word problem

Question

Thomasita was thinking of a number less than 90 that she says when counting by sixes and when counting by fives but not when counting by fours. Of what number she thinking?

Answer 1

 

The number is evenly divisible by 6, and is a whole number multiple of 6.

 

The number is evenly divisible by 5 ... the number must end with 0 or 5.

 

The number is not evenly divisible by 4.

 

Since it is less than 90 and it must end with 0 or five, the number is one of these:

 

    5, 10, 15, 29, 25, 30, 35, 50, 45, 50, 55, 60, 65, 70, 75, 80, 85

 

Since it is evenly divisible by 6, we can remove the numbers that are not multiples of 6.  That leaves us with

 

    30, 60

 

Since it is not evenly divisible by 4, that leaves us with 30.

 

The number that she is thinking of is 30.