rupsk wrote:If you were to construct a 7 Ã- 7 checkered square (i.e., a 7 Ã- 7 chess board), how many rectangles would there be in total? You need to include squares too because a square is a special kind of rectangle.

Possible Answers
Selected Possible Answer

A. 625


B. 918


C. 842


D. 676


E. 784

The easiest way of doing this sum is using Combinations,
For a rectangle to be formed, we need 2 vertical lines and 2 horizontal lines.(This includes possibility of squares also)

A 7-by-7 chessboard has 8 vertical and 8 horizontal lines.
For a rectangle we need to pick 2 vertical and 2 horizontal lines from these 8 lines, so

we have, 8C2 * 8C2 = (8*7/2*1)*(8*7/2*1) = 16*49 = 784.



Another question

A block of wood in the form of a cuboid 4" Ã- 10" Ã- 13" has all its six faces painted pink. If the wooden block is cut into 520 cubes of 1" Ã- 1" Ã- 1", how many of these would have pink paint on them?

Possible Answers
Selected Possible Answer

A. 348


B. 352


C. 344


D. 340


E. 350

The fastest way of doing this is to determine the number of cubes which are not painted on any of its sides and then subtract that to the total cubes.

To find the number of cubes not painted on any side, imagine the cuboid beneath when all the small cubes painted pink are removed, the dimension of each of the sides would be reduced by 1cm on either side, so the cuboid formed will have dimension of (13-2) (10-2) and (4-2).
So, we have a cuboid of 11*8*2, when this is cut into cubes of 1cm, we have 176 cubes which are not shaded on any side.

So out of the 520 cubes, we now know 176 are not painted pink, so cubes painted pink = 520-176=344

rupsk wrote:thank you all.

What will be the formula when we have to identify no of squares in the first problem?