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

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

by Max@Math Revolution » Wed Dec 19, 2018 4:48 am
[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
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by Brent@GMATPrepNow » Wed Dec 19, 2018 5:59 am
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
--------------------------

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by Max@Math Revolution » Thu Dec 20, 2018 11:28 pm
=>

We need to count the 4-digit numbers with thousands digits 3, 5 and 7.
The number of 4-digit numbers beginning with 3 is 6.
The number of 4-digit numbers beginning with 5 is 6.
The number of 4-digit numbers beginning with 7 is 6.
Thus, the total number of such 4-digit numbers is 18 = 6 + 6 + 6.

Therefore, the answer is E.
Answer: E
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by Scott@TargetTestPrep » Sat Mar 02, 2019 8:55 am
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

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