odd & even propertiesmehaksal wrote:Is the product of three integers p,q, and r even?
1. (p-1)(r+1)is odd
2. (q-r)^2 is odd
1) odd * odd = odd
2) odd - even = odd or even - odd = odd
3) odd + odd = even
4) odd^2 = odd*odd = odd
5) even^2 = even*even = even
question
is p*r*q is even ?
or is any one of p, q and r even?
statement 1
(p-1) is odd
(r+1) is odd
looking at the second property we can say that
p = odd + 1 = even
r = odd - 1 = even
p*q*r = even*even*? = even
Hence sufficient
Statement 2:
(q-r)^2 is odd
(q-r)*(q-r) = odd
odd*odd = odd
=> q-r is odd
from the second property we can say that either q or r is even.
p*q*r = ?*even*odd = even
or p*q*r = ?*odd*even = even
Hence sufficient
The correct answer is D
