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We select two distinct numbers (a, b) in the range 1 to 99 (inclusive). How many ways can we pick a and b such that their sum is even and a is a multiple of 9?

 Feb 6, 2020
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There are 99 numbers in the range 1...99, 50 are odd and 49 are even.

For the sum of two numbers to be even, either both are even or both are odd.

We have to remember that a and b must be different numbers.

 

If a = 9, b can be 49 of the 50 odd numbers.

If a = 18, b can be 48 of the 49 even numbers.

If a = 27, b can be 49 of the 50 odd numbers.

 

Continue this pattern and add the results.

 Feb 6, 2020

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