Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 May 2016, 18:56

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The line represented by which of the following equation does

Author Message
TAGS:

### Hide Tags

Intern
Joined: 11 Apr 2012
Posts: 42
Followers: 0

Kudos [?]: 39 [0], given: 93

The line represented by which of the following equation does [#permalink]

### Show Tags

25 Aug 2012, 04:20
9
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

72% (01:55) correct 28% (01:17) wrong based on 186 sessions

### HideShow timer Statistics

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

@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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Jun 2013, 05:52, edited 2 times in total.
Edited the question.
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 90

Kudos [?]: 771 [2] , given: 43

Re: The line represented by which of the following equation does [#permalink]

### Show Tags

25 Aug 2012, 04:39
2
KUDOS
1
This post was
BOOKMARKED
vinay911 wrote:
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.

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).
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Joined: 11 Apr 2012
Posts: 42
Followers: 0

Kudos [?]: 39 [0], given: 93

Re: The line represented by which of the following equation does [#permalink]

### Show Tags

25 Aug 2012, 09:54
EvaJager wrote:
vinay911 wrote:
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.

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!
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 90

Kudos [?]: 771 [0], given: 43

Re: The line represented by which of the following equation does [#permalink]

### Show Tags

25 Aug 2012, 10:06
vinay911 wrote:
EvaJager wrote:
vinay911 wrote:
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.

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!

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.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Director
Joined: 24 Aug 2009
Posts: 505
Schools: Harvard, Columbia, Stern, Booth, LSB,
Followers: 12

Kudos [?]: 586 [0], given: 241

Re: The line represented by which of the following equation does [#permalink]

### Show Tags

10 Sep 2012, 15:23
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
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Intern
Joined: 28 Sep 2012
Posts: 9
GMAT Date: 01-25-2013
GPA: 3.38
Followers: 0

Kudos [?]: 3 [2] , given: 9

Re: The line represented by which of the following equation does [#permalink]

### Show Tags

06 Nov 2012, 10:34
2
KUDOS
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.
Manager
Joined: 04 Apr 2013
Posts: 153
Followers: 1

Kudos [?]: 36 [0], given: 36

Re: The line represented by which of the following equation does [#permalink]

### Show Tags

01 Jun 2013, 07:35
manjusu wrote:
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.
_________________

MGMAT1 - 540 ( Trying to improve )

Manager
Joined: 27 Feb 2012
Posts: 137
Followers: 1

Kudos [?]: 44 [0], given: 22

Re: The line represented by which of the following equation does [#permalink]

### Show Tags

01 Jun 2013, 08:17
manjusu wrote:
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
_________________

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Please +1 KUDO if my post helps. Thank you.

Math Expert
Joined: 02 Sep 2009
Posts: 33000
Followers: 5751

Kudos [?]: 70481 [0], given: 9847

Re: The line represented by which of the following equation does [#permalink]

### Show Tags

02 Jun 2013, 05:58
Expert's post
BangOn wrote:
manjusu wrote:
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

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.
_________________
Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 43

Kudos [?]: 462 [0], given: 355

Re: The line represented by which of the following equation does [#permalink]

### Show Tags

31 Mar 2014, 13:43
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.

Hope this helps
Cheers
J
Current Student
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 993
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)
Followers: 147

Kudos [?]: 1110 [0], given: 226

Re: The line represented by which of the following equation does [#permalink]

### Show Tags

19 Jun 2014, 09:41
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 [ 34.26 KiB | Viewed 1710 times ]

_________________

Piyush K
-----------------------
Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison
Don't forget to press--> Kudos
My Articles: 1. WOULD: when to use? | 2. All GMATPrep RCs (New)
Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

Manager
Joined: 03 May 2013
Posts: 71
Followers: 0

Kudos [?]: 5 [0], given: 101

The line represented by which of the following equations doe [#permalink]

### Show Tags

03 Jul 2015, 03:29
The line represented by which of the following equations does not interact 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

Source - Jamboree
Math Expert
Joined: 02 Sep 2009
Posts: 33000
Followers: 5751

Kudos [?]: 70481 [0], given: 9847

Re: The line represented by which of the following equation does [#permalink]

### Show Tags

03 Jul 2015, 03:31
Expert's post
vipulgoel wrote:
The line represented by which of the following equations does not interact 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

Source - Jamboree

Merging topics.

Refer to the discussion above.
_________________
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1181
Followers: 375

Kudos [?]: 1230 [2] , given: 4

Re: The line represented by which of the following equation does [#permalink]

### Show Tags

03 Jul 2015, 04:32
2
KUDOS
Expert's post
GMATBaumgartner wrote:
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.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2606
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 97

Kudos [?]: 1091 [0], given: 777

The line represented by which of the following equation does [#permalink]

### Show Tags

03 Jul 2015, 06:01
Expert's post
IanStewart wrote:
GMATBaumgartner wrote:
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.

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 [ 7.88 KiB | Viewed 894 times ]

_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

The line represented by which of the following equation does   [#permalink] 03 Jul 2015, 06:01
Similar topics Replies Last post
Similar
Topics:
Which of the following equations represents a line that is perpendicul 2 29 Nov 2015, 10:47
7 Which of the following equations represents a line on xy-plane that 1 15 Oct 2015, 18:21
The line represented by which of the following equations doe 0 03 Jul 2015, 03:29
1 Which of the following equations represents a line perpendicular to li 2 04 Jun 2015, 04:08
2 Which of the following equations represents a line that is perpendicul 2 29 Oct 2014, 09:11
Display posts from previous: Sort by