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

It is currently 23 Oct 2019, 12:11

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

For which of the following functions is f(−1/2) > f(2)?

  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: 58464
For which of the following functions is f(−1/2) > f(2)?  [#permalink]

Show Tags

New post 22 Aug 2018, 02:04
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

90% (01:11) correct 10% (01:18) wrong based on 46 sessions

HideShow timer Statistics

VP
VP
User avatar
D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1011
WE: Supply Chain Management (Energy and Utilities)
Re: For which of the following functions is f(−1/2) > f(2)?  [#permalink]

Show Tags

New post 22 Aug 2018, 02:12
Bunuel wrote:
For which of the following functions is f(−1/2) > f(2)?


A. f(x) = 3x^2

B. f(x)= 3x

C. f(x)= 3 + x^2

D. f(x)= 3 + 1/x

E. f(x)= 3/x^2


Since x^2 is in the denominator in option E, it may yield a greater value of f(-1/2).

f(-1/2)=\(\frac{3}{(-1/2)^2}\)=\(3*2^2=12\)
f(2)=\(\frac{3}{2^2}\)=3/4

Ans. (E)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1177
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
For which of the following functions is f(−1/2) > f(2)?  [#permalink]

Show Tags

New post 22 Aug 2018, 02:13
Bunuel wrote:
For which of the following functions is f(−1/2) > f(2)?


A. f(x) = 3x^2

B. f(x)= 3x

C. f(x)= 3 + x^2

D. f(x)= 3 + 1/x

E. f(x)= 3/x^2


Move through the options -

A. \(f(x) = 3x^2\) -------------this will lead to positive value but here \(2^2>(-\frac{1}{2})^2\). Reject

B. \(f(x)= 3x\) ------------ this will make \(f(-\frac{1}{2})\) negative and \(f(2)\) positive. Reject

C. \(f(x)= 3 + x^2\) ----------- Same reasoning as Option A. Reject

D. \(f(x)= 3 + \frac{1}{x}\) ------------ Same reasoning as Option B. \(\frac{1}{x}<x\), hence the value for \(f(-\frac{1}{2})<f(2)\). Reject

E. \(f(x)= \frac{3}{x^2}\) ----------- This should be our Answer, we can check it by solving

\(f(x)= \frac{3}{x^2} => f(-\frac{1}{2})=\frac{3}{(-1/2)^2}=>3*4=12\)

and \(f(2)=\frac{3}{2^2}=\frac{3}{4}=0.75\). Clearly \(f(-\frac{1}{2})>f(2)\)

Option E
Senior Manager
Senior Manager
User avatar
V
Joined: 22 Feb 2018
Posts: 419
For which of the following functions is f(−1/2) > f(2)?  [#permalink]

Show Tags

New post Updated on: 22 Aug 2018, 02:30
Bunuel wrote:
For which of the following functions is f(−1/2) > f(2)?


A. f(x) = 3x^2

B. f(x)= 3x

C. f(x)= 3 + x^2

D. f(x)= 3 + 1/x

E. f(x)= 3/x^2


OA:E
\(\begin{matrix}
& f(-\frac{{1}}{2}) & & f(2) \\
f(x)= 3x^2 & \frac{3}{4} & {<} & 12 \\
f(x)= 3x & -\frac{3}{2} & {<} & 6 \\
f(x)= 3+x^2 & \frac{13}{4} & {<} & 7 \\
f(x)= 3 + 1/x & 1 & {<} & \frac{7}{2} \\
f(x)= 3/x^2 & 12 & {>} & \frac{3}{4}
\end{matrix}\)
_________________
Good, good Let the kudos flow through you

Originally posted by Princ on 22 Aug 2018, 02:25.
Last edited by Princ on 22 Aug 2018, 02:30, edited 1 time in total.
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3332
Location: India
GPA: 3.12
For which of the following functions is f(−1/2) > f(2)?  [#permalink]

Show Tags

New post 22 Aug 2018, 02:29
1
Bunuel wrote:
For which of the following functions is f(−1/2) > f(2)?

A. f(x) = 3x^2

B. f(x)= 3x

C. f(x)= 3 + x^2

D. f(x)= 3 + 1/x

E. f(x)= 3/x^2


Of the 5 answer options, you can straight away eliminate Options A, B, and C because all of these
options have an x or x^2 in the numerator. Substituting -\(\frac{1}{2}\) can never be greater than substituting 2.

Now that we are down to two answer options,
we can substitute the values to check in which case, value of f(-\(\frac{1}{2}\)) > value of f(\(2\))

In Option D, f(-\(\frac{1}{2}\)) = 3 + (-2) = 1 (because \(\frac{1}{\frac{-1}{2}}\) = -2) but f(\(2\)) = \(3 + \frac{1}{2} = \frac{7}{2}\). Here, f(-\(\frac{1}{2}\)) < f(\(2\))

Therefore, the only answer option we are left with is f(x) = \(\frac{3}{x^2}\) (Option E) which is our answer!
_________________
You've got what it takes, but it will take everything you've got
GMAT Club Bot
For which of the following functions is f(−1/2) > f(2)?   [#permalink] 22 Aug 2018, 02:29
Display posts from previous: Sort by

For which of the following functions is f(−1/2) > f(2)?

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





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