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

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saurya_s
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If a, b, c, and d are positive integers, is (a/b)(c/d) > c/b? [#permalink] New post   Updated on: 21 Jan 2020, 05:44
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If a, b, c, and d are positive integers, is \((\frac{a}{b})(\frac{c}{d}) > \frac{c}{b}?\)

(1) c > b
(2) a > d
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B

Originally posted by saurya_s on 23 Sep 2004, 17:52.
Last edited by Bunuel on 21 Jan 2020, 05:44, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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bogos
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Re: If a, b, c, and d are positive integers, is (a/b)(c/d) > c/b? [#permalink] New post   02 Aug 2010, 01:51
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\((\frac{a}{b})(\frac{c}{d})=(\frac{a}{d})(\frac{c}{b})>(\frac{c}{b})\)
Since a, b, c, d are positive, so both sides can be divided by \((\frac{c}{b})\)
\(\frac{(\frac{a}{d})(\frac{c}{b})}{(\frac{c}{b})}>\frac{(\frac{c}{b})}{(\frac{c}{b})}\)
or
\(\frac{a}{d}>1\)
or a>d

Answer is B.
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Vijo
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Re: If a, b, c, and d are positive integers, is (a/b)(c/d) > c/b? [#permalink] New post   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.
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Re: If a, b, c, and d are positive integers, is (a/b)(c/d) > c/b? [#permalink] New post   02 Aug 2010, 00:34
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Stmt 2 is sufficient as follows:

LHS and RHS can be rearranged into (a/d)(c/b) > (c/b)
As c and b are both positive (you don't need Stmt 1 for that), they can be cancelled out from both sides - which leaves us with a/d > 1 ??

Stmt 2 says exactly that. Hence sufficient.

Hope this helps.
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Re: If a, b, c, and d are positive integers, is (a/b)(c/d) > c/b? [#permalink] New post   29 Aug 2010, 18:25
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udaymathapati wrote:
If a, b, c, and d are positive integers, is (a/b) (c/d) > c/b?
(1) c > b
(2) a > d



\(\frac{a}{b}*\frac{c}{d}>\frac{c}{b}\)

simplify

\(\frac{a}{d}>1\)

\(a>d\) ?

therefore B is enough, A is irrelevant
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Re: If a, b, c, and d are positive integers, is (a/b)(c/d) > c/b? [#permalink] New post   21 Mar 2013, 04:40
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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.

Answer: B.
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Re: If a, b, c, and d are positive integers, is (a/b)(c/d) > c/b? [#permalink] New post   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/b? [#permalink] New post   17 Mar 2016, 02:52
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angad87 wrote:
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


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/b? [#permalink] New post   18 Jul 2016, 00:53
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jakolik wrote:
If a,b,c and d are positive integers, is (a/b)(c/d) > c/b?

(1) c>b
(2) a>d


Given that a,b,c,d, are all positives; so we can take a deep breath of relief and carry on with this question because now we can apply any operation on the inequality without worrying about the sign reversal and other such restrictions
(1) c>b
(2) a>d

Simplify the original equation and see what the question stem reduces to :-
\(\frac{a}{b} * \frac{c}{d} >\frac{c}{b}\)

\(\frac{ac}{bd}>\frac{c}{d}\) {\(\frac{c}{b}\)will get cancelled on both the LHS & RHS}

\(\frac{a}{d}>1\)

\(a>d\)


SO THE REAL QUESTION IS :- IS \(a>d\)

(1) c>b
Doesn't tell about a and b ; INSUFFICIENT

(2) a>d
Tells us that a is always greater than d
SUFFICIENT

ANSWER IS B
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Re: If a, b, c, and d are positive integers, is (a/b)(c/d) > c/b? [#permalink] New post   30 Jul 2023, 00:45
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Re: If a, b, c, and d are positive integers, is (a/b)(c/d) > c/b? [#permalink]
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