GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Oct 2019, 14:41

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.

Close

Request Expert Reply

Confirm Cancel

If 3f(x) + 2f(-x) = 5x − 10, what is the value of f(1)?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
If 3f(x) + 2f(-x) = 5x − 10, what is the value of f(1)?  [#permalink]

Show Tags

New post 03 Jul 2017, 02:02
2
15
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (02:18) correct 42% (02:14) wrong based on 157 sessions

HideShow timer Statistics

CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: If 3f(x) + 2f(-x) = 5x − 10, what is the value of f(1)?  [#permalink]

Show Tags

New post 03 Jul 2017, 02:06
2
2
Bunuel wrote:
If 3f(x) + 2f(-x) = 5x − 10, what is the value of f(1)?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4



3f(x) + 2f(-x) = 5x − 10

@x=1, 3f(1) + 2f(-1) = 5 − 10 = -5

@x=-1, 3f(-1) + 2f(1) = -5 − 10 = -15

Multiply the equation 1 with 3 and equation 2 with 2 and subtract

5*f(1) = -15+30 = 15

f(1) = 3

Answer: Option D
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3333
Location: India
GPA: 3.12
Re: If 3f(x) + 2f(-x) = 5x − 10, what is the value of f(1)?  [#permalink]

Show Tags

New post 03 Jul 2017, 03:18
2
If x=1, 3f(1) + 2f(-1) = 5 − 10 = -5
If x=-1, 3f(-1) + 2f(1) = -5 − 10 = -15

Let f(1) = a and f(-1) = b
Now, the equations become :
3a + 2b = -5
2a + 3b = -15
Since we have been asked to find the value of f(1) or a, we have to eliminate f(-1) or b

Multiplying the first equation by 3 and subtracting from it the second equation(multiplied by 2)
3(3a + 2b) - 2(2a + 3b) = -15 + 30
9a - 4a = 15 -> 5a = 15 -> a(f(1)) =3 (Option D)
_________________
You've got what it takes, but it will take everything you've got
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8104
Location: United States (CA)
Re: If 3f(x) + 2f(-x) = 5x − 10, what is the value of f(1)?  [#permalink]

Show Tags

New post 16 Jul 2017, 17:30
Bunuel wrote:
If 3f(x) + 2f(-x) = 5x − 10, what is the value of f(1)?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4


If we let x = 1, we have 3f(1) + 2f(-1) = 5(1) - 10, i.e., 3f(1) + 2f(-1) = -5.

If we let x = -1, we have 3f(-1) + 2f(-(-1)) = 5(-1) - 10, i.e., 3f(-1) + 2f(1) = -15.

Now we need to “get rid” of f(-1) to find the value of f(1). To do that, we multiply the first equation by 3 and the second equation by 2:

3 x [3f(1) + 2f(-1) = -5] → 9f(1) + 6f(-1) = -15

2 x [3f(-1) + 2f(1) = -15] → 6f(-1) + 4f(1) = -30

Now if we subtract 6f(-1) + 4f(1) = -30 from 9f(1) + 6f(-1) = -15, we have:

5f(1) = 15

f(1) = 3

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Director
Director
avatar
P
Joined: 31 Jul 2017
Posts: 512
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: If 3f(x) + 2f(−x) = 5x − 10, what is the value of f (1)?  [#permalink]

Show Tags

New post 01 Oct 2018, 23:24
Bunuel wrote:
If 3f(x) + 2f(−x) = 5x − 10, what is the value of f (1)?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4


3f(x) + 2f(−x) = 5x − 10
2f(x) + 3f(-x) = -5x - 10

9f(x) + 6f(-x) = 15x - 30
4f(x) + 6f(-x) = -10x - 20

Subtract the above two equation -

5f(x) = 25x - 10
f(x) = 5x - 2
f(1) = 3

Hence, D.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3333
Location: India
GPA: 3.12
Re: If 3f(x) + 2f(−x) = 5x − 10, what is the value of f (1)?  [#permalink]

Show Tags

New post 01 Oct 2018, 23:50
2
1
Bunuel wrote:
If 3f(x) + 2f(−x) = 5x − 10, what is the value of f (1)?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4


If \(x=1\), the equation becomes \(3f(1) + 2f(-1) = 5 - 10 = -5\) -> (1)

If \(x=-1\), the equation becomes \(3f(-1) + 2f(1) = -5 - 10 = -15\) -> (2)

3*(1) - 2*(2) -> \(9f(1) - 4f(1) = -15 + 30 = 15\) -> \(5f(1) = 15\)

Therefore, the value of f(1) = \(\frac{15}{5}\) = 3(Option D)
_________________
You've got what it takes, but it will take everything you've got
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13261
Re: If 3f(x) + 2f(-x) = 5x − 10, what is the value of f(1)?  [#permalink]

Show Tags

New post 15 Oct 2018, 07:16
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
Re: If 3f(x) + 2f(-x) = 5x − 10, what is the value of f(1)?   [#permalink] 15 Oct 2018, 07:16
Display posts from previous: Sort by

If 3f(x) + 2f(-x) = 5x − 10, what is the value of f(1)?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne