Math Competition Problems Problem of the Week - 6

How many 2-digit odd numbers are greater than 30?

Source: MOEMS (Math Olympiad) Grades 4-6

Math Competition Problems - Problem of the Week 6

This can be easily solved if we make an ordered list. And yes this is one of the easier problems in MOEMS (Math Olympiad for Elementary and Middle Schools)

So let’s start from the 30’s and make a list

31, 33, 35, 37, 39

41, 43, 45, 47, 49

51, …..

61, …..

71, …..

81, …..

91, 93, 95, 97, 99.

99 is the last 2 digit number and the last 2 digit odd number

So each row has exactly 5 numbers and there are 7 rows.

Hence there are 35 2-digit odd numbers greater than 30.

Note: I still wrote the whole of last row to make sure that there are 5 numbers even in the last row (and nothing is missing). Always make sure that you list out the first and the last row to ensure that it follows the same pattern.

Solution 2 - Multiplication Principle

The tens digit has 7 options (3-9). The one's digit has 5 options (1,3,5,7 or 9).

Hence total number of options = 7*5=35.

Now try a similar problem on your own:

How many 2-digit even numbers are greater than 30?

Post the answer to the problem in the comments section below.

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