Counting Methods : GMAT Problem Solving

Question

How many odd 4 digit positive integers that are multiples of 5 can be formed without using the digit 3?
a. 900
b. 729
c. 3240
d. 648
e. 1296

Correct Answer : Choice D. 648

Explanatory Answer

Following conditions are stated

1. The number is a 4 - digit number.

2. It is an odd number.

3. It is a multiple of 5. 

4. 3 cannot be a digit in the number.

Combining conditions 2 and 3, we can conclude that the unit digit is 5. Therefore, the unit digit has only one option.

The thousands place, the left most digit cannot be 0. It also cannot be 3. So, it has 8 options.
The hundreds place cannot be 3. So, it has 9 options.
The tens place cannot be 3. So, it has 9 options.

Therefore, there are 8 * 9 * 9 * 1 = 648 numbers.