gauravsoni wrote:
If |x + 2| = |y + 2|, what is the value of x + y ?
(1) xy < 0
(2) x > 2 and y < 2
Given: |x + 2| = |y + 2| Key property: If |a| = |b|, then EITHER a = b OR a = -b So, if |x + 2| = |y + 2|, then there are two possible cases:
case i: x + 2 = y + 2 Subtract 2 from both sides of the equation to get:
x = ycase ii: x + 2 = -(y + 2)Simplify: x + 2 = -y - 2
Subtract 2 from both sides of the equation to get: x = -y - 4
Add y to both sides to get:
x + y = -4Target question: What is the value of x + y? Statement 1: xy < 0 If the product xy is negative, we can conclude that one of the values (x or y) is POSITIVE, and the other value is NEGATIVE.
This means that
x cannot equal y, which means
case i cannot be true, which means
case ii (x + y = -4) MUST BE TRUE
The answer to the target question is
x + y = -4Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: x > 2 and y < 2Combine inequalities to get: y < 2 < x
This means that
x cannot equal y, which means
case i cannot be true, which means
case ii (x + y = -4) MUST BE TRUE
The answer to the target question is
x + y = -4Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
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