Graph Prob-- Need help

Expert replies

selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Thu May 20, 2010 9:30 pm

SOURCE: OG 12, Prob:9

On the graph above,when x=1/2,y=2;and when x=1 y=1. The graph is symmetric with respect to the vertical line at x=2.
According to the graph when x=3 y=?

A) -1

B) -1/2

C) 0

D) 1/2

E) 1

Can anyone solve this in detail?

Attachments

Like this post

Source: Beat The GMAT — Problem Solving | Thu May 20, 2010 9:30 pm

liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Thu May 20, 2010 9:34 pm

The graph is symmetric with respect to the vertical line at x=2
this mean for x=2+a and x=2-a value of y will be same

if we take a=1..x=2+a=3 and x=2-a=1

so value of y at x=1 and x=3 will be same [spoiler]which is y=1[/spoiler]

Ans option E

"If you don't know where you are going, any road will get you there."
Lewis Carroll

Like this post

selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Thu May 20, 2010 9:44 pm

Thanks for the reply

Can you explain what s meant by symmetric in detail?

Is there any formula?

Like this post

liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Thu May 20, 2010 9:49 pm

selango wrote:Thanks for the reply

Can you explain what s meant by symmetric in detail?

Is there any formula?

symmetric means the graph will be mirror image wrt the line ie here the parabola has two halves wrts x=2 where one half is mirror image of the other taking x=2 as the mirror line.There is no formula for this as per my knowledge.

"If you don't know where you are going, any road will get you there."
Lewis Carroll

Like this post

selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Thu May 20, 2010 9:52 pm

Thanks

Like this post

winnerhere: Master | Next Rank: 500 Posts; Posts: 231; Joined: Thu Apr 12, 2007 2:45 amFollowed by: 1 member; Thanked: 5 times

by winnerhere » Sat May 14, 2011 10:33 pm

did anyone try to applu

y = ax^2 + bx + c formula

and derive a,b,c for the three equations and find the answer? The answer is different with this method.

Like this post

Karly: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Thu Jul 03, 2014 1:34 am

by Karly » Tue Jul 29, 2014 7:40 pm

winnerhere wrote:did anyone try to applu

y = ax^2 + bx + c formula

and derive a,b,c for the three equations and find the answer? The answer is different with this method.

I can prove that it is a mistake made by GMAC. I plugged in (1/2,2), (1,1) and (2,0) into the equation:y=ax^2+bx+c and I got when x=3, y should be equal to -5/3.

Did anyone else notice that?

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Tue Jul 29, 2014 10:38 pm

Hi Karly,

The GMAT limits its Quant subject-matter; most of it can be handled by someone who's taken basic algebra and geometry in school. There are a few exceptions of course (probability, permutations, combinations, etc.), but there are certain categories that the GMAT will NEVER test you on (eg. Logarithms, Algebra 2, Trigonometry, Calculus, etc.).

The GMAT does NOT expect you to know how to graph a parabola, so using that formula was not a requirement to answer this question. You ARE expected to know what the word "symmetric" means though. That's essentially ALL this question is about. You can even "avoid the math" altogether (let's pretend that you don't know what the word "symmetric" means) and just use the drawing to estimate the answer.

Part of scoring at a high level on the GMAT is in learning how to answer the various question types in the most efficient ways possible. If you can answer a question in 3 minutes or in 1 minute, then you really have to do so in the 1-minute "way." Doing lots of complex math is rarely what is required to solve a Quant question, so make sure you're practicing more than just that approach.

GMAT assassins aren't born, they're made,
Rich

Last edited by [email protected] on Wed Jul 30, 2014 6:59 pm, edited 1 time in total.

Contact Rich at [email protected]

Like this post

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Wed Jul 30, 2014 6:03 am

selango wrote:SOURCE: OG 12, Prob:9

On the graph above,when x=1/2,y=2;and when x=1 y=1. The graph is symmetric with respect to the vertical line at x=2.
According to the graph when x=3 y=?

A) -1

B) -1/2

C) 0

D) 1/2

E) 1

Can anyone solve this in detail?

Since the Graph is Symmetric about x=2 therefore the value of y if we moved an amount amount on right side of x=2 will be same as if we moved the same distance on the left side from x=2

x=3 is 1 unit to the right of x, where the value of y will be same as the value of y if we moved 1 unit to the left i.e. at x=1
at x=1, y = 1
therefore, at x = 3 also , y = 1

Answer: Option E

"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour

Like this post

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Wed Jul 30, 2014 6:08 am

Karly wrote:
winnerhere wrote:did anyone try to applu

y = ax^2 + bx + c formula

and derive a,b,c for the three equations and find the answer? The answer is different with this method.
I can prove that it is a mistake made by GMAC. I plugged in (1/2,2), (1,1) and (2,0) into the equation:y=ax^2+bx+c and I got when x=3, y should be equal to -5/3.

Did anyone else notice that?

The graph intersect at x = 2 i.e. the equation has two roots and both are equal i.e. x=2
equation of the graph becomes
y = (x - 2)^2
i.e. y = x^2 - 4x + 4
at x = 3, y = 9-12+4 = 1

Answer : Option E

Like this post

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Wed Jul 30, 2014 6:10 am

Hi Karly,

Please keep in mind that GMAC is NEVER wrong. These question are made scientifically and they don't have any potential to be incorrect.

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Graph Prob-- Need help

by Brent@GMATPrepNow » Fri Aug 01, 2014 3:03 pm

As Rich mentioned, you don't need to know how to find the equation of a parabola on the GMAT. All that matters is that parabolas are symmetrical about an axis.

For the visual learners out there, here's my solution:

Cheers,
Brent

Last edited by Brent@GMATPrepNow on Mon Apr 16, 2018 1:18 pm, edited 2 times in total.

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Sat Aug 02, 2014 11:02 am

Brent@GMATPrepNow wrote:As Rich mentioned, you don't need to know how to find the equation of a parabola on the GMAT. All that matters is that parabolas are symmetrical about an axis.

This is not current, I don't think. The 2014 GMAT does assume you know a number of things about parabolas, specifically:

* The impact of the a coefficient (what happens if it's negative, what happen if it's positive)
* The impact of the discriminant (specifically its relationship to the y-intercepts)
* The relationship between the roots of a quadratic and the intercepts of a parabola

and there may be other expectations as well.

Save $100 on any VP online course!

Like this post

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Sat Aug 02, 2014 11:06 am

GMATinsight wrote:Hi Karly,

Please keep in mind that GMAC is NEVER wrong. These question are made scientifically and they don't have any potential to be incorrect.

This is not true. Any standardized test has the potential to err, and most of them make mistakes at some point. The LSAT seems to remove a question from scoring at least once a year due to error or ambiguity, and even a math test as venerable as the AMC has had this issue in the past, so I don't see why the GMAT is exempt.

The difference with the GMAT is that it is very hard to catch their test writers in a mistake, as you'd need to memorize the question, then somehow verify independently after the fact that it was wrong; the question will almost never be released for public scrutiny. (This lack of transparency is a major issue, in my opinion.)

That said, GMAT questions are very seldom wrong or flawed, as they go through many checks and reviews; I'd imagine fewer than 1% of questions on the actual GMAT are flawed or ambiguous. (In other words, if you think there's a flaw, YOU'RE probably wrong ... but not always!)

Save $100 on any VP online course!

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Aug 02, 2014 12:59 pm

Matt@VeritasPrep wrote:
Brent@GMATPrepNow wrote:As Rich mentioned, you don't need to know how to find the equation of a parabola on the GMAT. All that matters is that parabolas are symmetrical about an axis.
This is not current, I don't think. The 2014 GMAT does assume you know a number of things about parabolas, specifically:

1) The impact of the a coefficient (what happens if it's negative, what happen if it's positive)
2) The impact of the discriminant (specifically its relationship to the y-intercepts)
3) The relationship between the roots of a quadratic and the intercepts of a parabola

and there may be other expectations as well.

Hey Matt,

My point was more about whether or not we need to know how to find the equation of a parabola. That said, I consider point #3 relating more to finding the roots of an equation/x-intercepts than knowing how the graph of the parabola looks (although the concepts are linked).

As for point #2, I'm not sure what you mean by the relationship between the discriminant and the y-intercept. For any quadratic in the form y = axÂ² + bx + c, the y-intercept will be at (0, c). If you're referring to the x-intercept (and not the y-intercept), then points #2 and #3 are kind of the same and can be handled without knowing a great deal about how the parabola actually looks.

I'd be surprised to learn that test-takers are required to know how the a coefficient impacts the graph of a parabola, other than perhaps whether a is negative or positive (in which case students can just as easily easily plot a few points to see the effect). IF that is required knowledge, I'd say that's as far as the test-takers would go. That is, I don't believe we're required to know how the magnitude of a (i.e., y = 2xÂ² - 3x + 1 vs y = xÂ² - 3x + 1) affects the parabola.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Post new topic Post Reply

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review