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Re: How many integers between 2,000 and 6,999 are even and have a digit th
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03 Jan 2019, 08:43
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Bunuel wrote:
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.
Re: How many integers between 2,000 and 6,999 are even and have a digit th
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03 Jan 2019, 08:53
Bunuel wrote:
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
The thousands digit can be 2/3/4/5/6 (note that all integers with these thousands digit are a part of our range) -> 5 ways The hundreds place can be any of the 10 digits -> 10 ways The tens place can be 2/3/5/7 -> 4 ways The units place must be one of 0/2/4/6/8 -> 5 ways
Total = 5*10*4*5 = 1000 such numbers
Answer (E)
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Re: How many integers between 2,000 and 6,999 are even and have a digit th
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03 Jan 2019, 09:30
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
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