Data Sufficiency

26.In the xy-plane, the graph represented by y=x^2+px+r have how many intersects with axis-x?
1). p^2>r
2). r^2>p

An intersection with axis X is the equivalent of y = x^2+px+r = 0. This is a second degree equation, which could have from 0 to maximum two roots, depending on the discriminant, which will be p^2 - 4r.

Let me explain from the top with equations so that you may understand a bit better.
Second degree equations have the following pattern: a*x^2 + b*x + c = 0. The discriminant for these equations is called delta and is equal to b^2 - 4ac. Delta helps you to figure out how many solutions there are to your equation, meaning how many x-es fulfill a*x^2 + b*x + c = 0. You have three cases:

1. delta < 0 means that there is no x with a*x^2 + b*x + c = 0. Example: x^2 + 2x + 6 = 0 (in this case, the equation will always be positive).
2. delta = 0 means that there is just one x with a*x^2 + b*x + c = 0. Example: x^2 + 2x + 1 =0 (equivalent to (x+1)^2 = 0, giving you x = -1)
3. delta > 0 means that there are two x'es with a*x^2 + b*x + c = 0. Example: x^2 -6x +8 = 0 (equivalent to (x-4)(x-2) = 0, with x either 4 or 2).

Now let's get back to our problem.... We need to figure out if p^2 - 4r is smaller, greater than or equal to 0.
Stmt 1 doesn't shed light on whether p^2 is greater than 4r, just on whether p^2 is greater than r. So it is not sufficient by itself.
Stmt 2 is again insufficient by itself, largely for the same reason: you do not know the relationship between p^2 and 4r.

The two statements taken together do not help much either.

So my guess is E... Hope I'm not wrong, seeing as how my explanation is so long...

Dana this is sooo over my head its not even funny. If I get a question like this on the GMAT, I'm playing the guessing game and moving on. I can't afford to waste more than 10 seconds on this type of question that I will ultimately get wrong anyway.

I'm assuming
A) you have an excllent math background
B) are much brighter than I
C) I'm just an idiot
D) all of the above

In all seriousness, whats your math background?

Well it's nothing impressive, I suppose... Just your average sciences high school and college - finance is my major... I'm no rocket scientist, that's for sure... Just that, here, in Romania, they force feed us math... I for one learned in the 9th grade what a friend of mine was learning in college. But don't get me wrong, a lot of people can't keep up... I'm just one of the lucky ones who did...

yvichman: Oh and I forgot - don't ever say that you are an idiot! That is most certainly not true... I guarantee that if I were to sit next to you for half an hour and explain second degree equations using examples you'd master them!

oa E