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# If a, b, c, and d are positive integers, is (a/b) (c/d) > c/

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If a, b, c, and d are positive integers, is (a/b) (c/d) > c/ [#permalink]  23 Sep 2004, 16:52
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68% (01:49) correct 32% (01:24) wrong based on 145 sessions
If a, b, c, and d are positive integers, is (a/b) (c/d) > c/b?

(1) c > b
(2) a > d
[Reveal] Spoiler: OA

Last edited by Bunuel on 21 Mar 2013, 03:35, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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30sec
B it is
a/b*c/d = b/c*a/d
All we need to know is for a to be greater than d to create a larger product than b/c on the other side of the inequality. B gives that away
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Director
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Can you plz explain with numbers. Suppose c=1000,b=1. Does this any answer or be interchanging the value of b and c?
S
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Saurya,

Whithout using any number, what you get from the stem is (a/b) (c/d)
in another way it is equal to a/d . c/b so greater than c/b if a/d > 1
That is exactly the purpose of second statement.
Director
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Thanks twixt. I still haven't got it. a/d has to greater than 1 provided b/c is not very small. Say if b/c is 0.001 and c/b is 1000, then does B alone anaswer the Q. so if a/d is 5 then, 5*0.001>1000 which is not true. If we reverse it, it becomes 5*1000>0.001. whic is true. So I am not sure if B alone can answer.
Plz bear with me as i am really not getting it.
S
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We have to calculate whether (a/b)*(c/d)>(c/b) or not?

which is equivalent to

(a/d)*(c/b)>c/b
divide both sides by c/b
a/d>1
since a>d, a/d >1.

Thus, B is enough.
Manager
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saurya_s wrote:
Thanks twixt. I still haven't got it. a/d has to greater than 1 provided b/c is not very small. Say if b/c is 0.001 and c/b is 1000, then does B alone anaswer the Q. so if a/d is 5 then, 5*0.001>1000 which is not true. If we reverse it, it becomes 5*1000>0.001. whic is true. So I am not sure if B alone can answer.
Plz bear with me as i am really not getting it.
S

I am not sure what do you try to say here. The question does not ask you whether (a/b) x (c/d) > (b/c), unless you typed it wrong in the first place.
Director
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Yes, that is what I have been reading. The q is correct but I have been reading as you said.
Thanks a lot for noting that.
Director
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no need for picking numbers

just simplify the equation you will get Statement II

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Re: Q36: If a, b, c, and d are positive integers, is (a/b) (c/d) [#permalink]  21 Mar 2013, 03:25
saurya_s wrote:
Q36:
If a, b, c, and d are positive integers, is (a/b) (c/d) > c/b?
(1) c > b
(2) a > d

ac/bd > c/b
a/d > 1
a>d
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Re: If a, b, c, and d are positive integers, is (a/b) (c/d) > c/ [#permalink]  21 Mar 2013, 03:40
Expert's post
If a, b, c, and d are positive integers, is (a/b) (c/d) > c/b?

Is $$\frac{a}{b}*\frac{c}{d}>\frac{c}{b}$$? --> is $$\frac{c}{b}*\frac{a}{d}>\frac{c}{b}$$? --> since all variables are positive, then we can safely reduce by c/b: is $$\frac{a}{d}>1$$? --> cross-multiply: is $$a>d$$?

(1) c > b. Not sufficient.
(2) a > d. Sufficient.

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Re: If a, b, c, and d are positive integers, is (a/b) (c/d) > c/   [#permalink] 21 Mar 2013, 03:40
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