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Math Expert V
Joined: 02 Sep 2009
Posts: 57999
Given that m = n + 2, what is the value of m^2 − 4m + 4?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 54% (01:10) correct 46% (01:11) wrong based on 149 sessions

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

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

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7873
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Given that m = n + 2, what is the value of m^2 − 4m + 4?  [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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

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

When you modify the original condition, they become m=n+2 -> m-2=n, which also becomes m^2 − 4m + 4=(m-2)^2=n^2.
Therefore, the answer is D.

-> Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Joined: 12 Sep 2015
Posts: 3958
Re: Given that m = n + 2, what is the value of m^2 − 4m + 4?  [#permalink]

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Top Contributor
Bunuel wrote:
Given that m = n + 2, what is the value of m^2 − 4m + 4?

(1) n = 20
(2) n² = 400

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: We have a video (below) with tips on rephrasing the target question

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:
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

RELATED VIDEO

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Re: Given that m = n + 2, what is the value of m^2 − 4m + 4?  [#permalink]

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_________________ Re: Given that m = n + 2, what is the value of m^2 − 4m + 4?   [#permalink] 05 Mar 2019, 07:35
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# Given that m = n + 2, what is the value of m^2 − 4m + 4?

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