How many 4-digit numbers greater than 3,000 have the digits:

Max@Math Revolution wrote:How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5, and 7?
A. 6
B. 9
C. 12
D. 15
E. 18

Take the task of creating 4-digit numbers and break it into stages.
We’ll begin with the most restrictive stage.

Stage 1: Select the first digit (to go in the thousands place)
Since the 4-digit number must be GREATER THAN 3000, the first digit must be greater than or equal to 3
This means the first digit must be 3, 5 or 7.
So, we can complete stage 1 in 3 ways

IMPORTANT: We're told that the 4-digit number must contain the digits 1, 3, 5, AND 7. So, each digit is used ONCE

Stage 2: Select the hundreds digit
Since we selected a digit in stage 1, there are now 3 digits left to choose from
So, we can complete this stage in 3 ways.

Stage 3: Select the tens digit
There are now 2 digits left to choose from
So, we can complete this stage in 2 ways.

Stage 4: Select the units digit
We can complete this stage in 1 way.

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a 4-digit number) in (3)(3)(2)(1) ways (= 18 ways)

Answer: E
--------------------------

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat- ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

How many 4-digit numbers greater than 3,000 have the digits: 1, 3, 5, and 7?

A. 6
B. 9
C. 12
D. 15
E. 18

We see that we have 3 options for the thousands digit, 3 for the hundreds digit, 2 for the tens digit and 1 for the units digit. Thus, the total number of options is 3 x 3 x 2 x 1= 18.

Answer: E