Bunuel
How many integers between 2,000 and 6,999 are even and have a digit that is a prime number in the tens place?
(A) 200
(B) 120
(C) 510
(D) 110
(E) 1000
Take the task of creating 4-digit integers and break it into
stages.
Stage 1: Select a thousands digit
Since the numbers range from 2000 to 6999, the thousands digit can be 2, 3, 4, 5 or 6
So, we can complete stage 1 in
5 ways
Stage 2: Select a hundreds digit
This digit can be any digit from 0 to 9.
We can complete stage 2 in
10 ways
Stage 3: Select a tens digit
This digit must be prime (2, 3, 5, or 7)
We can complete stage 3 in
4 ways
Stage 4: Select a units digit
This digit must be EVEN (2, 4, 6, 8, or 0)
We can complete stage 4 in
5 ways
By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a 4-digit number) in
(5)(10)(4)(5) ways (= 1000 ways)
Answer: E
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
RELATED VIDEOS