Data Sufficiency

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

（1）a+b=-1

(2)The graph intersects the y-axis at (0,-6)

Please show me the way to solve such type of questions.....

Ok, here you go...

given :- y=(x+a)(x+b)

to find where it intersects x-axis, y co-ordinate should be 0.

Subsititue y=0 in the equation. you get

(x+a)(x+b) = 0 ------> Equation 1

meaning x can be -a or -b.
So the two co-ordinates are (-a,0) and (-b,0).

Now, using other given information -

(1) a + b = -1.

(2)The graph intersects the y-axis at (0,-6)
For this, do the same thing, subsitiute x=0 and y=-6 in the equation,
you get : x^2 + x(a+b) + ab = y
=> ab = -6

Now you have a+b = -1 and ab = -6

Substitute this back into the equation (1) to find out values for x


(x+a)(x+b) = 0
=> x^2 + x(a+b) + ab = 0
=>x^2 -x - 6 = 0
=>(x-3)(x+2) = 0

Hence, the two points where graph intersects are (3,0) and (-2,0)

Problem Solved


Whenever you get such co-ordinate geomtry problems, trying using the given data and subsituting in the equations given.

Just realized this question was from DS and not a problem solving question. But anyways, you need both the options to answer your question.

So Answer is [C]. Both stmts together are sufficient and neither stmt alone.

Tons of thanks for such an excellent explanation.
Would you please mail me some math materials from which I can bush my math concept at [email protected]?
On the other hand, I may sometime mail you some problems in doc format.
I am weak in some specific areas of maths.
PLEASE HELP ME.
Again thanks in advance for help.

I really don't have any particular material for Math. All I have is GMAT books(hard copies).

I am weak in verbal so I am spending all my time on that as of now... I have also forgotten some concepts in Permutations,Combinations ,probability which I need to revise.

The solution that I gave was just off my head from whatever high school math knowledge I have.. So, for such problems only practicing will give u confidence... The more u practice the more ur mind will get used to solving such kind of problems....

And when you are consideing problems for practicing doesnt mean they shuld be GMAT type. If you type co-ordinate geometry problems in Google, I am sure you will get many tutorials and practice problems in general.

Solve as many as u can!!

You are most welcome to ask for help in Math. I will try to help as much as I can, provided I am able to solve your questions