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Let a, b, c, d, e, be real numbers such that a + b < c + d, b + c < d + e, c + d < e + a, d + e < a + b. Then
(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
Let a, b, c, d, e, be real numbers such that a + b < c + d, b + c < d + e, c + d < e + a, d + e < a + b. Then
(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
Correct option (A) The largest is a and the smallest is b
Explanation:
(i) a + b < c + d
(ii) b + c < d + e
(iii) c + d < e + a
(iv) d + e < a + b
from (i) & (iii)
a + b < e + a
⇒ b < e
from (ii) & (iv)
b + c < a + b
c < a
(i) – (ii)
a – c < c – e
⇒c > e
(i) – (iv)
(a – e) + (b – d) < (c – a) + (d – b)
from thus d > b
(i) + (iii) – (ii
c > d
overall a is greatest, b is least