2.
But, these values will not give an unique value to the expression. Hence, not sufficient.
(2) |6−x|=4
x can take values 2 and 10
But these values will give an unique value to the expression. Hence,sufficient(Option B)

Got the process right, but the answer wrong. Thanks for pointing out the error.. Please find corrected solution
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Originally posted by pushpitkc on 28 Apr 2017, 03:10.
Last edited by pushpitkc on 28 Apr 2017, 06:32, edited 1 time in total.
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Re: What is the value of |4−|3−x||? (1) |x−4|=6 (2) |6−x|=4  [#permalink]

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28 Apr 2017, 06:23
Taking the First statement, |x-4|=6 can be written as

x-4=6 or x-4=-6 and we get x=10 or x=-2 on substituting these values we get 3 and 1 respectively

Taking the second statement alone, |6-x|=4 can be written as

6-x=4 or 6-x=-4 and we get x=2 or x=10 on substituting these values we get 3 and 3 respectively

So statement B alone is sufficient to answer this question.
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What is the value of |4−|3−x||? (1) |x−4|=6 (2) |6−x|=4  [#permalink]

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28 Apr 2017, 20:54
In statement 2 x has two values and it end up to single value.
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Re: What is the value of |4−|3−x||? (1) |x−4|=6 (2) |6−x|=4  [#permalink]

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11 Jul 2017, 05:51
Hi everyone, how it will ended up in one value, can anyone explain this to me
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Re: What is the value of |4−|3−x||? (1) |x−4|=6 (2) |6−x|=4  [#permalink]

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11 Jul 2017, 06:57
sananoor wrote:
Hi everyone, how it will ended up in one value, can anyone explain this to me

To solve any question related to absolute value, you need to remember this rule:

\(|x| = x \) if \(x \geq 0\) and \(|x|= - x\) if \(x < 0\)

Now, the question asks for the value of \(|4−|3−x||\)

(1) \(|x−4|=6\)
This one leads to two possible outcomes:

Case 1: \(x-4 = 6 \implies x = 10.\)
Case 2: \(x-4=-6 \implies x=-2\)

From case 1, we have \(x=10 \implies |4−|3−x||=|4-|3-10||=|4-|-7||=|4-7|=|-3|=3\)
From case 2, we have \(x=-2 \implies |4−|3−x||=|4-|3-(-2)||=|4-|5||=|4-5|=|-1|=1\)

From this statement, we could have 2 possible values. Hence insufficient.

(2) |6−x|=4
The same way to solve this one, we have \(x=2\) or \(x=10\).

If \(x=10 \implies |4−|3−x|| = 3\)
If \(x=2 \implies |4−|3−x|| = 3\)

Now, from 2 possible cases, we could have only one possible value. Hence, sufficient.

Hope this helps
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Re: What is the value of |4−|3−x||? (1) |x−4|=6 (2) |6−x|=4  [#permalink]

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05 Apr 2019, 22:15
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Re: What is the value of |4−|3−x||? (1) |x−4|=6 (2) |6−x|=4   [#permalink] 05 Apr 2019, 22:15
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