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.

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from 2000 to 6999
thousand's digiti can have 5 ways: 2,3,4,5,6
hundreds digit: any number from 0 to 9: 10 ways
tens digit: 2,3,5,7: 4 ways
unit digit has to be even so, 0,2,4,6,8: 5 ways
Total ways = 5*10*4*5
1000
Answer E