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If a list of eleven distinct positive integers has a median of 41 and

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If a list of eleven distinct positive integers has a median of 41 and [#permalink] New post   03 Jul 2022, 07:55
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If a list of eleven distinct positive integers has a median of 41 and a range of 21, what is the largest possible value of the average (arithmetic
mean) of this list?

A) 41

B) 46

C) 49

D) 57

E) 62
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B
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Re: If a list of eleven distinct positive integers has a median of 41 and [#permalink] New post   03 Jul 2022, 08:36
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sjuniv32 wrote:
If a list of eleven distinct positive integers has a median of 41 and a range of 21, what is the largest possible value of the average (arithmetic
mean) of this list?

A) 41

B) 46

C) 49

D) 57

E) 62


Median is 41. In order to maximize the average, we want the other ten values to be the largest possible. The five that are smaller than 41 must be 40, 39, 38, 37, 36. If 36 is the smallest and the range is 21, the largest must be 57. The remaining numbers are 56, 55, 54, 53.

So, we have
36
37
38
39
40
41
53
54
55
56
57

We can create pairs that total 93 with everything other than the 41. So all the pairs will average to 46.5. The 41 lowers that just a tiny bit. 46.

Answer choice B.
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Re: If a list of eleven distinct positive integers has a median of 41 and [#permalink] New post   23 Apr 2024, 20:07
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Re: If a list of eleven distinct positive integers has a median of 41 and [#permalink]
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