Bunuel wrote:
\(a^2 - b^2 = b^2 - c^2\). Is \(a = |b|\)?
(1) \(b = |c|\)
(2) \(b = |a|\)
Target question: Is a = |b|? Given: a² - b² = b² - c² Statement 1: b = |c| This tells us a few things, but with regard to this question, it tells us that b and c have the same magnitude
This also means that
b² = c²With this information, let's test some values that satisfy both statement 1 and the given information:
Case a: a = 0, b = 0 and c = 0. In this case, the answer to the target question is
YES, a does EQUAL |b|Case b: a = -1, b = 1 and c = -1. In this case, the answer to the target question is
NO, a does NOT equal |b|Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: b = |a| Let's test values again.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: a = 0, b = 0 and c = 0. In this case, the answer to the target question is
YES, a does EQUAL |b|Case b: a = -1, b = 1 and c = -1. In this case, the answer to the target question is
NO, a does NOT equal |b|Since we cannot 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: a = 0, b = 0 and c = 0. In this case, the answer to the target question is
YES, a does EQUAL |b|Case b: a = -1, b = 1 and c = -1. In this case, the answer to the target question is
NO, a does NOT equal |b|Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent