If p^2, a perfect square number, is divisible by 5, and q, an integer,

p can either be a multiple of 5 or10 so that \(p^2\) is divisible by 5 and q has to be an even or odd number (if odd it should not be a multiple of 5)

What we can try to do is see if we can prove that a certain Option is Not true (Not divisible by 10) for any of the combinations of p and q

Option 1: pq + 5. If p = 5 and q = 2, then pq + 5 = 15. Not True.


Option 2: p + q. If p = 5 and q = 2, then p + q = 7. Not True.


Option 3: 2(p + 5q)

p = 5, q = 2 then 2(5 + 10) = 30. True

p = 5, q = 3 then 2(5 + 15) = 40. True

p = 10, q = 2 then 2(10 + 10) = 40. True

p = 10, q = 3 then 2(10 + 15) = 50. True


We can prove that the other 2 options are not true as we have done for Options 1 and 2, but it is not necessary.


Option C

Arun Kumar