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

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Director
Joined: 08 Jul 2004
Posts: 596
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
[Reveal] Spoiler: OA

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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23 Sep 2004, 18:11
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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Paul

Director
Joined: 08 Jul 2004
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13 Jan 2005, 09:23
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
Director
Joined: 31 Aug 2004
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13 Jan 2005, 09:46
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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13 Jan 2005, 10:05
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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Joined: 01 Jan 2005
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13 Jan 2005, 11:43
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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
Joined: 31 Aug 2004
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13 Jan 2005, 19:45
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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14 Jan 2005, 03:18
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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14 Jan 2005, 16:22
no need for picking numbers

just simplify the equation you will get Statement II

Intern
Joined: 06 Mar 2013
Posts: 1
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
Math Expert
Joined: 02 Sep 2009
Posts: 39622
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
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]

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13 Jan 2016, 10:50
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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.

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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
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.

5/6 is a positive number so it's more than 0.
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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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Posts: 39622
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
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?

Yes, check complete solution here: if-a-b-c-and-d-are-positive-integers-is-a-b-c-d-c-10147.html#p1200227

Hope it helps.
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Manager
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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
Director
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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/   [#permalink] 09 Apr 2016, 05:21
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