GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 25 Feb 2020, 14:17

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

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

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 61484
In the xy-plane, line L intersects y = x^2 + 2 at how many points?  [#permalink]

Show Tags

New post 01 Nov 2019, 06:48
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (01:30) correct 43% (01:50) wrong based on 96 sessions

HideShow timer Statistics

VP
VP
avatar
V
Joined: 20 Jul 2017
Posts: 1331
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: In the xy-plane, line L intersects y = x^2 + 2 at how many points?  [#permalink]

Show Tags

New post 01 Nov 2019, 07:07
Bunuel wrote:
In the xy-plane, line L intersects y = x^2 + 2 at how many points?

(1) The slope of Line L is 0
(2) The Line passes through (4,5)


Are You Up For the Challenge: 700 Level Questions


y = x^2 + 2 is a parabola facing upwards with vertex = (0, 2)

(1) The slope of Line L is 0
--> The line is parallel to x-axis and equation of line is y = k, for any number k
--> Many intersections are possible.

Case 1: If k = 1, Equation of line is y = 1 --> no intersections
Case 2: If k = 2, Equation of line is y = 2 --> 1 intersection
Case 3: If k = 3, Equation of line is y = 3 --> 2 intersections
--> Insufficient

(2) The Line passes through (4,5)
Since we do not know the slope of the line, we cannot say exact number of intersections --> Insufficient

Combining (1) & (2),
slope of line is 0 and passes through (4, 5)
--> Equation of line is y = 5
--> Number of intersections = 2 --> Sufficient

IMO Option C
Senior Manager
Senior Manager
User avatar
P
Joined: 21 Jun 2017
Posts: 413
Location: India
Concentration: Finance, Economics
Schools: IIM
GMAT 1: 620 Q47 V30
GPA: 3
WE: Corporate Finance (Commercial Banking)
Re: In the xy-plane, line L intersects y = x^2 + 2 at how many points?  [#permalink]

Show Tags

New post 01 Nov 2019, 11:01
A line is defined by 1. Slope ( direction ) and 2. a point

Hence C

Posted from my mobile device
VP
VP
avatar
P
Joined: 24 Nov 2016
Posts: 1229
Location: United States
CAT Tests
Re: In the xy-plane, line L intersects y = x^2 + 2 at how many points?  [#permalink]

Show Tags

New post 28 Jan 2020, 04:00
Bunuel wrote:
In the xy-plane, line L intersects y = x^2 + 2 at how many points?

(1) The slope of Line L is 0
(2) The Line passes through (4,5)


Parabolas: a line in quadratic form means its a parabola;

Transform y=x^2+2 in the form y=ax^2+bx+c
a=1 (upwards parabola), b=0, c=2

If a > 0 (positive) then the parabola opens upward.
If a < 0 (negative) then the parabola opens downward.

Find the vertex to see where the parabola originates.

Vertex(x)=-b/2a=-(0)/2(1)=0
Vertex(y): y=x^2+2, y=(0)+2=2
Vertex(x,y)=(0,2)

(1) The slope of Line L is 0 insufic

mL=0, then L is a horizontal line, y=mx+b becomes y=0+b, y=b
If y<2, then number of intersections is 0
If y=2, then number of intersections is 1
If y>2, then number of intersections is 2

(2) The Line passes through (4,5) insufic

(1&2) sufic
Line L is y=5, a horizontal parallel to the x-axis;
It intersects 2 points.

Ans (C)
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8594
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: In the xy-plane, line L intersects y = x^2 + 2 at how many points?  [#permalink]

Show Tags

New post 28 Jan 2020, 10:14
Bunuel wrote:
In the xy-plane, line L intersects y = x^2 + 2 at how many points?

(1) The slope of Line L is 0
(2) The Line passes through (4,5)


Are You Up For the Challenge: 700 Level Questions


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Assume the equation of the line L is \(y=mx+b\).

Since we have 2 variables (\(m\) and \(b\)) and 0 equations, C is most likely the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

Since we have \(y=x^2+2\) and \(y=mx+b\), the number of intersections is the number of roots of the equation \(x^2 + 2 = mx + b\) or \(x^2 - mx + (2-b) = 0\).
Then we can determine the number of roots of the equation \(x^2 - mx + (2-b) = 0\) using its discriminant \(m^2 - 4(2-b)\).

Since the line passes through \((4,5)\), we have \(5 = 4m + b\) or \(b = 5 - 4m\).
Then the discriminant is \(m^2 - 4(2-b) = m^2 - 4(2-5+4m) = m^2 -16m + 12\).

Since the slope of the line is \(0\), we have \(m = 0\).
Then the discriminant is \(m^2 - 16m + 12 = 12 > 0\), which tells the line L, \(y=mx+b\) and \(y=x^2+2\) have two intersection.

Since both conditions together yield a unique solution, they are sufficient.

Therefore, C is the answer.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
_________________
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 $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
GMAT Club Bot
Re: In the xy-plane, line L intersects y = x^2 + 2 at how many points?   [#permalink] 28 Jan 2020, 10:14
Display posts from previous: Sort by

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

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne