If (1+3+5+.....+p) + (1+3+5+.....+q) = (1+3+5+.....+r) where each set of parentheses contains the sum of consecutive integers as shown, the smallest possible value of p+q+r, (where p>6) is

(a) 12

(b) 21

(c) 45

(d) 54

Dear student,

The correct option is c)

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Askiitians Expert

Sagar Singh - IIT Delhi

sagar singh....u r mad....

ans is 21.

i''ll show u how...--->

no. of terms--> (p+1)/2, (q+1)/2, (r+1)/2

sum of 1st n odd nos. =n^2

 ((p+1)/2)^2 +  ((q+1)/2)^2 =  ((r+1)/2)^2

(p+1)^2 + (q+1)^2 = (r+1)^2

p+1,q+1,r+1 are pythagorean triplets

p>6...........p+1>7

therfore the smallest set is (8,6,10)......p+1=8,q+1=6,r+1=10................p+q+r=21......ans....simple