NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 20:55 It is currently 24 Apr 2024, 20:55
Decision Tracker
My Rewards
New posts
New comers' posts

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

In the xy plane, line P intersects y = x^2 + 3 at how many points?

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
happyapple123
Intern
Intern
Joined: 10 Nov 2018
Posts: 8
Own Kudos [?]: 16 [12]
Given Kudos: 88
Send PM
In the xy plane, line P intersects y = x^2 + 3 at how many points? [#permalink] New post   Updated on: 30 May 2020, 01:43
1
Kudos
11
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

59% (01:40) correct 41% (01:39) wrong based on 156 sessions
Hide Show timer Statistics
In the xy plane, line P intersects \(y=x^2 + 3\) at how many points?

(1) Line P has a slope of 0
(2) Line P passes through (-2, 7)

Show Spoiler
Side question- how do we find the two roots for y=x2 + 3 given that we can't square root negative 3?

Thanks!
ShowHide Answer
Official Answer
C

Originally posted by happyapple123 on 29 May 2020, 22:33.
Last edited by Bunuel on 30 May 2020, 01:43, edited 2 times in total.
Edited
User avatar
L
madgmat2019
Director
Director
Joined: 01 Mar 2019
Posts: 592
Own Kudos [?]: 506 [0]
Given Kudos: 207
Location: India
Concentration: Strategy, Social Entrepreneurship
GMAT 1: 580 Q48 V21
GPA: 4
Send PM
Reviews Badge
Re: In the xy plane, line P intersects y = x^2 + 3 at how many points? [#permalink] New post   29 May 2020, 23:12
is it y=x^2+3 or y=2x+3 ?
User avatar
L
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Posts: 3137
Own Kudos [?]: 2769 [0]
Given Kudos: 1510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Send PM
Re: In the xy plane, line P intersects y = x^2 + 3 at how many points? [#permalink] New post   Updated on: 30 May 2020, 00:14
happyapple123 wrote:
In the xy plane, line P intersects \(y=x^2 + 3\) at how many points?

(1) Line P has a slope of 0
(2) Line P passes through (-2, 7)

Show Spoiler
Side question- how do we find the two roots for y=x2 + 3 given that we can't square root negative 3?

Thanks!


Solve by putting values of x in equation y=x^2+3
We will get value of y
Plot them in quadrant.
It will be a parabola at the end.

Now statement 1: Line P slope is zero, that means line is parallel to x axis. But we don't know from where its parallel to x axis. (Insufficient)

Statement 2: P passes through (-2,7) but to draw equation of line we need another point on line P (insufficient)

Statement 1&2: slope is zero and it passes through point (-2,7) . so the parallel line is at 7 point distance from x axis. If you plot this straight parallel line and the line drew from y=x^2+3 you will get the point at which they intersect. Which is 2 ( hence both statements together is sufficient)
Answer is C

Posted from my mobile device

Originally posted by yashikaaggarwal on 29 May 2020, 23:21.
Last edited by yashikaaggarwal on 30 May 2020, 00:14, edited 1 time in total.
User avatar
L
AnirudhaS
LBS Moderator
Joined: 30 Oct 2019
Posts: 836
Own Kudos [?]: 775 [0]
Given Kudos: 1577
Send PM
Re: In the xy plane, line P intersects y = x^2 + 3 at how many points? [#permalink] New post   30 May 2020, 00:10
madgmat2019 wrote:
is it \(y=x^2+3\) or y=2x+3 ?

it is \(y=x^2+3\)
this is in the form of a parabola, so not a straight line. (it is not a straight line as you suggested y=2x+3)
So now we know its a parabola, and a straight line with slope 0 will either intersect in 2 places or not intersect at all.

Also yashikaaggarwal , according to me you were also thinking that it will intersect in one place, but IMO it would be 2 or 0.
Let us expand on this,
So the equation of the parabola given is \(y=x^2+3\)..........(i)
and equation of line with slope 0 and passing through (-2,7), y=7..............(ii)
Solving (i) and (ii), we get x=+2, -2
This proves the straight line intersects the parabola in 2 places.

Answer would be C as we need both conditions to know if the straight line intersects the parabola or not.
User avatar
L
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Posts: 3137
Own Kudos [?]: 2769 [0]
Given Kudos: 1510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Send PM
Re: In the xy plane, line P intersects y = x^2 + 3 at how many points? [#permalink] New post   30 May 2020, 00:13
AnirudhaS wrote:
madgmat2019 wrote:
is it \(y=x^2+3\) or y=2x+3 ?

it is \(y=x^2+3\)
this is in the form of a parabola, so not a straight line. (it is not a straight line as you suggested y=2x+3)
So now we know its a parabola, and a straight line with slope 0 will either intersect in 2 places or not intersect at all.

Also yashikaaggarwal , according to me you were also thinking that it will intersect in one place, but IMO it would be 2 or 0.
Let us expand on this,
So the equation of the parabola given is \(y=x^2+3\)..........(i)
and equation of line with slope 0 and passing through (-2,7), y=7..............(ii)
Solving (i) and (ii), we get x=+2, -2
This proves the straight line intersects the parabola in 2 places.

Answer would be C as we need both conditions to know if the straight line intersects the parabola or not.


Yea sadly I solved it keeping equation of line in mind, thanks for correcting

Posted from my mobile device
User avatar
B
Mannisha
Tutor
Joined: 14 Apr 2020
Posts: 25
Own Kudos [?]: 39 [4]
Given Kudos: 1
Location: India
Send PM
In the xy plane, line P intersects y = x^2 + 3 at how many points? [#permalink] New post   Updated on: 07 Jun 2020, 11:14
3
Kudos
1
Bookmarks
Expert Reply
In the xy plane, line P intersects \(y=x^2 + 3\) at how many points?

(1) Line P has a slope of 0
(2) Line P passes through (-2, 7)


Thanks

Please find the solution below:
Attachments

IMG-20200530-WA0009 (1).jpg
IMG-20200530-WA0009 (1).jpg [ 123.37 KiB | Viewed 2593 times ]


Originally posted by Mannisha on 30 May 2020, 00:52.
Last edited by Mannisha on 07 Jun 2020, 11:14, edited 1 time in total.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618836 [0]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: In the xy plane, line P intersects y = x^2 + 3 at how many points? [#permalink] New post   30 May 2020, 01:43
Expert Reply
happyapple123 wrote:
In the xy plane, line P intersects \(y=x^2 + 3\) at how many points?

(1) Line P has a slope of 0
(2) Line P passes through (-2, 7)

Show Spoiler
Side question- how do we find the two roots for y=x2 + 3 given that we can't square root negative 3?

Thanks!


Similar question to practice: https://gmatclub.com/forum/in-the-xy-pl ... 09607.html
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32658
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: In the xy plane, line P intersects y = x^2 + 3 at how many points? [#permalink] New post   05 Jun 2023, 21:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: In the xy plane, line P intersects y = x^2 + 3 at how many points? [#permalink]
05 Jun 2023, 21:15
Moderator:
Bunuel
Math Expert
92900 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions