How many 4 digit numbers are there?

Mitch provides a great solution here: https://www.beatthegmat.com/4-digit-numbers-t106108.html

Cheers,
Brent

Hi binaras,

This question has a lot of details to it, but the math involved isn't too bad (however, you will have to account for a series of 4-digit numbers that are NOT allowed, since they contain more than one 2 in their digits).

We're given a series of facts about the 4 digit number:
The first digit is EVEN: 2, 4, 6 or 8 (but not 0, since a 4-digit number can't start with 0)
The second digit is ODD: 1, 3, 5, 7, 9
The third digit is PRIME: 2, 3, 5, 7
The fourth digit is divisible by 3: 3, 6, 9, 0

If there were NO other restrictions, then the total number of 4-digit numbers would be:

(4)(5)(4)(4) = 320 options

However, there IS a restriction - the digit "2" can be used no more than once. Thus, any number that includes MORE than one 2 has to be removed... Thankfully, there aren't that many numbers that fit that description. If the first and third digits are both 2s, then the there are...

(1)(5)(1)(4) = 20 numbers with two 2s in the digits. Those 20 options have to be removed, which leaves us with...

320 - 20 = 300 4-digit numbers.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich