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

It is currently 10 Dec 2018, 20:38

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free lesson on number properties

     December 10, 2018

     December 10, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

In the x-y plane, y = f(x) = ax^2+bx+c passes through (1,0) an

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

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6616
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
In the x-y plane, y = f(x) = ax^2+bx+c passes through (1,0) an  [#permalink]

Show Tags

New post 06 Jul 2018, 00:43
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

22% (02:17) correct 78% (01:59) wrong based on 27 sessions

HideShow timer Statistics

[GMAT math practice question]

In the x-y plane, \(y = f(x) = ax^2+bx+c\) passes through \((1,0)\) and \((2,0)\). Is \(f(3)>0?\)

\(1) a > 0\)
\(2) f(0) > 0\)

_________________

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 $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Senior Manager
Senior Manager
avatar
S
Joined: 04 Aug 2010
Posts: 310
Schools: Dartmouth College
Re: In the x-y plane, y = f(x) = ax^2+bx+c passes through (1,0) an  [#permalink]

Show Tags

New post 06 Jul 2018, 03:08
MathRevolution wrote:
[GMAT math practice question]

In the x-y plane, \(y = f(x) = ax^2+bx+c\) passes through \((1,0)\) and \((2,0)\). Is \(f(3)>0?\)

\(1) a > 0\)
\(2) f(0) > 0\)


\(f(x) = ax^2+bx+c\) will be a U-shaped parabola if a>0.
\(f(x) = ax^2+bx+c\) will be a -shaped parabola if a<0.

Since \(f(x) = ax^2+bx+c\) has x-intercepts at (1, 0) and (2, 0), \(f(3)>0\) if the parabola is U-shaped.
Question stem, rephrased:
Is the parabola U-shaped?

Statement 1:
Since a>0, the parabola is U-shaped.
SUFFICIENT.

Statement 2:
x=0 is to the LEFT of the x-intercept at (1, 0).
Since x=0 yields a POSITIVE y-value, the parabola must be U-shaped.
SUFFICIENT.


_________________

GMAT and GRE Tutor
Over 1800 followers
Click here to learn more
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6616
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: In the x-y plane, y = f(x) = ax^2+bx+c passes through (1,0) an  [#permalink]

Show Tags

New post 08 Jul 2018, 03:17
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Since f(x) passes through (1,0) and (2,0), 1 and 2 are roots of f(x) and we have f(x) = a(x-1)(x-2). If f(x) is concave up, then f(3) > 0. Thus, knowing that f(x) is concave up will allow us to answer the question. In addition, since we have 3 variables (a, b, c) and 2 conditions, D is most likely to be the answer.

Condition 1)
If a > 0, then f(x) is concave up.
Thus, condition 1) is sufficient.

Condition 2)
Since 1 and 2 are roots of f(x) = 0, f(0) > 0 implies that f(x) is concave up.
Thus, condition 2) is sufficient, too.

Therefore, D is the answer.

Answer: D

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).
_________________

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 $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

GMAT Club Bot
Re: In the x-y plane, y = f(x) = ax^2+bx+c passes through (1,0) an &nbs [#permalink] 08 Jul 2018, 03:17
Display posts from previous: Sort by

In the x-y plane, y = f(x) = ax^2+bx+c passes through (1,0) an

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.