HelloKitty wrote:
The sum of n consecutive positive integers is 45. What is the value of n?
(1) n is even
(2) n < 9
In how many ways can you write n consecutive integers such that their sum is 45?
n = 1 -> 45
n = 2 -> 22, 23
n = 3 -> 14, 15, 16
n = 4 X
n = 5 -> 7, 8, 9, 10, 11
n = 6 -> 5, 6, 7, 8, 9, 10
n = 7 X
n = 8 X
n = 9 -> 1, 2, 3, 4, 5, 6, 7, 8, 9
n can be 2 or 6 hence statement 1 is not sufficient.
n can take many values less than 9 hence statement 2 is not sufficient.
Since n can take values 2 or 6 which are even and less than 9, both statements together are not sufficient.
Answer (E)
Now, the interesting thing is how to get these values of n. How do I know which values can n take and which can it not?
Its pretty easy really. Follow my thought here.
"Of course n can be 1.
n can be 2 since when I divide 45 by 2, I get 22.5. So 2*22.5 is 45 so I have to find 2 consecutive integers whose mean is 22.5. The integers are obviously 22 and 23.
When I divide 45 by 3, I get 15. So I need 3 consecutive integers whose mean is 15. They are 14, 15, 16
When I divide 45 by 4, I get 11.25. Do I have 4 consecutive integers such that their mean is 11.25? No because mean of consecutive integers is always an integer or of the form n.5
When I divide 45 by 5, I get 9 so I need 5 consecutive integers whose mean is 9. They must be 7, 8, 9, 10, 11
and so on....."
Obviously, I just need to focus on getting 2 even values of n. So I check for 2, 4, 6 and I would know that answer is (E).
_________________
Karishma
Veritas Prep GMAT Instructor
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