gettinit wrote:
Would p be directly proportional to i as well if e is proportional to p? I am thinking it should be, however the constant proportion will be different between p and e and e and i and thus entirely separate between p and i? thanks.
\(a\) is directly proportional to \(b\) means that as the absolute value of \(b\) gets bigger, the absolute value of \(a\) gets bigger too, so there is some non-zero constant \(x\) such that \(a=xb\);
So if \(a\) is directly proportional to \(b\) (\(a=xb\)), then vise-versa is also correct: \(b\) is directly proportional to \(a\) (\(b=\frac{1}{x}*a\) as the absolute value of \(a\) gets bigger, the absolute value of \(b\) gets bigger too).
\(a\) is inversely proportional to \(b\) means that as the absolute value of \(b\) gets bigger, the absolute value of \(a\) gets smaller, so there is some non-zero constant constant \(y\) such that \(a=\frac{y}{b}\).So if \(a\) is inversely proportional to \(b\) (\(a=\frac{y}{b}\)), then vise-versa is also correct: \(b\) is inversely proportional to \(a\) (\(b=\frac{y}{a}\) as the absolute value of \(a\) gets bigger, the absolute value of \(b\) gets smaller).
As for the question:
In a certain business, production index p is directly proportional to efficiency index e, which is in turn directly proportional to investment i. What is p if i = 70?Given: \(p=ex\) and \(e=iy\) (for some constants \(x\) and \(y\)), so \(p=ixy\). Question: \(p=70xy=?\) So, basically we should find the value of \(xy\).
(1) e = 0.5 whenever i = 60 --> as \(e=iy\) then \(0.5=60y\) --> we can find the value of \(y\), but still not sufficient.
(2) p = 2.0 whenever i = 50 --> as \(p=ixy\) then \(2=50xy\) --> we can find the value of \(xy\). Sufficient.
Answer: B.
Hope it's clear.
When you break it down like that, it makes complete sense but I made the following error. Can you please clarify why this isn't true?
\(\frac{p}{.5}\) = \(\frac{.5}{60}\) and solve for p. If the ratios are proportional, shouldn't .5/60 give me a relationship for p/e since I already know E? This led me to choose "D" as the answer choice.