1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# 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 tha smallest is b
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
The largest is a and tha smallest is c
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
The largest is c and tha smallest is e
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
The largest is c and tha smallest is b
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A The largest is a and tha smallest is ba+b<c+d ⋯(1)b+c<d+e ⋯(2)c+d<e+a ⋯(3)d+e<a+b ⋯(4) From (1) and (3) a+b<e+a⇒b<e ⋯(A) From (2) and (4) b+c<a+b⇒c<a ⋯(B) (1)−(2), we get a−c<c−e⇒c>e ⋯(C) From (A),(B),(C), we get b<e<c<a (1)−(4), we get (a−e)+(b−d)<(c−a)+(d−b)⇒0<(a−e)+(a−c)<2(d−b)⇒d>b (1)+(3)−(2), we get c>d ∴a>c>(d,e)>b where d and e lies between a and b. Hence a is the largest and b is the smallest.

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Sum of n Terms of an AP
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program