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

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Re: If |4 – x| = 8, what is the value of x? [#permalink]
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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Re: If |4 – x| = 8, what is the value of x? [#permalink]
can anyone solve this using critical point method ?
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Re: If |4 – x| = 8, what is the value of x? [#permalink]
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.

|4-x|=8
=> x = 4+/-8 = -4 or 12

S1:
$$x^2$$ is an even number
$$(-4)^2 = 16$$ is an even number
$$12^2 = 144$$ is also an even number
INSUFFICIENT

S2:
|x| is the square of a prime number.
|-4| = 4 is the square of a prime number 2.
|12| = 12 is NOT a square of a prime number
x=-4
SUFFICIENT

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

RELATED VIDEO

——————————————————————————————-
x = 12 —> is clearly an extraneous root of give Equation, as per how you’ve taught. Thus, let’s focus only on x = -4 .

x = -4 —(Eq. 1)

I’ve solved Statement 2 below. Pls let me know if my steps of solution for Statement 2 are correct.

Statement 2: |x| is the square of a prime number

Statement 2: |x| = (prime number)^2 —(Eq. 2)
Note: P is a variable for [P = Prime Number]

=> |x| = (prime number)^2 —(Eq. 2)
=> |-4| = (Prime Number)^2 — (Eq.1) Putting x’s value
=> 4 = (Prime Number)^2 —Bringing ‘|-4|‘ out as ‘+4’
=> \sqrt{ (4) } = prime number
=> +2 or -2 = Prime Number
=> Since, we know (-ive)Intergers are NOT Prime numbers. Therefore, +2 is that only possible Prime number.

Finally, we’ve just ONE answer i.e. +2. Therefore, Statement 2 is Sufficent & Answer is ‘B’.
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Re: If |4 x| = 8, what is the value of x? [#permalink]
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Re: If |4 x| = 8, what is the value of x? [#permalink]
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