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

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Manager
Joined: 10 Oct 2008
Posts: 56
If a, b, c, and d are positive integers, is (a/b) (c/d) >  [#permalink]

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09 Nov 2008, 20:50
If a, b, c, and d are positive integers, is (a/b) (c/d) > c/b?
(1) c > b
(2) a > d

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Intern
Joined: 07 Nov 2008
Posts: 29
Re: a b c d --28  [#permalink]

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09 Nov 2008, 21:28
Jcpenny wrote:
If a, b, c, and d are positive integers, is (a/b) (c/d) > c/b?
(1) c > b
(2) a > d

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

(a/b) (c/d) > c/b ---> ac/db > c/b ---> a > d

B
VP
Joined: 17 Jun 2008
Posts: 1474
Re: a b c d --28  [#permalink]

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09 Nov 2008, 23:28
$$(a/b)(c/d) > c/b$$
or, $$c/b(a/d-1) > 0$$
and since a,b,c,d are positive integers,
$$a/d>1$$
or, $$a>d$$

Hence, B is sufficient.
Director
Joined: 14 Aug 2007
Posts: 692
Re: a b c d --28  [#permalink]

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10 Nov 2008, 00:07
abc - bdc > 0
bc (a-d) > 0
b & c being positive , ensuring that a-d>0 is required

B tells us that precisely.

Hence B
Retired Moderator
Joined: 05 Jul 2006
Posts: 1731
Re: a b c d --28  [#permalink]

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10 Nov 2008, 11:54
[quote="Jcpenny"]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

ac/bd - dc/ bd> 0

is c(a-d)/bd> 0 fo this to be +ve a has to be > d

from one

insuff

from 2 suff......B

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This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: a b c d --28 &nbs [#permalink] 10 Nov 2008, 11:54
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