Another GMAT prep PS questn

[meghamehta15]

In the xy-plane, at what point 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)


a. Statement 1 alone is sufficient
b. Statement 2 alone is sufficient
c. Both statements together are sufficient
d. Each statement alone is sufficient
e. Statements one and two together are not sufficient

Pls explain! :roll:

[luvaduva]

We are looking for the x-intercept(s).

I. a+b = -1
y = x^2 +ax +bx +ab

-We have two equations and 4 unknowns. Cannot solve this. This is not sufficient.
-Answer is B,C, or E.

II. The graph intersects the Y-axis at (0, -6)
-6 = (0)^2 + a(0) + b(0) + ab

-6 = ab
y = x^2 +ax +bx +ab

-We have two equations and 4 unknowns still. Cannot solve this. This is not sufficient.
-Answer is C or E.

Using I and II...

a + b = -1
ab = -6

-We have two equations and 2 unknowns now. This can be solved. You CAN find the x-intercept(s)

Answer is C.

[subbu123]

Hi ,

I believe the ans is e as we can't uniquely find out values for a,b

They can be -3,2 or 2,-3.

[nishantb]

i too believe the answer should be E. Unique answers cannot be found out.

GmatPrep says the answer is C.

Can the moderators or some gmat gurus throw some light on what should be the correct answer? or did gmatPrep got this wrong?

[ikant]

Well.. we are trying to find the points where a quadratic euation in x intersects x - axis.

Now by the calculation you have solved a quadratic in a or b to get two values :: -3, 2

But here lies the rub. These calues are for a or b and not for x.

The eqn becomes (x-3)(x+2)=0.

This uniquely gives two points (3,0) and (-2,0).
And this is logical since a quadratic can have two points of intersection.

[camitava]

Guys, I agree with the fact that GMAT always look for unique and clear answer in DS. But here the Qs is asking for the X-intercept of the curve. As the curve is a curve of parabola, I guess, it will intercept X-axis at two points. So this answer is giving a clear and in detail answer. So in one word, agree with iKant and luvaduva. The OA should be C but not E.

[rey.fernandez]

I suspect that the question was misquoted in the original post. If the official answer is C, then I'd be willing to bet the question asks "at which two points does the graph intersect the x-axis." meghamehta15, will you please check to make sure?

If, in fact, it asks for exactly one point, then it's an illogical question, since it must cross at two points, (a,0) and (b,0). The only exception would be if a = b. But the data given in the statements rules out this possibility.

[nishantb]

I suspect that the question was misquoted in the original post. If the official answer is C, then I'd be willing to bet the question asks "at which two points does the graph intersect the x-axis." meghamehta15, will you please check to make sure?

If, in fact, it asks for exactly one point, then it's an illogical question, since it must cross at two points, (a,0) and (b,0). The only exception would be if a = b. But the data given in the statements rules out this possibility.

I just checked up the original question on gmatprep. It reads:

In the xy-plane, at what two points does the graph of y = (x+a)(x+b) intersect the x-axis?

So the answer is C! Thanks everyone for their valuable responses.

[supershick]

I'm still confused in this question.

I solve the possible values for b=2,-3 & a=2,-3 .

To fulfill the data, they can be any combination though. (a,b) = (-3,2) or (2,-3)

The two points that intersect the X-axis is (0,-a) & (0,-b).

How do you know which combo is it? Is it (0,3)&(0,-2) or (0,-2)&(0,3) ?

Am I missing something? I'm asking because I just encountered this on the GMATPrep and I answered (E) as well and this was my reasoning.

[ranagaurav]

There can be more than 2 points at which the equation will intersect X Axis.
But these points will not be integers and the question doesnot say that a and b have to integers.. so answer should be E.. isnt it???

[supershick]

I calculated them to be integers. How did you get non-integer values?

[rey.fernandez]

supershick, you'll notice that the question does not specifically ask for values for a and b. It asks for the two points through which the graph crosses the x-axis. The information given (in both statements together) is enough to answer the question: (2, 0) and (-3,0). It doesn't matter which value is a and which one is b -- all that matters is that you know the two x-intercepts.

ranagaurav, as this function is quadratic, it will have at most two distinct x-intercepts. Read the earlier posts to see exactly how to calculate the x-intercepts correctly.

Rey

[supershick]

Rey, thanks for the response,

I understand what you're saying but the question does ask "...what two points intersect the x-axis..."

The two points are (0,-a) and (0,-b), right?

Now that we have that, if we have enough data to pinpoint the values of 'a' and 'b', then we're good to go right?

With the two pieces of information combined, the possible values for 'a' are -3 and 2. The two possible values for b are -3 and 2 as well.

I gathered this information from (2), "ab = -6" and from (1), "a + b = -1". Solving for 'a' and 'b' would give the aforementioned values right? To fulfill the data given, it can be (-3)(2) = -6 or (2)(-3) = -6. Therefore, the values for 'a' and 'b' change.

This is my thinking process. I must be thinking way too deeply into this. Haha.

[ranagaurav]

I also calculated it the way supershick has done, instead of the quadratc equations way... I thought fractions cud come.. but was wrong..
Anyway now with these 2 set of eqautions as written above how do we know which is right

[aj5105]

(C)