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Re: A set of 31 integers has a median of 31 and a range of 31. What is the [#permalink]
Expert Reply
Hoozan wrote:
A set of 31 integers has a median of 31 and a range of 31. What is the greatest possible value of the highest integer in the set?

(A) 46
(B) 47
(C) 60
(D) 61
(E) 62


Solution:

We can let x be the smallest integer of the set, and thus x + 31 is the largest integer of the set. Since we want the greatest possible value of the largest integer, we can let the 16 smallest integers all be x. Since these 16 smallest integers include the value of the median, x must be 31, and therefore, we have the greatest possible value of the largest integer as 31 + 31 = 62.

Answer: E
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Re: A set of 31 integers has a median of 31 and a range of 31. What is the [#permalink]
Why are we considering duplicate elements in the set?
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Re: A set of 31 integers has a median of 31 and a range of 31. What is the [#permalink]
Expert Reply
PriyeshLakar wrote:
Why are we considering duplicate elements in the set?


You are correct. Mathematically, a set is a group of unique elements. However, if there are repeating elements, the GMAT uses terms such as "list," "list of number," "data set," or "set of measurements" instead of "a set." In the current question, the term "a set" should be replaced with one of these alternative terms, otherwise the answer should be 46 instead of 62.
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Re: A set of 31 integers has a median of 31 and a range of 31. What is the [#permalink]
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