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03 Jan 2019, 09:31
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (02:04) correct
27%
(02:13)
wrong
based on 125
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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
(A) 200
(B) 120
(C) 510
(D) 110
(E) 1000
03 Jan 2019, 09:43
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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
(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.
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03 Jan 2019, 09:53
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Bookmarks
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
(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)
