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

Type: Problem Solving

Difficulty: 5 star rating

The coordinates (x,y) of each corners of rectangle ABCD are such that x and are integers and satisfy the equations mathematical expression and mathematical expression. 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.

mathematical expression

For the x coordinates it is selecting 2 from 4 so

mathematical expression

mathematical expression

mathematical expression

mathematical expression

For the y coordinates it is selecting 2 from 5 so

mathematical expression

mathematical expression

mathematical expression

mathematical expression

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

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