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If a, b, c, and d are positive integers, is (a/b) (c/d) > c/ [#permalink]
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23 Sep 2004, 17:52
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If a, b, c, and d are positive integers, is (a/b) (c/d) > c/b? (1) c > b (2) a > d
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Last edited by Bunuel on 21 Mar 2013, 04:35, 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.



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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.



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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.



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no need for picking numbers
just simplify the equation you will get Statement II
Answer B



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Re: Q36: If a, b, c, and d are positive integers, is (a/b) (c/d) [#permalink]
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21 Mar 2013, 04:25
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]
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21 Mar 2013, 04:40



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Re: If a, b, c, and d are positive integers, is (a/b) (c/d) > c/ [#permalink]
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Re: If a, b, c, and d are positive integers, is (a/b) (c/d) > c/ [#permalink]
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17 Mar 2016, 02:36
I have a query with this qsn. Even though c,b are positive integers but if c<b and a>d then their product will not be >0 in all cases.
For e.g i take c/b=2/3 and a/d=5/4 then (c/b)*(a/d) =5/6 which is <0 and if c/b is 3/2 and a/d=5/4 then their product is 15/8 which is >0. So ,shouldn't C be the option than only considering B option where the relation of b and c is not considered.
Please help with query



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Re: If a, b, c, and d are positive integers, is (a/b) (c/d) > c/ [#permalink]
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17 Mar 2016, 02:52



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Re: If a, b, c, and d are positive integers, is (a/b) (c/d) > c/ [#permalink]
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17 Mar 2016, 03:21
Thanks Bunuel. That was a silly doubt. So in all cases it will be >0 as long as we know relation of a and d?is that right?



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Re: If a, b, c, and d are positive integers, is (a/b) (c/d) > c/ [#permalink]
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17 Mar 2016, 03:24



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Re: If a, b, c, and d are positive integers, is (a/b) (c/d) > c/ [#permalink]
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19 Mar 2016, 08:36
From Question Stem ac/bd > c/b a/d > 1 a>d This is what is given in Option B



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Re: If a, b, c, and d are positive integers, is (a/b) (c/d) > c/ [#permalink]
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09 Apr 2016, 05:21
saurya_s wrote: If a, b, c, and d are positive integers, is (a/b) (c/d) > c/b?
(1) c > b (2) a > d (a/b) (c/d) > c/b rewrite : (a/d) (c/b) > (c/b) it is given that all are +ve integers. so we can divide by (c/b). so inequality becomes is (a/d) > 1? or say is a > d?? option B says this. correct.
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Re: If a, b, c, and d are positive integers, is (a/b) (c/d) > c/
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