Sue was thinking of a number between 40 and 50 that is a multiple of 3 and 4. Of what number was she thinking?

Answer 1

First, let's find the multiples of 3 between 40 and 50. You can tell if any number is divisible by 3 by adding the digits and seeing if those are divisible by 3. (30 => 3+0 =3, thus 3 is divisible by 3. 31 => 3+1 =4, thus 31 is not.)

We see that 40 and 41 are not divisible. What about 42? 4+2 = 6 which is divisible by 3, thus 42 is divisible by 3. Multiples of 3 must by 3 apart, so we can find the others by adding 3 to 42:

45, 48

Since the next number divisible by three is 51, we stop here.

What about divisible by 4? Since 40/4 =10, we know 40 is divisible by 4. We can again add 4 to find the others:

44, 48.

Thus we have the multiples of 3 between 40 and 50: 42, 45, 48 and the multiples of 4: 40, 44, 48.

Since they have 48 in common, Sue must have been thinking of 48.

Answer 2

48