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

It is currently 11 Dec 2019, 22:16

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

A function f(x) satisfies 2f(x)+3f(1-x)=x^2. What is the expression of

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

Hide Tags

Find Similar Topics 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8251
GMAT 1: 760 Q51 V42
GPA: 3.82
A function f(x) satisfies 2f(x)+3f(1-x)=x^2. What is the expression of  [#permalink]

Show Tags

New post 08 Oct 2019, 00:45
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (02:08) correct 44% (01:41) wrong based on 25 sessions

HideShow timer Statistics

[GMAT math practice question]

A function \(f(x)\) satisfies \(2f(x)+3f(1-x)=x^2.\) What is the expression of \(f(x)\)?

\(A. \frac{(x^2 +6x +3)}{7}\)

\(B. \frac{(x^2 -6x +3)}{7}\)

\(C. \frac{(x^2 -6x +1)}{3}\)

\(D. \frac{(x^2 -6x +3)}{5}\)

\(E. \frac{(x^2 +6x +3)}{5}\)

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
VP
VP
User avatar
V
Joined: 19 Oct 2018
Posts: 1171
Location: India
Premium Member CAT Tests
A function f(x) satisfies 2f(x)+3f(1-x)=x^2. What is the expression of  [#permalink]

Show Tags

New post 08 Oct 2019, 01:10
\(2f(x)+3f(1-x)=x^2.\) .......(1)


put x=1-x, we get

\(2f(1-x)+3f(x)=(1-x)^2.\) ........(2)

Multiply equation (1) by 2 and equation (2) by 3 and subtract both equations

we'll get

f(x)= \(\frac{(x^2 -6x +3)}{5}\)


MathRevolution wrote:
[GMAT math practice question]

A function \(f(x)\) satisfies \(2f(x)+3f(1-x)=x^2.\) What is the expression of \(f(x)\)?

\(A. \frac{(x^2 +6x +3)}{7}\)

\(B. \frac{(x^2 -6x +3)}{7}\)

\(C. \frac{(x^2 -6x +1)}{3}\)

\(D. \frac{(x^2 -6x +3)}{5}\)

\(E. \frac{(x^2 +6x +3)}{5}\)
SVP
SVP
User avatar
D
Joined: 03 Jun 2019
Posts: 1882
Location: India
Premium Member Reviews Badge CAT Tests
Re: A function f(x) satisfies 2f(x)+3f(1-x)=x^2. What is the expression of  [#permalink]

Show Tags

New post 08 Oct 2019, 01:53
MathRevolution wrote:
[GMAT math practice question]

A function \(f(x)\) satisfies \(2f(x)+3f(1-x)=x^2.\) What is the expression of \(f(x)\)?

\(A. \frac{(x^2 +6x +3)}{7}\)

\(B. \frac{(x^2 -6x +3)}{7}\)

\(C. \frac{(x^2 -6x +1)}{3}\)

\(D. \frac{(x^2 -6x +3)}{5}\)

\(E. \frac{(x^2 +6x +3)}{5}\)


Given: A function \(f(x)\) satisfies \(2f(x)+3f(1-x)=x^2.\)

Asked: What is the expression of \(f(x)\)?

For x = 0
2f(0) + 3f(1) = 0

For x = 1
2f(1) + 3f(0) = 1

f(0) - f(1) = 1
f(0) + f(1) = .2

f(0) = .6
f(1) = -.4

Only D \(D. \frac{(x^2 -6x +3)}{5}\) satisfies the conditions

IMO D
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8251
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: A function f(x) satisfies 2f(x)+3f(1-x)=x^2. What is the expression of  [#permalink]

Show Tags

New post 10 Oct 2019, 01:34
=>

We have \(4f(x)+6f(1-x)=2x^2\) when we multiply the equation in the original condition by \(2\).

If we substitute \(x\) by \(1-x,\) then we have \(2f(1-x)+3f(x) = (1-x)^2.\)

If we multiply the equation by \(3\), we have \(6f(1-x)+9f(x) = 3(1-x)^2.\)

If we subtract equations \([4f(x)+6f(1-x)=2x^2] - [6f(1-x)+9f(x) = 3(1-x)^2]\), then we have \(-5f(x) = 2x^2 – 3(1-x)^2, -5f(x) = 2x^2 - 3(1-2x+x^2), -5f(x) = 2x^2 - 3 + 6x - 3x^2, -5f(x) = -x^2 + 6x – 3\) or \(f(x) = (\frac{1}{5})(x^2-6x+3).\)

Therefore, the answer is D.
Answer: D
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Intern
Intern
avatar
B
Joined: 28 Jan 2019
Posts: 37
CAT Tests
Re: A function f(x) satisfies 2f(x)+3f(1-x)=x^2. What is the expression of  [#permalink]

Show Tags

New post 27 Nov 2019, 07:23
MathRevolution, could you please explain why you chose those operations: substituting, multiplying by 3, etc.?
GMAT Club Bot
Re: A function f(x) satisfies 2f(x)+3f(1-x)=x^2. What is the expression of   [#permalink] 27 Nov 2019, 07:23
Display posts from previous: Sort by

A function f(x) satisfies 2f(x)+3f(1-x)=x^2. What is the expression of

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





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