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Largest possible integer

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by chieftang » Tue Jan 03, 2012 10:45 am
A set of five different positive integers has a median of 18 and a mean of 15. What is the largest possible integer in the set?

(A) 19
(B) 24
(C) 32
(D) 35
(E) 40

Source: AMC question bank

I thought it was a nifty little question. It was more than 2 minutes before the solution dawned on me. Enjoy.
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by LalaB » Tue Jan 03, 2012 11:08 am
to maximize one value, we need to minimize the rest values

since we are said, that the set consists of DIFFERENT POSITIVE integers, then we have the following set-

1 2 18 19 x

median=18
mean=15=(1+2+18+19+x)/5
so x=35 (max integer)
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by karthikpandian19 » Tue Jan 03, 2012 10:22 pm
Answer is D - 35

Since, it is 5 numbers and median is 18

Left: The 2 nos on the left is to be very less and positive integers so take 1 & 2

Right: The 2 nos on the right - One of them we need to find it, so other should be minimum which is 19 (next to 18)

So now: (1+2+18+19+n)/5 = 15

Solving will get n = 35
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