Bunuel
What is the value of xy?
(1) y = x + 1
(2) y = x² + 1
Target question: What is the value of xy? Statement 1: y = x + 1 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, the answer to the target question is
xy = (0)(1) = 0Case b: x = 1 and y = 2. In this case, the answer to the target question is
xy = (1)(2) = 2Since we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: y = x² + 1 The statement doesn't feel sufficient either, so let's test some more values.
Strategy: When considering possible values to test for statement 2, you can save yourself some time by seeing if any of the values you used when testing statement 1 also work for statement 2. In this case, BOTH pairs of values that satisfied statement 1 also satisfy statement 2, which means we can repurpose them to get...
Case a: x = 0 and y = 1. In this case, the answer to the target question is
xy = (0)(1) = 0Case b: x = 1 and y = 2. In this case, the answer to the target question is
xy = (1)(2) = 2Since we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED. In other words,
Case a: x = 0 and y = 1. In this case, the answer to the target question is
xy = (0)(1) = 0Case b: x = 1 and y = 2. In this case, the answer to the target question is
xy = (1)(2) = 2Since we can’t answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Important: Some students will conclude that since the combined statements include 2 different equations with 2 variables, the combined statement should be sufficient. However, this rule applies only to situations in which the two equations are LINEAR equations. Cheers,
Brent