Data Sufficiency

Brent@GMATPrepNow wrote: Always plug in the results (to ensure the solution does not have extraneous roots) when solving equations involving absolute value.

Cheers,
Brent

jainpiyushjain wrote:Question courtesy Manhattan GMAT CAT

Is x > 0?

(1) |x + 3| = 4x - 3

(2) |x + 1| = 2x - 1

OA to be posted lated

My question is [spoiler] when should we plug the values back in the absolute value equation to ensure the solution? I got this question wrong because I failed to plug the derived value of x back into the original equation and test them. Is it the case always or am I missing some information in the question? [/spoiler]

Thank you for the help

Brent@GMATPrepNow wrote:

jainpiyushjain wrote:Question courtesy Manhattan GMAT CAT

Is x > 0?

(1) |x + 3| = 4x - 3

(2) |x + 1| = 2x - 1

Here's the algebraic approach.

Target question: Is x > 0?

Statement 1: |x + 3| = 4x - 3
We'll use the following rule: If |A| = B then A = B or A = -B
Here, we get: We get:
x + 3 = 4x - 3 or x + 3 = -(4x - 3)
Solve each equation to get: x = 2 or x = 0
IMPORTANT: Plug in both solutions to confirm that there are no extraneous roots.

x = 2
|x + 3| = 4x - 3
|2 + 3| = 4(2) - 3
5 = 5
Perfect, x = 2 is a solution

x = 0
|x + 3| = 4x - 3
|0 + 3| = 4(0) - 3
3 = -3
No good. So x = 0 is an extraneous solution.

Since we now know that x = 2, we can be certain that x > 0
So, statement 1 is SUFFICIENT


Statement 2: |x + 1| = 2x - 1
x + 1 = 2x - 1 or x + 1 = -(2x - 1)
Solve each equation to get: x = 2 or x = 0
Once again, when we plug the two values into the equation, we see that x = 0 is an extraneous root and that x = 2 works.
Since we now know that x = 2, we can be certain that x > 0
So, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent