<p>Whenever I do practices I keep getting about one wrong. ... anyway</p>
<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>is there any other way to do this other than by trial/error =/ ? thanks</p>
<p>Is there some relationship between the four that you did not mention?</p>
<p>But anyway.
Look at them, c and d are true, so eliminate those two. You can also eliminate the other answers using those two choices.
Using d, a/c = b/f, mess around with it and you get af=bc, and so af/bc=1, so e is true. Now you can either pick arbitrary numbers and try to eliminate the other two, or multiply both sides of equation e by b/a, giving you f/c=b/a, eliminating b, and thus you are left with a as the answer</p>
<p>Or you can look at the problem like this. Glance at all the choices and ask yourself, “What’s different about one of these?”. It should be immediately obvious to you that c and d should be true because taking the inverse of both equal numbers should not affect whether they are equal or not because they are nonzero. Then work from those two. You should soon see that if a and c are on the same side of the equation, one will be in the numerator and the other will be in the denominator. The same thing goes for b and f. Likewise you should also see that if you bring a and c to different sides of the equation, then if a is in the numerator, c must also be in the numerator, and same goes for the denominator.
Now which one of the choices doesn’t fit the conditions? Choice a, because a is in the numerator for one side of the equation and c is in the denominator for the other side.</p>
<p>Easiest approach is to cross multiply the values in the choices and then eliminate the one that stands out.</p>
<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>You don’t need more information to solve this. It’s asking which of these equations isn’t the same as the others.</p>
<p>(a) a/f = b/c –> ac = bf
(b) f/c = b/a –> af = cb
(c) c/a = f/b –> bc = af
(d) a/c = b/f –> af = cb
(e) af/bc = 1/1 –> af = bc</p>
<p>The correct answer is A, because it is the only equation that doesn’t say af = cb.</p>
<p>I’ve seen the problem before. I put numbers in because it confused me the other way.</p>