duahsolo wrote:
What is the value of xy?
(1) y – 1 = x
(2) x² + x – 6 = 0
Target question: What is the value of xy? Statement 1: y – 1 = x This statement doesn't FEEL sufficient (namely because we have 1 equation with 2 variables), so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 0 and y = 1. In this case,
xy = (0)(1) = 0Case b: x = 1 and y = 2. In this case,
xy = (1)(2) = 2Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values Statement 2: x² + x – 6 = 0 Since we have no information about y, there's no way to determine
the value of xySince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that: y – 1 = x
Statement 2 tells us that x² + x – 6 =
Factor: (x + 3)(x - 2) = 0
Solve to get: x = -3 or x = 2
It SEEMS like these 2 different values of x will yield 2 different values for xy.
Let's see if that's the case.
If x = -3, then y = -2 (since statement 1 tells us that y - 1 = x). In this case,
xy = (-3)(-2) = 6If x = 2, then y = 3 (since statement 1 tells us that y - 1 = x). In this case,
xy = (2)(3) = 6So, when we COMBINE the statements, we get only ONE answer to the target question:
xy = 6Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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