Mitch provides a great solution here: https://www.beatthegmat.com/4-digit-numbers-t106108.html
Cheers,
Brent
How many 4 digit numbers are there?
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
GMAT/MBA Expert
-
[email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
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
