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

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

Answer: D




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 ???
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Re: Given that m = n + 2, what is the value of m^2 4m + 4? [#permalink]
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Expert Reply
VasooliBhai wrote:
BrentGMATPrepNow wrote:
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

Answer: D




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 ???


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