Last visit was: 31 Aug 2024, 19:44 It is currently 31 Aug 2024, 19:44
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 95291
Own Kudos [?]: 654407 [2]
Given Kudos: 87117
Send PM
CAT Tests Forum Quiz Mode
If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one [#permalink] If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one   14 Feb 2022, 07:15
2
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

88% (01:09) correct 12% (01:13) wrong based on 125 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one possible value of k?

A. \(\sqrt{2}\)
B. 2
C. 4
D. \(2\sqrt{2}\)
E. \(14\)
ShowHide Answer
Official Answer
D
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 31158 [2]
Given Kudos: 799
Location: Canada
Send PM
If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one [#permalink] If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one   14 Feb 2022, 07:27
1
Kudos
1
Bookmarks
Expert Reply
Top Contributor
Bunuel wrote:
If \(f(x) = x^2 + 4\) and \(f(2k) = 36\), then which of the following is one possible value of k?

A. \(\sqrt{2}\)
B. 2
C. 4
D. \(2\sqrt{2}\)
E. \(14\)


STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can test each answer choice by plugging it into the function to see which value satisfies the equation f(2k) = 36.
So, that's one option.
Now we should give ourselves 15-20 seconds to identify a faster approach.
In this case, we can also solve the equation.
I'm pretty sure I can quickly solve the equation so I'm going to go with that approach.


If \(f(x) = x^2 + 4\), then \(f(2k) = (2k)^2 + 4= 4k^2 + 4\)

Since we are told \(f(2k) = 36\), we can write: \(4k^2 + 4 = 36\)
Divide both sides of the equation by \(4\) to get: \(k^2 + 1 = 9\)
Subtract \(1\) from both sides to get: \(k^2 = 8\)

So, EITHER \(k = \sqrt{8} \) OR \(k = -\sqrt{8} \)
Check the answer choices...... Not there. It looks like we need to simplify \(\sqrt{8}\)

\(\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2}= 4 \sqrt{2}\).
So, EITHER \(k = 2\sqrt{2} \) OR \(k = -2\sqrt{2} \)

Answer: D
User avatar
P
kungfury42
Director
Director
Joined: 07 Jan 2022
Posts: 585
Own Kudos [?]: 455 [0]
Given Kudos: 725
Schools: NUS '25 (A)
GMAT 1: 740 Q51 V38
GPA: 4
Send PM
Reviews Badge
Re: If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one [#permalink] If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one   14 Feb 2022, 13:54
Bunuel wrote:
If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one possible value of k?

A. \(\sqrt{2}\)
B. 2
C. 4
D. \(2\sqrt{2}\)
E. \(14\)


\(f(x) = x^2 + 4\)
\(f(2k) = (2k)^2 + 4 = 4k^2 + 4\)

\(4k^2 + 4 = 36\)
\(4k^2 = 32\)
\(k^2 = 8\)
\(k = 2\sqrt{2}\)

Hence, our answer is \(2\sqrt{2}\), option D.
User avatar
D
BrushMyQuant
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1824
Own Kudos [?]: 2173 [0]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
Re: If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one [#permalink] If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one   25 Aug 2022, 10:58
Expert Reply
Top Contributor
Given that f(x) = \(x^2\) + 4 and f(2k) = 36 and we need to find one possible value of k

To find f(2k) we need to compare what is inside the bracket () * in f(2k) and f(x)

=> We need to substitute x with 2k in f(x) = \(x^2\) + 4 to get the value of f(2k)

=> f(2k) = \((2k)^2\) + 4 = \(4k^2\) + 4 = 36 (given)
=> \(4k^2\) = 36-4 = 32
=> \(k^2\) = \(\frac{32}{4}\) = 8
=> k = \(\sqrt{8}\) = \(2\sqrt{2}\)

So, Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 34662
Own Kudos [?]: 872 [0]
Given Kudos: 0
Send PM
Re: If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one [#permalink] If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one   31 Aug 2024, 12:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If f(x) = x^2 + 4 and f(2k) = 36, then which of the following is one [#permalink]
31 Aug 2024, 12:59
Moderator:
Bunuel
Math Expert
95291 posts