SAT Math Multiple Choice Practice Question 236: Answer and Explanation
16. For all non-zero integers a and b, let .
If , which of the following must be true?
is an integer.
A. II only
B. I and II only
C. II and III only
D. I and III only
E. I, II, and III
Correct Answer: C
C Use the definition to translate the equation:
Now think about what values of m and n will work. Notice that 3 and 1 will work, but so will –3 and –1. Now plug these into the statements, and see if any are false. Since –3 is not greater than –1, statement I can be eliminated, and so can answers (B), (D), and (E). Notice that this means you don't have to check statement II, because it's in both remaining answers. Statement III must be true because if , then must equal 3 or –3. Therefore, equals 1 or –1, so it is an integer.