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

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Manager
Joined: 16 Apr 2010
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If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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02 Aug 2010, 00:01
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15% (low)

Question Stats:

76% (00:59) correct 24% (01:45) wrong based on 80 sessions

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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
Intern
Joined: 03 Mar 2010
Posts: 37
Re: If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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02 Aug 2010, 01:51
7
$$(\frac{a}{b})(\frac{c}{d})=(\frac{a}{d})(\frac{c}{b})>(\frac{c}{b})$$
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

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##### General Discussion
Intern
Joined: 06 Apr 2010
Posts: 17
Re: If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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02 Aug 2010, 00:34
1
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.
Intern
Joined: 10 Apr 2008
Posts: 21
Re: If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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02 Aug 2010, 20:47
According to stmt2 (a/b) > 1.

So, a number greater than 1 multiplied with (c/b) will be greater than (c/b)
Manager
Joined: 09 Jun 2010
Posts: 101
Re: If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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28 Aug 2010, 06:03
1
is (a/b) (c/d) > c/b ? simplify => a/d>1? => is a>d?

(2) a > d

"B" it is
Manager
Joined: 16 Feb 2010
Posts: 176
Re: If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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29 Aug 2010, 18:25
1
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) >  [#permalink]

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30 Aug 2010, 03:59
The key here is in the given ( a,b,c,d) are +ve if this wasn't stated then we can't multiply or simplify
Manager
Joined: 07 Feb 2010
Posts: 127
Re: If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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30 Aug 2010, 08:06
1
If a, b, c, and d are positive integers, is (a/b) (c/d) > c/b?
(1) c > b
(2) a > d

change the question it becomes a > d
Director
Joined: 04 Jun 2016
Posts: 566
GMAT 1: 750 Q49 V43
If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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18 Jul 2016, 00:53
1
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

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Location: Hungary
Schools: Queen's MBA'20
Re: If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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27 Feb 2019, 09:58
Can someone pls explain me , how does

(a/b)(c/d) > c/b
become
a/d>1 ?
i know that its simplification, but i just cant get it
Re: If a,b,c and d are positive integers, is (a/b) (c/d) >   [#permalink] 27 Feb 2019, 09:58
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