GRE math thinking skills - 3

 GRE 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

 Lets say,  you didn’t know the concept of counting and permutation and combination

First focus on the 8x8 grid...

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

these numbers follow the cube series

 

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

these numbers follow the cube series

 

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

 Hence 1³ +2³ + 3³+4³ +5³ +6³ +7³ +8³ =1296

  

 

 

Method 2:Using principles of counting

The chess board has 8 rows and 8 columns. a 8x8 grid.

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 = ⁹C₂

To select 2 vertical lines = ⁹C₂

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

 My contact link is here:

LinkedIn profile : https://www.linkedin.com/in/georgeanand/

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Lets try another sum

Solution is here

http://letsgre.blogspot.com/2021/01/gre-math-thinking-skills-1.html