Problem Solving

BTGmoderatorLU wrote:Source: e-GMAT

How many 4 digit numbers greater than 4000 can be formed using the digits from 0 to 8 such that the number is divisible by 4?

A. 508
B. 827
C. 828
D. 1034
E. 1035

The OA is D

Recall that, in order for a number to be divisible by 4, the last two digits of the number have to be divisible by 4. So the last two digits of the number must be one of the following:

00, 04, 08, 12, 16, ..., 80, 84, 88, 92, and 96.

However, since we can't use the digit 9, we have to omit 92 and 96. This still leaves us with
(88 - 0)/4 + 1 = 23 possibilities for the last two digits of the number.

For the first two digits of the number, it must be one of the following:

40, 41, 42, ..., 48, 50, 51, 52, ... , 58, ..., 80, 81, 82, ..., 88

We see that the first two digits of the numbers have 5 x 9 = 45 possibilities.

Therefore, there are 45 x 23 = 1035 such numbers. However, these 1035 numbers include the number 4000; the problem says the number must be greater than 4000. So we have to remove 4000 from the list and this leaves us with 1034 numbers.

Answer: D