Let a,b,c,d,e, be real numbers such that `a+b lt c+d , b+c lt d+e, c+d lt e+a, d+e lt a+b`. Then

Options

A. The largest is a and the smallest is b
B. The largest is a and the smallest is c
C. The largest is c and the smallest is e
D. The largest is c and the smallest is b

Answer

A

Explanation

(i) `a+b lt c+d `
(ii) `b+c lt d+e`
(iii) ` c+d lt e+a`
(iv) ` d+e lt a+b`
from (i) & (iii)
`a+b lt e+a`
`implies b lt e`
from (ii) &(iv)
`b+c lt a+b`
`implies c lt a `
(i)-(ii)
`a-c lt c-e`
`implies c lt e `
(i)-(iv)
`(a-e)+(b-d) lt (c-a)+(d-b)`
from thus `d gt b`
(i)+(iii)-(ii)
`c gt d`
overall a is greatest , b is least