Question

Is $(x^2-y^2)$ an odd number?
(I) x and y are integers.
(II) x+y is an odd number

• A. Statement (I) ALONE is sufficient, but statement (II) alone is not sufficient
• B. Statement (II) ALONE is sufficient, but statement (I) alone is not sufficient
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
• D. EACH statement ALONE is sufficient

Answer 1

The correct option is B Statement (II) ALONE is sufficient, but statement (I) alone is not sufficient

From I, we cannot say that (x2−y2)(x2−y2) is odd or even. Statement (II) ⇒x+y⇒x+y is odd ⇒x⇒x is even and y is odd or vice versa.
⇒x−y⇒x−y is odd ⇒(x2−y2)⇒(x2−y2) is odd.