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real numbers

by shashank.ism » Mon Feb 08, 2010 9:10 am
a, b, c, d and e be non-negative real numbers such that a + b + c + d + e = 10. Let X be the maximum of the numbers a + b, b + c, c + d and d + e. The least possible value of X lies in the interval

a) [0, 2]
b) [2, 3]
c) [3, 4]
d) [5,7]
e) [5, 10]
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by harsh.champ » Mon Feb 08, 2010 10:15 am
shashank.ism wrote:a, b, c, d and e be non-negative real numbers such that a + b + c + d + e = 10. Let X be the maximum of the numbers a + b, b + c, c + d and d + e. The least possible value of X lies in the interval

a) [0, 2]
b) [2, 3]
c) [3, 4]
d) [5,7]
e) [5, 10]
Non-negative numbers mean one or more of them can be zero also.
suppose all of the them are equal then we get X as 4 which is the least.

[spoiler]In any other case ,X would be greater than 4,This can be seen by substituting b=2.2 and c=1.8,rest =2.
Hence,ans is C.[/spoiler]
Shashank,can you post the OA.
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