How many numbers could it be?

Question

I left my glasses at home so I couldn't quite see the number on the board. The first digit was a 7 and the last was a 4, but I couldn't make out the middle numbers. It was certainly a 4 digit number. My friend Sally told me that the number was divisible by 4. How many numbers could it be?

 

 

a. 50    b. 64    c. 40    d. 36

Answer 1

So the number was 7--4 and it was divisible by 4.

 

The rule for divisibility by 4 is that if the number formed by last 2 numbers is divisible by 4, then the entire number is divisible by 4. 

 

So first of all, it doesn't matter what number is in the hundreds place.  It could be any number from 0 to 9.  So that's 10 possible choices there.

 

As for the last two numbers, there are 5 numbers between 0 and 99 that end in 4 and are divisible by 4:  4, 24, 44, 64, and 84.  So the number in the tens place could be 0, 2, 4, 6, or 8.

 

So there are 10 possible choices for the hundreds place, and 5 possible choices for the tens place.  And any combination of those choices will work.  So you multiply 10 by 5 to get to total number of combinations, and that gives 50.  So a is the correct answer.