Problem Solving

Came across this question in Kaplan. What is the best way to attack this particular question

If x and y are distinct factors of 24, then which of the following CANNOT be a factor of 24?

I. (x+y)2
II. x2−y2
III. xy+y2

A. I only
B. I and II only
C. II and III only
D. II only
E. III only

OA A

Thank you

jainpiyushjain wrote: If x and y are distinct factors of 24, then which of the following CANNOT be a factor of 24?

I. (x+y)2
II. x2−y2
III. xy+y2

A. I only
B. I and II only
C. II and III only
D. II only
E. III only

OA A

Try to DISPROVE I, II and III by showing that each CAN be a factor of 24.
Plug in the smallest possible values for x and y, since small values are more likely to divide into 24.
If we plug x=2 and y=1 into I, II and III, we get:

I: (2+1)² = 9, which is not a factor of 24.
Hold onto I.

II: 2² - 1² = 3, which is a factor of 24.
Eliminate B, C and D, each of which includes II.

III: 2*1 + 1² = 3, which is a factor of 24.
Eliminate E, which includes III.

The correct answer is A.

No need to worry about why answer choice I cannot be a factor of 24, since A is the only remaining answer choice.