Given that m=n+2, what is the value of m^2-4m+4?

[BTGmoderatorLU]

Given that m=n+2, what is the value of m^2-4m+4?

1) n=20.
2) n^2=400.

The OA is D.

I'm really confused with this DS question. Please, can any expert assist me with it? Thanks in advanced.

[Brent@GMATPrepNow]

Given that m = n+2, what is the value of m² - 4m + 4?

1) n = 20.
2) n² = 400.

The OA is D.

I'm really confused with this DS question. Please, can any expert assist me with it? Thanks in advanced.

Given: m = n+2

Target question: What is the value of m² - 4m + 4?
This is a good candidate for rephrasing the target question.

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Take the expression m² - 4m + 4 and factor it to get: (m - 2)(m - 2), which is the same as (m - 2)²
So, the target question is really asking us to find the value of (m - 2)²
However, we can take this even farther.
Since we're told that m = n+2, we can rewrite this equation as m-2 = n
Now take the expression (m - 2)² and replace m-2 with n to get: n²
Perfect!
Now, we can REPHRASE the target question....
REPHRASED target question: What is the value of n² ?

Statement 1: n = 20
This means n² = (20)² = 400
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: n² = 400
This is EXACTLY what we need!
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent