XAT 2018 Question 57
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XAT
It has been given that A+B+C = 41.
Let the common root be B.
All the roots are positive integers.
The product of the roots of one of the equations is 35.
35 can be obtained only in 2 ways - either as 5*7 or 35*1.
A+B+C = 41.
If A and B are 5 and 7 in any order, then C = 41 - 5 - 7 = 29.
If A and B are 35 and 1 in any order, then C = 41 - 35 - 1 = 5.
As we can see, in either case, 5 is one of the 3 roots.
Therefore, option C is the right answer.