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# If |4 – x| = 8, what is the value of x?

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Math Expert
Joined: 02 Sep 2009
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If |4 – x| = 8, what is the value of x?  [#permalink]

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23 Nov 2016, 02:12
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8
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Difficulty:

25% (medium)

Question Stats:

75% (01:19) correct 25% (01:36) wrong based on 364 sessions

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If |4 – x| = 8, what is the value of x?

(1) x^2 is an even number.
(2) |x| is the square of a prime number.

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Re: If |4 – x| = 8, what is the value of x?  [#permalink]

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23 Nov 2016, 02:55
Bunuel wrote:
If |4 – x| = 8, what is the value of x?

(1) x^2 is an even number.
(2) |x| is the square of a prime number.

IMO B
4-x=8, x=-4 or x-4=8, x=12

From statement 1
x^2 is even number
Insufficient as both values will yield even numbers upon squaring

From statement 2
mod x is the square of a prime number
|x|= 4 hence x=-4
Sufficient
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Joined: 11 Sep 2015
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Re: If |4 – x| = 8, what is the value of x?  [#permalink]

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23 Nov 2016, 08:14
Top Contributor
Bunuel wrote:
If |4 – x| = 8, what is the value of x?

(1) x² is an even number.
(2) |x| is the square of a prime number.

When solving equations involving ABSOLUTE VALUE, there are 3 steps:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

Target question: What is the value of x?

Given: |4 – x| = 8
So, 4 - x = 8 or 4 - x = -8
If 4 - x = 8, then x = -4
If 4 - x = -8, then x = 12
So, x = -4 or x = 12

Statement 1: x² is an even number
We already know that x = -4 or x = 12, so there are two cases to consider:
case a: If x = -4, then x² = (-4)² = 16, which is an even number. So, x could equal -4
case b: If x = 12, then x² = (12)² = 144, which is an even number. So, x could equal 12
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: |x| is the square of a prime number
We already know that x = -4 or x = 12, so there are two cases to consider:
case a: If x = -4, then |-4| = 4, and 4 IS the square of a prime number (2). So, x could equal -4
case b: If x = 12, then |12| = 12, BUT 12 is NOT the square of a prime number. So, x cannot equal 12
So, x MUST equal -4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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Re: If |4 – x| = 8, what is the value of x?  [#permalink]

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01 Sep 2017, 14:25
Bunuel wrote:
If |4 – x| = 8, what is the value of x?

(1) x^2 is an even number.
(2) |x| is the square of a prime number.

Two ways to approach abs. value

4-x =8
x =-4

-l4-xl =8
-4 +x =8
x =12

Stmnt 1

Insuff because both are even

Stmtn 2

Suff because the only x value that could be a square of a prime number is 2
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Joined: 18 Aug 2017
Posts: 1
Re: If |4 – x| = 8, what is the value of x?  [#permalink]

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13 Feb 2018, 05:15
can anyone solve this using critical point method ?
Re: If |4 – x| = 8, what is the value of x? &nbs [#permalink] 13 Feb 2018, 05:15
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