# The sum of five distinct positive integers is 90. what can be the second largest number of the five at most ?

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by thirumalai

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by thirumalai

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a + b + c + d + e = 90

let a,b,c,d,e be in increasing order. If d and e are to be the largest, then the others have to be the least. This is because the sum is always the same.

least positive integer is 1. so a = 1. b = 2.. c = 3.

d + e = 90-1-2-3 = 84

so d can be from 4 (as it is more than c) to 41 (less than 84/2).

As e is more than d, so it is from 80 to 43.

second largest number can at most be 41.

let a,b,c,d,e be in increasing order. If d and e are to be the largest, then the others have to be the least. This is because the sum is always the same.

least positive integer is 1. so a = 1. b = 2.. c = 3.

d + e = 90-1-2-3 = 84

so d can be from 4 (as it is more than c) to 41 (less than 84/2).

As e is more than d, so it is from 80 to 43.

second largest number can at most be 41.

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