May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 29 Nov 2006
Posts: 284
Location: Orange County, CA

In the xyplane, at what two points does the graph of
[#permalink]
Show Tags
Updated on: 01 Jun 2013, 03:28
Question Stats:
71% (01:50) correct 29% (01:57) wrong based on 1948 sessions
HideShow timer Statistics
In the xyplane, at what two points does the graph of y= (x+a)(x+b) intersect the xaxis? (1) a + b = 1 (2) The graph intersects the yaxis at (0, 6) OPEN DISCUSSION OF THIS QUESTION IS HERE: inthexyplaneatwhatpointsdoesthegraphofy88398.html
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by misterJJ2u on 21 Jan 2007, 00:36.
Last edited by Bunuel on 01 Jun 2013, 03:28, edited 2 times in total.
Edited the question and added the OA




Math Expert
Joined: 02 Sep 2009
Posts: 55271

Re: graph question  gmat prep
[#permalink]
Show Tags
Updated on: 22 Oct 2009, 13:47
In the xyplane, at what two points the graph of y=(x+a)(x+b) intersect the xaxis? (1) a+b=1 (2) The graph intersects yaxis at (0,6) Xintercepts of the function \(f(x)\) or in our case the function (graph) \(y=(x+a)(x+b)\) is the value(s) of \(x\) for \(y=0\). So basically the question asks to find the roots of quadratic equation \((x+a)(x+b)=0\). \((x+a)(x+b)=0\) > \(x^2+bx+ax+ab=0\) > \(x^2+(a+b)x+ab=0\). Statement (1) gives the value of \(a+b\), but we don't know the value of \(ab\) to solve the equation. Statement (2) tells us the point of yintercept, or the value of \(y\) when \(x=0\) > \(y=(x+a)(x+b)=(0+a)(0+b)=ab=6\). We know the value of \(ab\) but we don't know the value of \(a+b\) to solve the equation. Together we know the values of both \(a+b\) and \(ab\), hence we can solve the quadratic equation, which will be the xintercepts of the given graph. Answer: C. Hope it's clear.
_________________
Originally posted by Bunuel on 22 Oct 2009, 13:28.
Last edited by Bunuel on 22 Oct 2009, 13:47, edited 1 time in total.




SVP
Joined: 01 May 2006
Posts: 1740

For me (C)
y= (x+a)(x+b) intersect the xaxis is equivalent to search the solutions of :
(x+a)(x+b) =0
<=> x^2 + (a+b)*x + a*b = 0 (1)
From 1
a+b = 1
implies:
(1) <=> x^2 x + a*(a1) = 0
we need to know a.
INSUFF.
From 2
(0, 6) is the Y interceptor. That implies:
a*b = 6.
we need another equation with a & b, in other words, the values of a and b.
INSUFF.
Both (1) and (2)
a+b = 1
a*b = 6
These equations give us (a,b), what we need to find the roots.
SUFF.




Senior Manager
Joined: 06 Apr 2008
Posts: 361

Re: DS: Coordinate Geometry (intersection)
[#permalink]
Show Tags
19 Aug 2008, 08:58
lordw wrote: In the xy plane at what two points does the graph of y= (x+a) (x+b) intersect the x axis?
(1) a+b= 1
(2) The graph intersects the y axis at (0,6).
Guys I felt lost in this problem with all the letters. Any idea of how to put this in a more "visible" way? For instance, may be picking numbers? Many tks. Lw. Graph intersects xaxis when y=0 , therefore two points where graph intersects is x=a, x=b Statement 1) is insuff Statement 2) just tells one point Combining both , points are 6 and 5 Answer is C)



Senior Manager
Joined: 19 Mar 2008
Posts: 332

Re: DS: Coordinate Geometry (intersection)
[#permalink]
Show Tags
19 Aug 2008, 10:00
In the xy plane at what two points does the graph of y= (x+a) (x+b) intersect the x axis?
(1) a+b= 1
(2) The graph intersects the y axis at (0,6).
for point intersect the x axis, we need to find x when y = 0 so 0 = (x+a) (x+b) x = a or b So, we need to find a and b
(1) +(2) is sufficient to find two unknown
(C)



Manager
Joined: 27 Sep 2008
Posts: 73

Re: xy plane
[#permalink]
Show Tags
11 Oct 2008, 12:15
The answer is (E) y=(x+a)(x+b) y=x^2+ax+ab+ab y=x^2+x(a+b)+ab statement 1 a+b = 1 y=x^2x+ab 0=x^2x+ab insufficient statement 2 y=x^2+x(a+b)+ab ab=6 0=x^2+x(a+b)6 insufficient both statements 0=x^2x6 6=x(x1) x can be 2 or 3 insufficient



Senior Manager
Joined: 21 Apr 2008
Posts: 256
Location: Motortown

Re: xy plane
[#permalink]
Show Tags
11 Oct 2008, 14:36
I agree with fresinha12, I get 3 and 2
in the question, it asks for points, so I guess it is okay to say that the answer is C



VP
Joined: 17 Jun 2008
Posts: 1162

Re: xy plane
[#permalink]
Show Tags
12 Oct 2008, 11:51
redbeanaddict wrote: In the xy plane, at what points does the graph of y=(x+a)(x+b) intersect the x axis? 1. a+b = 1 2. The graph intersects the y axis at (0, 6) the graph intersects x axis hen y=0 => x=a and x=b are the points to get the points we must know a and b but how to find 1) does not help 2)does not help => gives ab=6 combine 1 and 2 we get a and b hence is SUFFI to answr IMO C
_________________



Manager
Joined: 22 Jul 2009
Posts: 161

Re: GMAT PREP_DS_XY plane
[#permalink]
Show Tags
20 Aug 2009, 19:06
The answer provided above is incorrect.
The question does not ask for the values of a and b.
It asks for the values of x when y=0. In other words, it asks for the roots of the quadratic.
Statement 2 is sufficient, as it says that ab=6.
Thus: x^26x6=0 > Roots are 0.87 and 6.87.
Answer is B.



Manager
Joined: 29 Jul 2009
Posts: 157

graph question  gmat prep
[#permalink]
Show Tags
22 Oct 2009, 13:14
Hi, so here's what I did: y= x^2+ xb+xa+ab I replace y with 6 and x with 0 6=0+0+ab so ab= 6 I replace ab with 6 and y with 0 in the first equation 0= x^2+ xb+xa+(6) 6=x(x+b+a) from statement A, we know that a+b=1 so 6 = x(x+1) x^2+x6 = 0 (x3)(x+2) x=3 or x = 2 I then got stuck so what is the value of x?
Attachments
Q19DS.jpg [ 49.7 KiB  Viewed 124589 times ]



Manager
Joined: 29 Jul 2009
Posts: 157

Re: graph question  gmat prep
[#permalink]
Show Tags
22 Oct 2009, 13:45
Bunuel wrote: In the xyplane, at what two points the graph of y=(x+a)(x+b) intersect the xaxis? (1) a+b=1 (2) The graph intersects yaxis at (0,6)
Q is in what two points graph intersect the xaxis. Which means we should be able to find two points: (x1,0) and (x2,0), so basiacally the roots of equation: (x+a)(x+b)=0.
y=(x+a)(x+b)=x^2+x(a+b)+ab. > We must now the values of (a+b) and ab.
(1) a+b=1 > not sufficient. (2) x=0, y=6 > 6=ab not sufficient
(1)+(2) a+b=1, ab=6 > y=x^2+x(a+b)+ab=x^2x6 > x intersection means y=0 > 0=x^2x6 > (x+2)(x3)=0  > x1=2, x2=3. Sufficient
Answer C. OMG!! I didnt realize that I need to find two points!! thats why when i ended up with 2 and 3, i got confused because i was left with two values!!! how did you find ab=6? (2) x=0, y=6 > 6=ab not sufficientdid you use the formula y=mx+b? thanks,



Math Expert
Joined: 02 Sep 2009
Posts: 55271

Re: graph question  gmat prep
[#permalink]
Show Tags
22 Oct 2009, 13:51
(2) The graph intersects yaxis at (0,6) > x=0, y=6 > y=x^2+x(a+b)+ab > 6=0^2+0(a+b)+ab > ab=6.
_________________



Manager
Joined: 05 Jul 2009
Posts: 152

Re: graph question  gmat prep
[#permalink]
Show Tags
23 Oct 2009, 04:34
Great Bunuel! I have been seeing your post and I have to say I am quite amazed at your math skills! Have you taken the GMAT yet? I would very much like to know your score.



Director
Joined: 01 Apr 2008
Posts: 739
Name: Ronak Amin
Schools: IIM Lucknow (IPMX)  Class of 2014

Re: graph question  gmat prep
[#permalink]
Show Tags
23 Oct 2009, 10:47
Yup Bunuel is awesome as always Here, we need to find the solution for (x+a)(x+b) = 0. Solutions are x=a, x=b. Thus we need to find unique values for a and b to answer the question. 1) we get a relation between a and b but not sufficient to derive unique values of a and b. insuff. 2) we get a point on the graph, so substituting values of x and y in the graph we get ab = 6. Again, this is insufficient to find unique values of a and b. insuff. Combining, we have, a+b=1 and ab= 6, two variables, two equations. So answer is C. The points will be (a,0), (b,0).



Manager
Joined: 22 Sep 2009
Posts: 183
Location: Tokyo, Japan

Re: GMAT PREP_DS_XY plane
[#permalink]
Show Tags
23 Nov 2009, 19:31
powerka wrote: The answer provided above is incorrect.
The question does not ask for the values of a and b.
It asks for the values of x when y=0. In other words, it asks for the roots of the quadratic.
Statement 2 is sufficient, as it says that ab=6.
Thus: x^26x6=0 > Roots are 0.87 and 6.87.
Answer is B. Fig is correct. You made a mistake on the equation, it is x^2(a+b)x+ab. Essentially, you are looking for a and b itself, or equations that tell you a+b and ab. Hence, C



Intern
Joined: 04 Dec 2009
Posts: 17

Re: graph question  gmat prep
[#permalink]
Show Tags
25 Dec 2010, 04:49
Bunuel wrote: In the xyplane, at what two points the graph of y=(x+a)(x+b) intersect the xaxis? (1) a+b=1 (2) The graph intersects yaxis at (0,6)
Xintercepts of the function \(f(x)\) or in our case the function (graph) \(y=(x+a)(x+b)\) is the value(s) of \(x\) for \(y=0\). So basically the question asks to find the roots of quadratic equation \((x+a)(x+b)=0\).
\((x+a)(x+b)=0\) > \(x^2+bx+ax+ab=0\) > \(x^2+(a+b)x+ab=0\).
Statement (1) gives the value of \(a+b\), but we don't know the value of \(ab\) to solve the equation.
Statement (2) tells us the point of yintercept, or the value of \(y\) when \(x=0\) > \(y=(x+a)(x+b)=(0+a)(0+b)=ab=6\). We know the value of \(ab\) but we don't know the value of \(a+b\) to solve the equation.
Together we know the values of both \(a+b\) and \(ab\), hence we can solve the quadratic equation, which will be the xintercepts of the given graph.
Answer: C.
Hope it's clear. I get your explanation.But using a+b=1 and ab=6 and solving it I get (ab)^2=25 .which means ab=+5 or 5.So since I cant be sure of the value of ab,I selected option e as the answer.Can you please help on this.



Math Expert
Joined: 02 Sep 2009
Posts: 55271

Re: graph question  gmat prep
[#permalink]
Show Tags
25 Dec 2010, 08:49
gautamsubrahmanyam wrote: Bunuel wrote: In the xyplane, at what two points the graph of y=(x+a)(x+b) intersect the xaxis? (1) a+b=1 (2) The graph intersects yaxis at (0,6)
Xintercepts of the function \(f(x)\) or in our case the function (graph) \(y=(x+a)(x+b)\) is the value(s) of \(x\) for \(y=0\). So basically the question asks to find the roots of quadratic equation \((x+a)(x+b)=0\).
\((x+a)(x+b)=0\) > \(x^2+bx+ax+ab=0\) > \(x^2+(a+b)x+ab=0\).
Statement (1) gives the value of \(a+b\), but we don't know the value of \(ab\) to solve the equation.
Statement (2) tells us the point of yintercept, or the value of \(y\) when \(x=0\) > \(y=(x+a)(x+b)=(0+a)(0+b)=ab=6\). We know the value of \(ab\) but we don't know the value of \(a+b\) to solve the equation.
Together we know the values of both \(a+b\) and \(ab\), hence we can solve the quadratic equation, which will be the xintercepts of the given graph.
Answer: C.
Hope it's clear. I get your explanation.But using a+b=1 and ab=6 and solving it I get (ab)^2=25 .which means ab=+5 or 5.So since I cant be sure of the value of ab,I selected option e as the answer. Can you please help on this. The question asks: at what two points the graph of \(y=(x+a)(x+b)\) intersect the xaxis? So we should find two points: (x1, 0) and (x2, 0), (points of intersection of the given graph with Xaxis). Basically the question asks to find the roots of quadratic equation \((x+a)(x+b)=0\) > \(x^2+(a+b)x+ab=0\). When we combine statement we have: \(a+b=1\) and \(ab=6\), so you should solve quadratic equation \(x^2x6=0\) > \(x_1=2\) and \(x_2=3\) > points of intersection are (2, 0) and (3, 0). Check on the diagram: Attachment:
MSP272919df1bed26600c1g0000673adafe5fce1fc2.gif [ 3.61 KiB  Viewed 123077 times ]
Hope it's clear.
_________________



Manager
Joined: 19 Dec 2010
Posts: 95

Re: xy plane
[#permalink]
Show Tags
17 Mar 2011, 22:27
This problem is easy when you don't start by rapidly trying to solve it. Think about it before you put pen to paper... "what two points does the graph intersect the x axis..." This is a simple problem asking for 2 values of x... statement 1 gives us a+b=1 statement 2 gives us ab
Start with the stem...multiply x+a and x+b, it will become very clear. Y = X^2 + X (a+b) + ab statement 1 gives you a+b, we need ab statement 2 says graph intersects y at (0,6). Plug this into the original statement, you will get ab. Solved = C!










