PhillyBound
If x and y are greater than 0, is x = 1 ?
(1) x/y = 1
(2) xy = 1
Target question: Is x = 1 ? Given: x and y are POSITIVE Statement 1: x/y = 1 Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 1 and y = 1. In this case, the answer to the target question is
YES, x DOES equal 1Case b: x = 2 and y = 2. In this case, the answer to the target question is
NO, x does NOT equal 1Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: xy = 1There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 1. In this case, the answer to the target question is
YES, x DOES equal 1Case b: x = 2 and y = 1/2. In this case, the answer to the target question is
NO, x does NOT equal 1Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that x/y = 1
Statement 2 tells us that xy = 1
Take x/y = 1 (statement 1) and multiply both sides by y to get:
x = yNow take xy = 1 (statement 2) and replace
y with
x to get: (x)(
x) = 1
Simplify: x² = 1
This means EITHER x = 1, OR x = -1
However, since we're told that x is POSITIVE, it must be the case that
x = 1 So, the answer to the target question is
YES, x DOES equal 1Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent