VJesus12 wrote:If a, b and c are positive integers, is a = b?
(1) (a + b)/(ab) is even.
(2) ac = c/b
(a + b)/(ab) is even.
If a and b are positive integers, it's almost always the case that a + b < ab (i.e., (a + b)/(ab) is a proper fraction).
Thus, in order for (a + b)/(ab) to be an even integer, a and b must be very small. The smallest integer a and b can be is 1, and we see that (a + b)/(ab) = 2/1 = 2.
However, if one of them is 1 and the other is not, then (a + b)/(ab) is a fraction between 1 and 2.
If both a and b are 2, then (a + b)/(ab) = 4/4 = 1.
In other words, for any of the other pairs of positive integers a and b, we will have (a + b)/(ab) < 1. So the only way for (a + b)/(ab) to be even is if a = b = 1. We see that statement one alone is sufficient.
Statement Two Alone:
ac = c/b
That means ab = c/c or ab = 1. Since a and b are positive integers, the only way ab = 1 is a = b = 1. We see that statement two alone is also sufficient.
Answer: D
