<p>If a, b, c, and f are four nonzero numbers, then all of the following proportions are equivalent EXCEPT</p>
<p>a) a/f = b/c
b) f/c =b/a
c) c/a = f/b
d) a/c= b/f
e) af/bc = 1/1</p>
<p>the answer is a, but i don't get how. any help greatly appreciated, thanks.</p>
<p>Ha ha. That’s got to be one of the wierder math problems on the SAT I’ve seen. You have to use the answer choices to give you information about what the answer is; if you were just given (A), you’d have no way of knowing it was (A)!</p>
<p>So, what you have to do is look at answer choice (E). Manipulate it and get af=bc. Various operations on this can yield all the answer choices except (A).</p>
<p>Cool problem. :)</p>
<p>It’s like those problems that say, “Which of the following does not belong?” The question is really only there to parametrize the variables as non-zero.</p>
<ol>
<li> My dumb way: make up numbers that fit anyone of the answer choices. Then see whether it fits the others. Depending on where you start, it will either fit all but one, or none of them except the one you started with. Either way, the odd man out is the one you want.</li>
</ol>
<p>That’s really the way I did this, because I am very biased toward making up numbers. But this time…</p>
<ol>
<li> It is much easier to just cross-multiply each answer. You’ll see immediately which one differs from the others.</li>
</ol>
<p>This is a rather weird question and the most logical way i think would be to give numbers for the variables and test the choices. </p>
<p>a, b, c, f</p>
<p>a) a/f = b/c
b) f/c =b/a
c) c/a = f/b
d) a/c= b/f
e) af/bc = 1/1</p>
<p>give numbers to them so that a proportion could work out between them… for example you want (b) to work right? so then give numbers so that f/c equals to b/a … then you could do
f=8 c=4 b=2 a=1… then (b) would be correct… then try (c) c/a = f/b = 4/1 = 8/2 that works too… now try (d) a/c = b/f = 1/4 = 2/8 … that works too. try (e) af/bc = 8/8 = 1/1
try (a) 1/8 = 2/4 ? no that doesn’t work… if you plugged in the numbers according to the proporion in (a), then none of the answers would have worked and you could have understood that (a) was incorrect… it is a weird question. but now if something like this comes up on the SAT, you’ll know what to do or at least, what it’s asking for</p>
<p>Cross multiply</p>
<p>a) a/f = b/c
ac = bf</p>
<p>b) f/c =b/a
af = bc</p>
<p>c) c/a = f/b
af = bc</p>
<p>d) a/c= b/f
af = bc</p>
<p>e) af/bc = 1/1
af = bc</p>
<p>Choice a is the odd man out.</p>
<p>^ well then…</p>