EMPOWERgmatRichC wrote:
QUANT 4-PACK SERIES Problem Solving Pack 3 Question 3 A set of 11 positive integers...A set of 11 positive integers has an average of 25. Which of the following is the greatest possible value for the median of this set?
A) 25
B) 30
C) 36
D) 45
E) 46
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This question is part of the Quant 4-Pack seriesScroll Down For Official Explanation Hi All,
When dealing with Quant questions involving Statistical terms (mean, median, mode, range, standard deviation), it's important to understand the specific definitions of the terms involved.
We're told that a set of 11 POSITIVE integers has an average of 25. We're asked for the GREATEST possible MEDIAN of that set.
To find the median, we have to first put the numbers in order from least to greatest. One of the 'keys' to this question is that the prompt does NOT state that the 11 terms have to be distinct (re: different), so duplicates can be used. To maximize the median, we need to minimize ALL of the other numbers though...
For the first 5 numbers, the smallest we can make each of them is 1. Once we do that, we can make the median (and each of the 5 other numbers) all X...
1 1 1 1 1 X X X X X X
Since the average of the 11 numbers is 25, the SUM of those numbers is 11(25) = 275.
Subtracting the five 1's from the sum gives us 275 - 5(1) = 270. Thus, the remaining 6 values are all the SAME and sum to 270. The largest possible median would be....
270/6 = 45
Final Answer:
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Rich
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