GMAT question - The coordinates (x,y) of each corners of rectangle A... - Review

The coordinates (x,y) of each corners of rectangle ABCD are such that x and are integers and satisfy the equations and . The edges of the rectangle are parallel to the X and Y axes. How many distinct rectangles could be formed which would satisfy these requirements?

1. 240
2. 60
3. 20
4. 18
5. 9

Explanation

In this question you are being asked to find the number of distinct selections of coordinates that can be made.

The key selections are the x coordinates of the left and right hand edges and the y coordinates of the top and bottom edges.

You need to select 2 x coordinates from a possible 4 for the left and right edges and 2 y coordinates from a possible 5 for the top and bottom edges.

Since order does not matter in this case we should use the combinations formula to work out the number of possibilities.

For the x coordinates it is selecting 2 from 4 so

For the y coordinates it is selecting 2 from 5 so

Therefore the total number of possible rectangles is 6 × 10 = 60 and the correct answer is C.