BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

co-ordinate geometry - GMAT Prep

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 29
Joined: Fri Sep 25, 2009 9:26 am

co-ordinate geometry - GMAT Prep

by Pugalenthi » Sat Jun 30, 2012 9:14 am
Hi, I am stumped on this question (particularly seeing x^2 in the equation whereas the line equation is y = mx + b)...any explanation would be much appreciated.

In the X-Y plane, at what 2 points does the graph y=(x+a)(x+b) intersect the X-axis?
(1)a + b = -1
(2) the graph intersects the Y-axis at (0,-6)

The answer is C.
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Sat Jun 30, 2012 9:33 am
Pugalenthi wrote:In the X-Y plane, at what 2 points does the graph y=(x+a)(x+b) intersect the X-axis?
(1)a + b = -1
(2) the graph intersects the Y-axis at (0,-6)
The equation given in the question does not represent a straight line. But we do not need to know what does it represent. The points where the graph of the equation intersects the X-axis will have zero as the y-coordinate.

Let's see for what values of x, y becomes zero.
--> (x + a)(x + b) = 0
Hence, x = -a and x = -b

Hence, the points where the graph intersects the X-axis are (-a, 0) and (-b, 0)

Statement 1: a and b can have many values --> Not sufficient

Statement 2: Hence, at x = 0, y = -6
Therefore, -6 = (0 + a)(0 + b) ---> ab = -6

a and b can have many values.

Not sufficient

1 & 2 Together: (a + b) = -1 and ab = -6
Now, y = (x + a)(x + b) = (x² + (a + b)x + ab) = (x² - x - 6) = (x + 2)(x - 3)

Hence, the graph intersects the X-axis at (-2, 0) and (3, 0)

Sufficient

The correct answer is C.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Post new topic Post Reply
• Page 1 of 1