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If (1+3+5++p)+(1+3+5++q)=(1+3+5++r) wher...

If `(1+3+5++p)+(1+3+5++q)=(1+3+5++r)` where each set of parentheses contains the sum of consecutive odd integers as shown, the smallest possible value of `p+q+r(w h e r ep >6)` is `12` b. `21` c. `45` d. `54`

A

12

B

21

C

45

D

54

Text Solution

Verified by Experts

The correct Answer is:
B
We know that 1+3+5+….+(2k-1)=`k^(2)`. Thus, the given equation can be written as
`((p+1)/2)^(2)+((q+1)/2)^(2)=((r+1)/2)^(2)`
`rArr(p+1)^(2)+(q+1)^(2)=(r+1)^(2)`
As `pgt6,p+1gt7`, we may take p+1=8,q+1=6,
`r+1=10`. Hence,
p+q+r=21
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