Bunuel wrote:
How many possible 4-digit numbers can be created where the thousands digit and the tens digit are both prime and the number is divisible by 5?
A. 10,000
B. 800
C. 320
D. 160
E. 32
Take the task of creating 4-digit numbers and break it into
stages.
Stage 1: Select a digit for the 1st position (i.e., the thousands digit)
This digit must be PRIME, which means it can be 2, 3, 5, or 7
So, we can complete stage 1 in
4 ways
Stage 2: Select a digit for the 2nd position (i.e., the hundreds digit)
There are no restrictions for this digit, so we can choose any digit from 0 to 9
We can complete stage 2 in
10 ways
Stage 3: Select a digit for the 3rd position (i.e., the tens digit)
This digit must be PRIME, which means it can be 2, 3, 5, or 7
So, we can complete stage 3 in
4 ways
Stage 4: Select a digit for the 4th position (i.e., the unit digit)
Since the resulting 4-digit number must be divisible by 5, we know that the unit's digit must be either 0 or 5
So we can complete stage 4 in
2 ways
By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a 4-digit number) in
(4)(10)(4)(2) ways (= 320 ways)
Answer: C
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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