Bunuel wrote:
What number is 6 more than x + y ?
(1) y is 3 less than x.
(2) y is twice x.
Target question: What is the value of x + y + 6? Statement 1: y is 3 less than x. We can write:
y = x - 3There are several values of x and y that satisfy this
equation. Here are two:
Case a: x = 3 and y = 0. In this case, the answer to the target question is
x + y + 6 = 3 + 0 + 6 = 9Case b: x = 4 and y = 1. In this case, the answer to the target question is
x + y + 6 = 4 + 1 + 6 = 11Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y is twice x.We can write:
y = 2xThere are several values of x and y that satisfy this
equation. Here are two:
Case a: x = 1 and y = 2. In this case, the answer to the target question is
x + y + 6 = 1 + 2 + 6 = 9Case b: x = 2 and y = 4. In this case, the answer to the target question is
x + y + 6 = 2 + 4 + 6 = 12Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that
y = x - 3Statement 2 tells us that
y = 2xWe have 2 DIFFERENT linear equations with 2 variables.
Since we COULD solve the system for x and y, we COULD determine the value of
x + y + 6ASIDE: Although we COULD solve the system of equations, we would never waste valuable time on test day doing so. We need only determine that we COULD answer the target question.
Since we COULD answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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