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

Question

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

MathRevolution · Answer

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.

BrentGMATPrepNow · Answer

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:  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

RELATED VIDEO
 https://www.youtube.com/watch?v=MyG1K3ee69w

Fdambro294 · Answer

Even if you were rushing and did not rephrase the target question in conjunction with the Given condition (you weren’t exactly thinking clearly *ahem*), this is a good question to think about a combination of topics.

From the question stem alone, you can see that the question asks for the Square of a Difference:

What is: (M - 2)^2 ?

s1: N = 20

Since we can find the value of M as = 22, we can solve.

S2: (N)^2 = 400

You can take the square root of both sides, in which case the absolute value of N = 20

And

N = +20
or
N = (-20)

If N = 20 —> M = 22
If N = (-20) —> M = (-)18

*Q*
What is: (M - 2)^2 = ?

The concept is that when you square a nonzero number, the magnitude of that number is all that matters for purposes of finding the result.

Whether the number is negative or positive is irrelevant: all we care about is the magnitude (in other words, the absolute value of that number ….. which is that number’s distance from 0 on the number line)

In this case: (M - 2)^2 = ?

Any two corresponding values of M that are equidistant from +2 on the number line will produce the same output.

e.g., try values (-1) and +5— both 3 units away from 2 on the number line

You will get the same answer as: (3)^2 = 9

Taking this concept forward, we have two possible values of M: +22 , (-)18

Since both are 20 units away from +2 on the number line, you will end up with the same value when you solve for (M - 2)^2:

(20)^2 = 400

OR

You can just be more careful in the future and always remember to rephrase the question stem in the first step.

D

Posted from my mobile device

D Posted from my mobile device

VasooliBhai · Answer

My doubt is that, since statement 2 gives us two values of n and we cannot exactly determine a singular value for the polynomial (m-2)^2 shouldn't that make statement 2 insufficient ???

Bunuel · Answer

The question asks us to find the value of m^2 - 4m + 4, which can be written as (m - 2)^2. From statement (2), n is either 20 or -20. Therefore, m could be either m = n + 2 = 22, or m = n + 2 = -18.. With each of these values, (m - 2)^2 equals 400. As you can see, we still get only one answer. That's why statement (2) is sufficient.

Hope this is clear.

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

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GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards