 It is currently 25 Nov 2020, 19:14 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If f(x) = x2, which of the following is equal to f(m + n) +  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3035 , given: 394

If f(x) = x2, which of the following is equal to f(m + n) + [#permalink]
Expert's post 00:00

Question Stats: 88% (00:30) correct 11% (00:33) wrong based on 36 sessions
If $$f(x) = x^2$$, which of the following is equal to $$f(m + n) + f(m - n)$$?

(A) $$m^2 + n^2$$
(B) $$m^2 - n^2$$
(C) $$2m^2 + 2n^2$$
(D) $$2m^2 - 2n^2$$
(E) $$m^2n^2$$
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Intern Joined: 10 Aug 2018
Posts: 33
Followers: 0

Kudos [?]: 24  , given: 0

Re: If f(x) = x2, which of the following is equal to f(m + n) + [#permalink]
1
KUDOS
It will save a lot of time for many problems if you keep in mind that (m+n)^2 = m^2+n^2+2mn and (m-n)^2 = m^2+n^2-2mn. Here it obviously gives you the answer:

f(m+n)+f(m-n)= m^2 + n^2 + 2mn + m^2 + n^2 - 2mn = 2m^2 + 2n^2

So C

But this also comes in handy when it comes to remembering the inequality:

m^2 + n^2 <= (m+n)^2
Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3035 , given: 394

Re: If f(x) = x2, which of the following is equal to f(m + n) + [#permalink]
Expert's post
Explanation

The problem provides the function $$f(x) = x^2$$ and asks for the quantity $$f(m + n) + f(m - n)$$.

Plug into this function twice—first, to insert m + n in place of x, and then to insert $$m - n$$ in place of x:

$$f(m + n) = (m + n)^2 = m^2 + 2mn + n^2$$

$$f(m - n) = (m - n)2 = m^2 - 2mn + n^2$$

$$(m^2 + 2mn + n^2) + (m^2 - 2mn + n^2) = 2m^2 + 2n^2$$
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Director Joined: 09 Nov 2018
Posts: 505
Followers: 0

Kudos [?]: 56 , given: 1

Re: If f(x) = x2, which of the following is equal to f(m + n) + [#permalink]
Romang67 wrote:
It will save a lot of time for many problems if you keep in mind that (m+n)^2 = m^2+n^2+2mn and (m-n)^2 = m^2+n^2-2mn. Here it obviously gives you the answer:

f(m+n)+f(m-n)= m^2 + n^2 + 2mn + m^2 + n^2 - 2mn = 2m^2 + 2n^2

So C

But this also comes in handy when it comes to remembering the inequality:

m^2 + n^2 <= (m+n)^2

Is it m^2 + n^2 <= (m+n)^2
or
m^2 + n^2 < (m+n)^2 (Without = sign).
Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3035 , given: 394

Re: If f(x) = x2, which of the following is equal to f(m + n) + [#permalink]
Expert's post
AE wrote:

Is it m^2 + n^2 <= (m+n)^2
or
m^2 + n^2 < (m+n)^2 (Without = sign).

If m and n are positive or both strictly negative (i.e non 0). Then:

$$m^2 + n^2 < (m+n)^2$$ because $$(m+n)^2= m^2 + n^2 + 2mn$$ now $$2mn$$ is positive for m and n being positive.

For $$m=n=0$$ they are equal.

If m and n have different signs then the inequality flips and $$m^2+n^2 > (m+n)^2$$.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Re: If f(x) = x2, which of the following is equal to f(m + n) +   [#permalink] 19 Nov 2018, 13:26
Display posts from previous: Sort by

# If f(x) = x2, which of the following is equal to f(m + n) +  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.