Sam thought of a number between ten and twenty.

Question

Sam thought of a number between ten and twenty.Then he gave a clue: You say the number when you count by twos and when you count by threes,but not when you count by fours. Of what number was Sam thinking ?

Answer 1

If the number is divisible by 2 and 3, then it is divisible by 6. So you want a multiple of 6 that's between 10 and 20. Only 12 and 18 work, but 12 is also divisible by 4, so the only number fitting the stipulations is 18.

Answer 2

When you count by 2, the number is a multiple of 2.  When you count by 3, the number is a multiple of 3.  The same concept goes for counting by 4.

 

Here are the possible list of numbers in the range:

 

11, 12, 13, 14, 15, 16, 17, 18, 19

 

Numbers that are multiple of 2:  12, 14, 16, 18

Numbers that are multiple of 3:  12, 15, 18

Numbers that are multiple of 4:  12, 16

 

We exclude 12 and 16 because they are multiples of 4.  The only numbers you have left are 14, 15, and 18.  The number that the criteria have in common is 18.