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

It is currently 22 Jul 2018, 18:38

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

On the x-y coordinate plane, a point (1,2) is on a parabola y=ax^2+bx+

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

Hide Tags

Expert Post
1 KUDOS received
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 5876
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
On the x-y coordinate plane, a point (1,2) is on a parabola y=ax^2+bx+  [#permalink]

Show Tags

New post 31 Jan 2016, 21:39
1
2
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

54% (01:18) correct 46% (01:29) wrong based on 112 sessions

HideShow timer Statistics

On the x-y coordinate plane, a point (1,2) is on a parabola y=ax^2+bx+c (a≠0), is a point (-1,2) on the parabola, too?

1) b=0
2) f(x)=f(-x)


* A solution will be posted in two days.

_________________

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"

Expert Post
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6281
On the x-y coordinate plane, a point (1,2) is on a parabola y=ax^2+bx+  [#permalink]

Show Tags

New post 31 Jan 2016, 23:31
MathRevolution wrote:
On the x-y coordinate plane, a point (1,2) is on a parabola y=ax^2+bx+c (a≠0), is a point (-1,2) on the parabola, too?

1) b=0
2) f(x)=f(-x)


* A solution will be posted in two days.


Hi,

here we have a parabola...
some properties of parabola that will help us nail the Q..
1) the max/min of the parabola occurs at -b/2a..
2) the point -b/2a acts as axis of symmetry...
3) If a in ax^2 is positive, the parabola opens upwards
4) If a in ax^2 is negative, the parabola opens downwards
...

lets see the Q stem for info now..
point (1,2) is on the parabola y=ax^2+bx+c (a≠0)..
parabola can open upwards or downwards as a can be positive/-ive..
IS (-1,2) also on the parabola...
so one way is to see if they both lie on either side of axis of symmetry..

lets see the statements..

1) b=0
since b=0, -b/2a=0 or the parabola has its vertex at x=0...
when x=0, y=c..
so axis of symmetry is y-axis..
so (-1,2) will be on parabola as (1,2) is on parabola
suff

2) f(x)=f(-x)
f(x)=ax^2+bx+c..
f(-x)=a(-x)^2+b(-x)+c=ax^2-bx+c..

if f(x)=f(-x), it is an even function and even function is symmetric about y axis..
same as above..
suff

D

SIDE NOTE:- even /odd functions are generally not seen too often
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Expert Post
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 5876
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: On the x-y coordinate plane, a point (1,2) is on a parabola y=ax^2+bx+  [#permalink]

Show Tags

New post 02 Feb 2016, 17:25
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

On the x-y coordinate plane, a point (1,2) is on a parabola y=ax^2+bx+c (a≠0), is a point (-1,2) on the parabola, too?

1) b=0
2) f(x)=f(-x)


When you modify the original condition and the question, the question is if y=ax^2+bx+c is symmetry of the y-axis as (1,2) passes parabola and the question asks if (-1,2) passes parabola as well.
1)=2) the both means y=ax^2+bx+c is symmetry of the y-axis, which is yes.
Therefore, the answer is 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 $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"

1 KUDOS received
Manager
Manager
avatar
B
Joined: 17 Sep 2017
Posts: 61
Re: On the x-y coordinate plane, a point (1,2) is on a parabola y=ax^2+bx+  [#permalink]

Show Tags

New post 02 Jan 2018, 21:21
1
Quote:
On the x-y coordinate plane, a point (1,2) is on a parabola y=ax^2+bx+c (a≠0), is a point (-1,2) on the parabola, too?

1) b=0
2) f(x)=f(-x)


Point (1,2) is on f(x) => 2 = a + b + c .
Is point (-1,2) on f(x) => 2 = a - b + c or else a + b + c = a - b + c ? or else b = 0?

A. b=0 => Suf
B. f(x) = f(-x)
=> ax^2 + bx + c = ax^2 - bx+c => 2bx = 0 => b=0 => Suf

My answer is D

Experts, could you please clarify whether I'm doing it right? Many thanks :)
Manager
Manager
avatar
B
Joined: 23 Oct 2017
Posts: 64
Re: On the x-y coordinate plane, a point (1,2) is on a parabola y=ax^2+bx+  [#permalink]

Show Tags

New post 02 Jan 2018, 22:13
y=ax2 + bx +c = f(x) (a not equal to 0)

since point (1,2) lies on y=f(x)
2= a+b+c - [1]

Now does (-1,2) lie on y= f(x) ? i.e. is 2= a-b+c ? -[2]
(on substituing -1,2 in the parabola equation)

stmt 1: b=0 eqn [2] is satsified
stmt 2: f(x)=f(-x) => a+b+c = a-b +c
=> b=0
Thus eqn [2] is satsified

Each stmt in itself satisfies
Re: On the x-y coordinate plane, a point (1,2) is on a parabola y=ax^2+bx+ &nbs [#permalink] 02 Jan 2018, 22:13
Display posts from previous: Sort by

On the x-y coordinate plane, a point (1,2) is on a parabola y=ax^2+bx+

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

Events & Promotions

PREV
NEXT


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®.