Vincen wrote:What is the value of x + y?
(1) x² + y² = 5
(2) xy = 2
Target question: What is the value of x + y?
Statement 1: x² + y² = 5
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 1 (notice that x² + y² = 2² + 1² = 5). In this case,
the answer to the target question is x + y = 2 + 1 = 3
Case b: x = -2 and y = 1 (notice that x² + y² = (-2)² + 1² = 5). In this case,
the answer to the target question is x + y = -2 + 1 = -1
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: xy = 2
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 2 and y = 1 (notice that xy = (2)(1) = 2). In this case,
the answer to the target question is x + y = 2 + 1 = 3
Case b: x = -2 and y = -1 (notice that xy = (-2)(-1) = 2). In this case,
the answer to the target question is x + y = (-2) + (-1) = -3
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that
x² + y² = 5
Statement 2 tells us that xy = 2
ASIDE: When you see the terms x², y² and xy, you should be thinking SPECIAL PRODUCTS
(x + y)² = (x + y)(x + y) = x² + 2xy + y²
(x - y)² = (x - y)(x - y) = x² - 2xy + y²
If xy = 2, then
2xy =
4
So,
x² +
2xy +
y² =
5 +
4 = 9
In other words, (x + y)² = 9, which means
x + y = 3
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
