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

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Bunuel
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Given that m = n + 2, what is the value of m^2 − 4m + 4? [#permalink] Given that m = n + 2, what is the value of m^2 − 4m + 4?   24 Jan 2016, 06:19
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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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D
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Re: Given that m = n + 2, what is the value of m^2 − 4m + 4? [#permalink] Given that m = n + 2, what is the value of m^2 − 4m + 4?   25 Jan 2016, 17:54
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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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BrentGMATPrepNow
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Re: Given that m = n + 2, what is the value of m^2 − 4m + 4? [#permalink] Given that m = n + 2, what is the value of m^2 − 4m + 4?   24 Jan 2018, 15:48
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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: 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

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Given that m = n + 2, what is the value of m^2 4m + 4? [#permalink] Given that m = n + 2, what is the value of m^2 − 4m + 4?   06 Mar 2022, 18:43
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] Given that m = n + 2, what is the value of m^2 − 4m + 4?   11 Jan 2024, 19:41
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: 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




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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Bunuel
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Re: Given that m = n + 2, what is the value of m^2 4m + 4? [#permalink] Given that m = n + 2, what is the value of m^2 − 4m + 4?   12 Jan 2024, 00:17
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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: 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




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.
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Re: Given that m = n + 2, what is the value of m^2 4m + 4? [#permalink]
12 Jan 2024, 00:17
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