In the rectangle coordinate system, triangle ABC has a

Question

In the rectangle coordinate system, triangle ABC has a vertex at point (0,56). If point B is at the origin, then how many points on line AC have integer values for both their x and y values?

(1) The third vertex of triangle ABC lies on the x-axis, and the triangle has an area of 196.
(2) Point A has a positive x coordinate and a y coordinate of zero.

shrouded1 · Answer

(1) Statement one gives us enough information to know that the triangle is right angled and we know one of the sides and therefore the third coordinate. Hence we know both point A and C are (0,56) & (7,0).
Given this information, it is easy to form the equation of the line and enumerate the exact number of integral points
Sufficient

(2) This statement only tells us the third point is on the X-axis, depending on where it is, AC can be one of an infinite number of lines and for each line the number of points that are integral can vary. So not sufficient to answer the question

Answer is (A)

Bunuel · Answer

(1) The third vertex of triangle ABC lies on the x-axis, and the triangle has an area of 196 --> ABC is a right triangle -->  \frac{|x|*56}{2}=196 , where  x  is the x-coordinate of the third vertex -->  |x|=7  --> the third vertex is at the point (7, 0)  OR  (-7, 0).

I think there is a little problem with the question stem: the line passing through the points A and C is either  y+8x=56 , if the third vertex is at (7, 0) or  y-8x=56 , if the third vertex is at (-7, 0). Now, there are infinitely many integer pairs of (x,y) satisfying each equation but on the GMAT for the question which asks for a certain value of an unknown, a statement is sufficient if it gives single numerical value of this unknown. So I think the question should say "how many points on line  segment  AC have integer values for both their x and y values". And in this case statement (1) would be sufficient.

(2) Point A has a positive x coordinate and a y coordinate of zero. Clearly insufficient.

tingle15 · Answer

Nice catch ("segment") Bunuel

iwillcrackgmat · Answer

Start by translating the question and understanding the pieces of the puzzle given and the pieces needed. The question tells us where two vertices are, point B at (0, 0) and another point at (0, 56). To answer the question, we need the coordinates of the last point. 
Statement (1) gives us the area of the triangle, which allows us to calculate the last side of the triangle, and also states that the triangle is a right triangle because the other leg lies on the x-axis. With this
information we can find the slope of AC, which allows us to answer the question. Eliminate choices BCE, and keep choices AD. 
Statement (2) only tells us that the other leg of the triangle is on the x-axis

so A is the answer

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In the rectangle coordinate system, triangle ABC has a

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

In the rectangle coordinate system, triangle ABC has a

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards