If y and z are integers, is y*(z + 1) odd? (1) y is odd (2)

Hi, and welcome to Gmat Club. Below is a solution for your problem.

The product of two integers (in our case \(y\) and \(z+1\)) to be odd both of them must be odd.

Question: is \(y*(z + 1)=odd\) --> so basically the question asks is \(y=odd\) and \(z+1=odd\), or \(z=even\)?

(1) \(y\) is odd, we don't know whether \(z=even\). Not sufficient.

(2) \(z\) is even, we don't know whether \(y=odd\). Not sufficient.

(1)+(2) \(y=odd\) and \(z=even\), so both necessary conditions are satisfied. Sufficient.

Answer: C.

As for your question: first of all, \(y\) can not be zero as \(y=odd\) and zero is an even integer, next if \(z=0=even\), then \(z+1=0+1=even+odd=odd\) and as from (1) \(y=odd\) we still have the product of two odd numbers which is odd.

For more on this issues please check Number Theory chapter of Math Book (link in my signature).

Hope it helps.