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

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Q50  V42
Re: If a, b, c, and d are positive integers, is (a/b)(c/d) > c/b? [#permalink]
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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]
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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]
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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.

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Re: If a, b, c, and d are positive integers, is (a/b)(c/d) > c/b? [#permalink]
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/b? [#permalink]
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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GMAT 1: 750 Q49 V43
Re: If a, b, c, and d are positive integers, is (a/b)(c/d) > c/b? [#permalink]
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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

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