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A set of 15 different integers has a median of 25 and a range of 25. What is the largest possible integer that could be in the set? 32 37 40 43 50
median is the 8th term and it must be 25 so to maximize the largest integer, we have to maximize the smallest integer we get the smallest term to be 18 (deduct one each from 8th term of 25 to find 1st term) so max value = 18+range = 43
Is there a way to solve this via equation? I started working it but did not hit the result...I had:
x - y = 25 (range)
(x + y)/2 = 25 (median)
Can anyone tell me where my logic failed?
median is not the average between max and min median is the middle value. In this case, when there are 15 numbers and we put them in order from min to max, median is the middle term (i.e. 8th term). If there are 16 numbers, then median will be the average between term 8th and 9th.
I dont think so, or if there is, it would be so hard to create because this type of question is not "single solution" question. I mean the question asks for maximum possible value so we have to somewhat have idea in our mind of how to maximize the answer.
I'm kinda of lost about how we maximize the top value, by max the bottom....can you provide more explaination for this?
This is because the "range" is given and it is fixed by the question. No matter what the minimum value is, the maximum value will be min+25. This is why, in order to come up with maximum possible value of greatest integer, we have to try to find the maximum possible value of least integer.
to illustrate, see example
8th term is fixed at 25 if we reduce one for each previous term 7th = 24 6th = 23 5th = 22 4th = 21 3rd = 20 2nd = 19 1st = 18 greatest = 18+25 = 43
if we reduce two for each previous term 23 21 19 17 15 13 11 then greatest =11+25 = 36
since question asks for maximum possible value, 43 would be the answer