if a, b, c, and d are positive

[RonPurewal]

um.
i think that everyone on this thread has missed something:

note that statement (i) says that
left side < c/d
and this is true.

now, when we get to statement (iii), there's no need to go through all this song and dance... because it says
left side < c/d + other stuff
people! we already know that c/d is bigger than the left side, all by itself... and now we're adding something to c/d, making it even bigger.
no algebra necessary; if statement (i) is true, then, a fortiori, this one has to be true as well.

[tim]

brilliant, Ron! i totally missed that too, and did a lot more algebra than i had to. :) nice use of legalese at the end there too..

[matthew.dukes]

if a, b, c, and d are positive numbers and a/b < c/d , which of the following must be true?

I. (a+c) / (b+d) < c/ d

II. (a+c) / (b+d) < a/b

III. (a+c) / (b+d) < a/b + c/d

a) none
b) I only
c) II only
d) I and II
e) I and III

OA: B


how do you solve this problem?

I believe III. was an equation, not an inequality, such that "(a+c) / (b+d) = a/b + c/d". Thus, III implies that "left side" is > c/d, in conflict with I which we know to be true.

[RonPurewal]

I believe III. was an equation, not an inequality, such that "(a+c) / (b+d) = a/b + c/d". Thus, III implies that "left side" is > c/d, in conflict with I which we know to be true.

If so, then, sure.

[RyanS806]

yes; I just did this question on GMAT prep software and statement three should be written as " a+c/b+d = a/b + c/d." This is false. So the answer is B. I only. I plugged in #'s here instead of cross multiplying.

What are the rules for when you can multiply inequalities? I seem to remember learning that you cannot multiply inequalities.. When can/can't you do so?

-Ryan

[tim]

Two things:

1) Can you explain what you mean by "multiplying inequalities"? The normal thing I think of when I see that phrase is totally irrelevant to this problem.

2) Please correct your quote from the software. I am almost 100% sure the software did not say that (the number a) plus (the fraction c/b) plus (the number d) equals (the fraction a/b) plus (the fraction c/d), which is effectively what you wrote. Perhaps a screen shot would help, as I requested several years ago?