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Manager  Joined: 16 Apr 2010
Posts: 180
If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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3 00:00

Difficulty:   15% (low)

Question Stats: 73% (01:00) correct 27% (01:34) wrong based on 102 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: 34
Re: If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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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

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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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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: 19
Re: If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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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: 98
Re: If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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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: 164
Re: If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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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
Retired Moderator B
Joined: 05 Jul 2006
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Re: If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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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: 116
Re: If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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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

change the question it becomes a > d
so answer is b
Director  B
Joined: 04 Jun 2016
Posts: 556
GMAT 1: 750 Q49 V43 If a,b,c and d are positive integers, is (a/b) (c/d) >  [#permalink]

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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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Manager  B
Joined: 16 May 2018
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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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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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