GMAT OG 11th ed PS #248

[tgf]

The problem:

Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallell to the x-axis. The x and y coordinates of P,Q and R are to be integers that satisfy the inequalities -4 <= x <=5 and 6<= y <=16. How many different triangles with these properties could be constructed?

The answer is C, 9900. I have no problems with understanding that. My problem is:

The question is how many _different_ triangles could be constructed. However the OA finds every possible allowed permutation of
coordiates for P,Q,R. In this way you find numerous identical triangles with
different location. E.g the triangle with P,Q,R-coordinates (-4,9), (-4,12),
(-2,9) is exactly the same as (-4,9), (-4,6), (-2,9) but flipped upside
down.

The way I interpreted the question I divided the allowed area by the
diagonal and found the number of _unique_ triangles (regardless of spatial placement), which is 10x11...?

Please explain. From the way the question is formulated, I just cannot see which answer is correct.

Also, this is my first question on this forum, and I was hoping I could throw in some practial test questions I've been wondering about (and can't find an answer to online):

1) Is there a limit on the amount of scrath paper available? What type of
scratch paper is it? Is it without grids? What color is it?

2) Do we bring our own pencil for the scratch work or are they supplied by
GMAC? If so, what type of pencil is issued? Pen, pencil, push pencil?

3) Are (my own) ear plugs allowed?

Thank you

[Ian Stewart]

It's an interesting interpretation of the question, but in co-ordinate geometry, two shapes are considered distinct if they are in different locations. The line y = x is different from y = x + 1, for example, despite the fact that both are lines.

As for practicalities in the test center, you're given a few (seven, I think) laminated sheets and a felt tip marker. The paper has grid lines, so can double as graph paper. You can request additional sheets by getting the attention of the proctor during your test. You can't bring anything with you to the test room besides your id - your marker, laminated sheets, and earplugs (if you want them) are all provided to you before you enter the room, and you must return everything before you leave (so that you can't record the questions you've seen and take them home with you). I've never used the earplugs, but I'm nearly certain they're the standard cheap foam variety.

[tgf]

"in co-ordinate geometry, two shapes are considered distinct if they are in different locations. The line y = x is different from y = x + 1, for example, despite the fact that both are lines. "


Thank you! That I'll have to keep in mind.