A 3-digit number, when divided by 4, has a remainder of 1. When the same number, when divided by 5, has a remainder of 2. What is the smallest possible number?
Lowest common multiple of 4 and 5 = 20

Since it is a 3-digit number, to be the smallest possible number, it has to be as close to 100 as possible.

100 ÷ 20 = 5 r 0

Quotient to be multiplied by 20 to produce the smallest 3-digit number 
= 5 + 1
= 6

Smallest 3-digit number that is divisible by 20
= 6 x 20
= 120

Since the number has a remainder of 1 when divided by 4 and it has to be the smallest possible 3-digit number, we can find the difference between the divisor and the reminder.

Number to be subtracted from the smallest 3-digit number that is divisible by 20
= 4 - 1
= 3

Then we use the smallest 3-digit number that is divisible by 20 and subtract it by the difference to find the answer.

Smallest 3-digit number so that there is a remainder of 1 when divided by 4 and a remainder of 2 when divided by 5
= 120 - 3
= 117

Answer(s): 117