alp80 wrote:there are 6 vertical and 5 horizontal line. there are 30 squares. How many rectangular does it contain?
a. 300
b. 315
c.340
d.336
I'm going to assume that the question is right and the diagram (which has 7 horizontal lines, not 5) is wrong. The wording of the question is also misleading (you can make more than 30 squares on a 6*5 grid) and there are only 4 choices, so it's clearly not a real GMAT question - where is it from?
On a 6*5 grid, there are 30 starting points for our rectangle.
To create a rectangle from our starting point, we need to select 1 horizontal point and 1 vertical point (once we select those two, our fourth point follows automatically).
For example, if we think of the 6*5 grid as a coordinate plane with (0,0) in the bottom left corner and (0,0) as the bottom left point of our rectangle, we need to pick one point (0,x) and one point (y,0) to create our rectangle, then the 4th point will automatically be (x,y).
After selecting a starting point, there are 5 possible horizontal points and 4 possible verticle points, for a total of 20 possibilities.
30*20 = 600, but that's not our final answer.
We need to recognize that not all of the rectangles we've chosen are unique. We can see that if we choose (0,0) as the starting point and then (0,4) as our other horizontal point, that's going to make the same rectangles as if we had chosen (0,4) as our starting point and then (0,0) our other horizontal point.
So, we've counted every possible rectangle twice, which means that there are 600/2 = 300 possible rectangles... choose A.
