GMAT tests your logical skills as well as your knowledge of math concepts. To score high, you need to remember various formulas, theorems. Also you need to master critical problem-solving skills.
Today I am going to take you through one problem -solving skill –
Counting skills
Take this problem .
This sum requires higher order thinking
There are two ways to solve this question
Method 1:Using pattern recognition
Take the smallest unit of chessboard. It’s a 2x2 grid
How many rectangles can you count?
All the squares are rectangles too.
First count squares there
are 5
How many rectangles can you count? There are 4.
In total there are 9 .
If you observe........ 9 = 1+8
Now take a 3x3 grid
How many rectangles can you count?
First count squares there
are 14
How many rectangles can you count? There are 22
In total there are 36 .
If you observe ..........36 = 1+8+27
Always remember
the number of rectangles in a grid follow
the cubic series 13 23 …33…
So in a chess board.. the number of rectangles is the sum of the cubes from 13 to 83
Method 2:Using principles of counting
All squares are rectangles. So you need to count the squares
also.
Okay.. First look at the gird..
Can you observe the number of horizontal lines? There are 9
lines
Similarly
Can you observe the number of vertical lines? There are 9
lines
If you observe… to draw a rectangle. You need to select two
horizontal lines and two vertical lines.
The point of intersection of these lines form a rectangle.
So how do we choose two lines out of 9.
Use combination.
To select 2 horizontal lines =
To select 2 vertical lines =
Now as per the rules of counting…you need to multiply
9C2 x 9C2 = ((9x8)/ (1x2) ) x ((9x8)/ (1x2) ) = 1296
There are 1296 rectangles in a chessboard.
To know more about Math problem solving skills.. Feel free to contact me
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