1.

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 

Answer»

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 


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