Math Multiple Choice
For positive integers a and b, let a 
b be defined as ab +1. If x and y are positive integers and x y = 16, which of the following could be a value of y?
| I. | 1 |
| II. | 2 |
| III. | 3 |
- (A) I only
- (B) II only
- (C) I and III only CORRECT ANSWER
- (D) II and III only
- (E) I, II, and III
Explanation:
For this question, you are given that x y = 16 where x y is defined as xy +1. You are asked which of three values are possible for y when xy +1 = 16.
The value of y could be 1 if x = 4, since 41+1 = 42 = 16. So I is correct. The value of y could be 3 if x = 2, since 23+1 = 24 = 16. So III is correct. Since there is no integer that can be raised to the (2 + 1) or 3rd power to obtain 16, II is not correct. The correct answer is (C).
(from the October 16, 1999 test)