Last visit was: 21 Apr 2026, 15:22 It is currently 21 Apr 2026, 15:22
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
GMATBaumgartner
User avatar
Joined: 11 Apr 2012
Last visit: 30 Jan 2013
Posts: 32
Own Kudos:
693
 [30]
Given Kudos: 93
Posts: 32
Kudos: 693
 [30]
The line represented by which of the following equation does Updated on: 06 Apr 2025, 23:39
Originally posted by GMATBaumgartner on 25 Aug 2012, 04:20.
Last edited by Bunuel on 06 Apr 2025, 23:39, edited 3 times in total.
Edited the question.
5
Kudos
Add Kudos
25
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

73% (01:10) correct 27% (01:46) wrong based on 278 sessions

History

Date
Time
Result
Not Attempted Yet
The line represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1

A. y = 2x^2+5x+1
B. y = x^2+5x+2
C. y = 3x^2+5x+2
D. y = 3x^2+7x+2
E. y = x^2+7x+1


Show Spoiler

Bunuel: i couldn't find this problem addressed in the forums(apologies if i have overlooked any).
Could some one clarify if the lines with ax^2+b equal would be parallel and thus WILL NOT intersect as the logic behind solving this problem quickly.
ShowHide Answer
Official Answer
C
Most Helpful Reply
avatar
manjusu
avatar
Joined: 28 Sep 2012
Last visit: 27 Jan 2013
Posts: 6
Own Kudos:
18
 [15]
Given Kudos: 9
Concentration: General Management, International Business
GMAT Date: 01-25-2013
GPA: 3.38
Posts: 6
Kudos: 18
 [15]
The line represented by which of the following equation does 06 Nov 2012, 10:34
12
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
We can also solve this problem as follows

the equation given in the question is
y= 3x^2 + 5x+1
=> y = x(3x + 5) + 1 (Taking x as common)

from the above equation we can say that m(slope) = 3x + 5
Therefore whichever equation in the answer choices has same slope as above, is our answer.
Because two lines having same slope are parallel to each other and does not intersect.

C. y= 3x^2 + 5x+2
=> y= x(3x + 5) + 2

m= 3x +5


Cheers,
Suman.
General Discussion
User avatar
EvaJager
User avatar
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 513
Own Kudos:
2,370
 [3]
Given Kudos: 43
WE:Science (Education)
Posts: 513
Kudos: 2,370
 [3]
The line represented by which of the following equation does 25 Aug 2012, 04:39
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
vinay911
The line represented by which of the following equation does not intersect with the line represented by y = 3x2+ 5x+1

a)y = 2x2+ 5x+1

b) y = x2+ 5x+2

c)y = 3x2+ 5x+2

d)y = 3x2+ 7x+2

e)y = x2 + 7x+1


@Bunuel: i couldn't find this problem addressed in the forums(apologies if i have overlooked any).
Could some one clarify if the lines with ax^2+b equal would be parallel and thus WILL NOT intersect as the logic behind solving this problem quickly.
Show more

Answer C:
Because \(y=3x^2+5x+2=(3x^2+5x+1)+1\) meaning the graph of C (which is a parabola) is that of the given equation, just shifted one unit up. Obviously, the two graphs don't intersect.

How to pick the right answer?
First of all, you can eliminate A and E, because for \(x=0,\) they both give the same value \(y=1,\) the same for the given expression in the stem.
Then, try to look for the expressions that have most terms in common with the given one. All the graphs of the given expressions are upward parabolas, so try to think when they cannot intersect. One case is the translation (moving the parabola vertically up or down).
User avatar
GMATBaumgartner
User avatar
Joined: 11 Apr 2012
Last visit: 30 Jan 2013
Posts: 32
Own Kudos:
693
Given Kudos: 93
Posts: 32
Kudos: 693
The line represented by which of the following equation does 25 Aug 2012, 09:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EvaJager
vinay911
The line represented by which of the following equation does not intersect with the line represented by y = 3x2+ 5x+1

a)y = 2x2+ 5x+1

b) y = x2+ 5x+2

c)y = 3x2+ 5x+2

d)y = 3x2+ 7x+2

e)y = x2 + 7x+1


@Bunuel: i couldn't find this problem addressed in the forums(apologies if i have overlooked any).
Could some one clarify if the lines with ax^2+b equal would be parallel and thus WILL NOT intersect as the logic behind solving this problem quickly.

Answer C:
Because \(y=3x^2+5x+2=(3x^2+5x+1)+1\) meaning the graph of C (which is a parabola) is that of the given equation, just shifted one unit up. Obviously, the two graphs don't intersect.

How to pick the right answer?
First of all, you can eliminate A and E, because for \(x=0,\) they both give the same value \(y=1,\) the same for the given expression in the stem.
Then, try to look for the expressions that have most terms in common with the given one. All the graphs of the given expressions are upward parabolas, so try to think when they cannot intersect. One case is the translation (moving the parabola vertically up or down).
Show more


@EvaJager/Bunuel: How did we conclude that the 2 parabolas (one that is shifted up vertically w.r.t the other) does NOT intersect each other ?
I guess i am missing something basic here.
Thanks!
User avatar
EvaJager
User avatar
Joined: 22 Mar 2011
Last visit: 31 Aug 2016
Posts: 513
Own Kudos:
2,370
Given Kudos: 43
WE:Science (Education)
Posts: 513
Kudos: 2,370
The line represented by which of the following equation does 25 Aug 2012, 10:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
vinay911
EvaJager
vinay911
The line represented by which of the following equation does not intersect with the line represented by y = 3x2+ 5x+1

a)y = 2x2+ 5x+1

b) y = x2+ 5x+2

c)y = 3x2+ 5x+2

d)y = 3x2+ 7x+2

e)y = x2 + 7x+1


@Bunuel: i couldn't find this problem addressed in the forums(apologies if i have overlooked any).
Could some one clarify if the lines with ax^2+b equal would be parallel and thus WILL NOT intersect as the logic behind solving this problem quickly.

Answer C:
Because \(y=3x^2+5x+2=(3x^2+5x+1)+1\) meaning the graph of C (which is a parabola) is that of the given equation, just shifted one unit up. Obviously, the two graphs don't intersect.

How to pick the right answer?
First of all, you can eliminate A and E, because for \(x=0,\) they both give the same value \(y=1,\) the same for the given expression in the stem.
Then, try to look for the expressions that have most terms in common with the given one. All the graphs of the given expressions are upward parabolas, so try to think when they cannot intersect. One case is the translation (moving the parabola vertically up or down).


@EvaJager/Bunuel: How did we conclude that the 2 parabolas (one that is shifted up vertically w.r.t the other) does NOT intersect each other ?
I guess i am missing something basic here.
Thanks!
Show more

For the same value of x, we get some y for one expression and y + 1 for the other expression. y cannot be equal to y + 1.
User avatar
fameatop
User avatar
Joined: 24 Aug 2009
Last visit: 09 Jun 2017
Posts: 382
Own Kudos:
2,550
Given Kudos: 275
Concentration: Finance
Schools:Harvard, Columbia, Stern, Booth, LSB,
Posts: 382
Kudos: 2,550
The line represented by which of the following equation does 10 Sep 2012, 15:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The other way to solve this question is to create a graph for -2,-1,0,1,2.

Now put these values in the option to see which option doesn't intersect.
This solution is not meant for those who are aware of parabola & base shift or twist

Hope it helps
User avatar
maaadhu
User avatar
Joined: 04 Apr 2013
Last visit: 16 Sep 2014
Posts: 96
Own Kudos:
194
Given Kudos: 36
Posts: 96
Kudos: 194
The line represented by which of the following equation does 01 Jun 2013, 07:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
manjusu
We can also solve this problem as follows

the equation given in the question is
y= 3x^2 + 5x+1
=> y = x(3x + 5) + 1 (Taking x as common)

from the above equation we can say that m(slope) = 3x + 5
Therefore whichever equation in the answer choices has same slope as above, is our answer.
Because two lines having same slope are parallel to each other and does not intersect.

C. y= 3x^2 + 5x+2
=> y= x(3x + 5) + 2

m= 3x +5


Cheers,
Suman.
Show more


Manju,

concept of slope for lines & parabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.
User avatar
BangOn
User avatar
Joined: 27 Feb 2012
Last visit: 22 Mar 2019
Posts: 94
Own Kudos:
193
Given Kudos: 22
Posts: 94
Kudos: 193
The line represented by which of the following equation does 01 Jun 2013, 08:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
maaadhu
manjusu
We can also solve this problem as follows

the equation given in the question is
y= 3x^2 + 5x+1
=> y = x(3x + 5) + 1 (Taking x as common)

from the above equation we can say that m(slope) = 3x + 5
Therefore whichever equation in the answer choices has same slope as above, is our answer.
Because two lines having same slope are parallel to each other and does not intersect.

C. y= 3x^2 + 5x+2
=> y= x(3x + 5) + 2

m= 3x +5


Cheers,
Suman.


Manju,

concept of slope for lines & parabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.
Show more


The general form of parabolic equ. is y^2= 4ax which implies the axis is x or x^2 = 4ay where axis is y.
We have a similar form as x^2 = 4ay.
here the vertex is origin.

So if we have same values of x and y but constant term changes then we will have parallel parabolas.
This is same as for straight line which are parallel for different values of constant term c
ax + by +c1 = 0 and ax +by+ c2 =0
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 21 Apr 2026
Posts: 109,728
Own Kudos:
810,465
 [2]
Given Kudos: 105,800
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,728
Kudos: 810,465
 [2]
The line represented by which of the following equation does 02 Jun 2013, 05:58
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
BangOn
maaadhu
manjusu
We can also solve this problem as follows

the equation given in the question is
y= 3x^2 + 5x+1
=> y = x(3x + 5) + 1 (Taking x as common)

from the above equation we can say that m(slope) = 3x + 5
Therefore whichever equation in the answer choices has same slope as above, is our answer.
Because two lines having same slope are parallel to each other and does not intersect.

C. y= 3x^2 + 5x+2
=> y= x(3x + 5) + 2

m= 3x +5


Cheers,
Suman.


Manju,

concept of slope for lines & parabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.


The general form of parabolic equ. is y^2= 4ax which implies the axis is x or x^2 = 4ay where axis is y.
We have a similar form as x^2 = 4ay.
here the vertex is origin.

So if we have same values of x and y but constant term changes then we will have parallel parabolas.
This is same as for straight line which are parallel for different values of constant term c
ax + by +c1 = 0 and ax +by+ c2 =0
Show more


We have quadratic equations. These equations when drawn give parabolas, not lines. The question is: which of the following parabolas does not intersect with the parabola represented by y=3x^2+5x+1.

This CANNOT be transformed to the question: "which of the following parabolas is parallel to the parabola represented by y=3x^2+5x+1." In the wast majority of cases the word "parallel" is used for lines. Well, we can say that concentric circles are parallel, BUT GMAT, as far as I know, uses this word ONLY about the lines. Next, the word "parallel" when used for curves (lines, ...) means that these curves remain a constant distance apart. So strictly speaking two parabolas to be parallel they need not only not to intersect but also to remain constant distance apart. In this case, I must say that this cannot happen. If a curve is parallel (as we defined) to the parabola it won't be quadratic: so curve parallel to a parabola is not a parabola.
User avatar
jlgdr
User avatar
Joined: 06 Sep 2013
Last visit: 24 Jul 2015
Posts: 1,302
Own Kudos:
2,974
Given Kudos: 355
Concentration: Finance
Schools: Wharton '17 (A) HBS '17 (WA$)
Schools: Wharton '17 (A) HBS '17 (WA$)
Posts: 1,302
Kudos: 2,974
The line represented by which of the following equation does 31 Mar 2014, 13:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi all,

Now we see from the statement that y = 3x^2+5x+1 is a parabola.

The y intercept represents the vertex therefore if +1 is replaced by +2 such as in answer choice C the parabola only move upwards but means that it will never intersect with the original equation.

Therefore answer is C

Hope this helps
Cheers
J :-D
User avatar
PiyushK
User avatar
Joined: 22 Mar 2013
Last visit: 31 Aug 2025
Posts: 588
Own Kudos:
5,053
Given Kudos: 235
Status:Everyone is a leader. Just stop listening to others.
Location: India
GPA: 3.51
WE:Information Technology (Computer Software)
Products:
My Reviews
Posts: 588
Kudos: 5,053
The line represented by which of the following equation does 19 Jun 2014, 09:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The line represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1

Calculate Discriminant (D) for each equation :\(\sqrt{b^2-4ac}\)

y = 3x^2+5x+1 ==> \(\sqrt{13}\) -- cutting Y axis at 1 -- to calculate intercept put x=0
A. y = 2x^2+5x+1 ==> \(\sqrt{17}\) -- D > \(\sqrt{13}\) means curve is below original curve cutting Y axis at 1 -- cutting at same point.
B. y = x^2+5x+2 ==> \(\sqrt{17}\) -- D > \(\sqrt{13}\) means curve is below original curve and Y intercept at 2-- cut is unavoidable.
C. y = 3x^2+5x+2 ==> \(\sqrt{1}\) -- D < \(\sqrt{13}\) means closest to X axis -- cutting y axis at 2 above 1 -- cutting right above on Y axis and curve is also passing above as D = 1.
D. y = 3x^2+7x+2 ==> \(\sqrt{25}\) -- D > \(\sqrt{13}\) means curve is below original curve and Y intercept at 2-- cut is unavoidable.-- not plotted on attached graph.
E. y = x^2+7x+1 ==> \(\sqrt{45}\) -- D > \(\sqrt{13}\) means curve is below original curve cutting Y axis at 1 -- cutting at same point.

Refer following graph to relate the nature of equations and value of D.
Attachment:
2014-06-19_1101.jpg
2014-06-19_1101.jpg [ 34.26 KiB | Viewed 11244 times ]
User avatar
IanStewart
User avatar
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 17 Apr 2026
Posts: 4,143
Own Kudos:
11,267
 [3]
Given Kudos: 99
Expert
Expert reply
Posts: 4,143
Kudos: 11,267
 [3]
The line represented by which of the following equation does 03 Jul 2015, 04:32
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
GMATBaumgartner
The line represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1

A. y = 2x^2+5x+1
...
Show more

I'd emphasize that none of the equations in this question represent lines, despite what the question appears to say. The equations represent parabolas, and you don't need to know about parabolas for the GMAT.

There is one concept in this question that is occasionally tested - the concept of translation. If you have any equation at all in coordinate geometry, say:

y = x^2

that will be some curve in the coordinate plane (technically it will be a 'parabola', or U-shape). If you then modify the equation by adding a constant on the right side, say by adding 5:

y = x^2 + 5

then the graph of this new equation will look exactly the same as the graph of the first equation, except that it will be exactly 5 units higher. So when we add a constant on the right side of an equation, we're simply moving the picture of the equation up or down.
User avatar
ENGRTOMBA2018
User avatar
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
Own Kudos:
3,889
 [1]
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
My Reviews
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
Posts: 2,319
Kudos: 3,889
 [1]
The line represented by which of the following equation does 03 Jul 2015, 06:01
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
IanStewart
GMATBaumgartner
The line represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1

A. y = 2x^2+5x+1
...

I'd emphasize that none of the equations in this question represent lines, despite what the question appears to say. The equations represent parabolas, and you don't need to know about parabolas for the GMAT.

There is one concept in this question that is occasionally tested - the concept of translation. If you have any equation at all in coordinate geometry, say:

y = x^2

that will be some curve in the coordinate plane (technically it will be a 'parabola', or U-shape). If you then modify the equation by adding a constant on the right side, say by adding 5:

y = x^2 + 5

then the graph of this new equation will look exactly the same as the graph of the first equation, except that it will be exactly 5 units higher. So when we add a constant on the right side of an equation, we're simply moving the picture of the equation up or down.
Show more

I think Bunuel and Ian have provided sufficient information to solve this problem.

Lines are always represented by LINEAR equations (equations that have maximum degree of the variables as 1). A quadratic equation (max. degree =2) can NEVER represent lines.

I would like to add one thing that people who are not familiar with 'conics', usually do not remember that \(y^2=4ax\) is the standard equation of a parabola. One way to eliminate such rote learning is to look at an equation and plot 2-3 points and see what shape of the curve do you get and then proceed from there. GMAT does not require you to remember fancy names.

\(y^2=4ax\) and \(y^2=4ax+Z\), where Z is any value (4,5,7.8,0.4 etc). These curves belong to 'same family' of parabolas with the only exception that these 2 curves will have their vertices offset by 'Z' amount.

Finally, for the curious minds out there, the attached picture shows all the possible combinations of 'simple' parabolas.
Attachments

Parabolas.png
Parabolas.png [ 7.88 KiB | Viewed 10294 times ]

Moderators:
Bunuel
Math Expert
109728 posts
Krunaal
Tuck School Moderator
853 posts