BrentGMATPrepNow
If \(\frac{x}{w}-\frac{x}{y}=0\), what is the value of \(y\)?
(1) \(w^2 + 4 = 4w\)
(2) \(w^2 + w - 6 = 0\)
I created this question to highlight an important consideration when comparing two equivalent fractions.
If we know that \(\frac{x}{w}=\frac{x}{y}\), we can't then conclude that \(w = y\) (even though both fractions have the same numerator), since it COULD be the case that \(x = 0\), in which case we have \(\frac{0}{w}=\frac{0}{y}\).
Notice that the equation \(\frac{0}{w}=\frac{0}{y}\) holds true for all nonzero values of \(w\) and \(y\).
So, we can't necessarily conclude that \(w = y\)Target question: What is the value of \(y\)?Since we now know that, when \(x=0\), the given equation (\(\frac{x}{w}=\frac{x}{y}\)) holds true for all nonzero values of \(w\) and \(y\), I'm going to jump straight to....
Statements 1 and 2 combined There are several values of \(w\), \(x\) and \(y\) that satisfy BOTH statements. Here are two:
Case a: \(w = 2\), \(x = 0\) and \(y = 2\). These values satisfy the given equation since \(\frac{0}{2}=\frac{0}{2}\)
In this case, the answer to the target question is
y = 1Case b: \(w = 2\), \(x = 0\) and \(y = 10\). These values satisfy the given equation since \(\frac{0}{2}=\frac{0}{10}\)
In this case, the answer to the target question is
y = 10Since we can’t answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent