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Set S is a 7 positive integer set with an average of 25 and a median

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Set S is a 7 positive integer set with an average of 25 and a median [#permalink]

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Set S is a 7 positive integer set with an average of 25 and a median of 30. If n is in S, what is the least possible value of n?

A) 1
B) 2
C) 3
D) 4
E) 5
[Reveal] Spoiler: OA

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Re: Set S is a 7 positive integer set with an average of 25 and a median [#permalink]

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New post 12 Apr 2017, 04:53
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amathews wrote:
Set S is a 7 positive integer set with an average of 25 and a median of 30. If n is in S, what is the least possible value of n?

A) 1
B) 2
C) 3
D) 4
E) 5


Set S is a 7 positive integer set with an average of 25
If the average is 25, then (sum of all 7 numbers)/7 = 25
Multiply both sides by 7 to get: sum of all 7 numbers = 175

Set S has a median of 30
So, if we arrange the 7 numbers in ascending order, the middlemost number is 30
So, we get: _ _ _ 30 _ _ _

We're trying to MINIMIZE one of the values (n).
Since we're already arranging the numbers in ascending order, let's MINIMIZE the first value.
We have n _ _ 30 _ _ _

So, let's first make n as smallest positive integer possible.
Let's see what happens if n = 1
We get: 1 _ _ 30 _ _ _
Since the only restriction on the numbers to the right of 30 is that they must be positive integers greater than or equal to 30, we have a LOT of freedom. All we need to do is make sure the total sum = 175

Let's try this: 1, 1, 1, 30, 30, 30, 30, _
At this point, the last number has to be such that the total sum = 175.
So, that last number must be 82
So, we get: 1, 1, 1, 30, 30, 30, 30, 82

DONE!
Answer:
[Reveal] Spoiler:
A


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Set S is a 7 positive integer set with an average of 25 and a median [#permalink]

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New post 12 Apr 2017, 09:32
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amathews wrote:
Set S is a 7 positive integer set with an average of 25 and a median of 30. If n is in S, what is the least possible value of n?

A) 1
B) 2
C) 3
D) 4
E) 5


1,24,30,30,30,30,30
n=1
A
Set S is a 7 positive integer set with an average of 25 and a median   [#permalink] 12 Apr 2017, 09:32
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