kiran120680
If x and y are non zero integers, Is x=y ?
I. x = 1/y
II. (x+y)² = 4xy
Given: x and y are non-zero integers Target question: Is x=y ? Statement 1: x = 1/y Multiply both sides by y to get:
xy = 1The key information is that x and y are
non-zero integersSo, there are only TWO possible solutions for the equation
xy = 1Case a: x = 1 and y = 1. In this case, the answer to the target question is
YES, x DOES equal yCase b: x = -1 and y = -1. In this case, the answer to the target question is
YES, x DOES equal ySo, it MUST be the case that
x = ySince we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: (x+y)² = 4xyExpand left side to get: x² + 2xy + y² = 4xy
Subtract 4xy from both sides to get: x² - 2xy + y² = 0
Factor: (x - y)(x - y) = 0
So, it must be the case that x - y = 0, which means
x = yThe answer to the target question is
YES, x DOES equal ySince we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent