akhilsuhag wrote:If |x| = |2y| what is the value of x - 2y ?
(1) x + 2y = 6
(2) xy > 0
Target question: What is the value of x - 2y?
Given: |x| = |2y|
This means that
EITHER x = 2y OR x = -2y
So, we need to consider these two possible CASES when examining each statement
Statement 1: x + 2y = 6
We'll examine the two possible CASES.
case a: x = 2y
So, we can replace 2y with x to get: x + x = 6
Solve, to get x = 3
This means that x = 3 and 2y = 3, so
x - 2y = 0
case b: x = -2y
We can also say that -x = 2y
So, we can replace 2y with -x to get: x + (-x) = 6
Simplify to get: 0 = 6
Hmmmm, doesn't make any sense, so we can RULE OUT case b, which means only case a applies.
So, we can be certain that
x - 2y = 0
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: xy > 0
This means that x and y are the
same sign.
It ALSO means that x and
2y are the
same sign
Let's check our two cases, and see what happens.
case a: x = 2y
This CONFORMS to our conclusion that x and
2y are the same sign
For case a, we already concluded that
x - 2y = 0
case b: x = -2y
This DOES NOT conform to our conclusion that x and
2y are the same sign
So we can RULE OUT case b, which means only case a applies.
So, we can be certain that
x - 2y = 0
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
SUFFICIENT
Answer =
D
Cheers,
Brent
