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# A, B, C, D are non zero numbers such that a/b = c/d and a/d

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CEO
Joined: 21 Jan 2007
Posts: 2736

Kudos [?]: 1024 [0], given: 4

Location: New York City
A, B, C, D are non zero numbers such that a/b = c/d and a/d [#permalink]

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06 Nov 2007, 10:54
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A, B, C, D are non zero numbers such that a/b = c/d and a/d = b/c

Which must be true?

|a| = |c|
|b| = |d|
|a| = |d|
|b| = |a|
|b| = |c|

How can i solve this quickly?

Kudos [?]: 1024 [0], given: 4

SVP
Joined: 29 Aug 2007
Posts: 2473

Kudos [?]: 835 [0], given: 19

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06 Nov 2007, 11:30
bmwhype2 wrote:
A, B, C, D are non zero numbers such that a/b = c/d and a/d = b/c

Which must be true?

|a| = |c|
|b| = |d|
|a| = |d|
|b| = |a|
|b| = |c|

How can i solve this quickly?

do not how to do it quickly, but i solved for a and b got a^2 = b^2.

so i got D. lal = lbl.

Kudos [?]: 835 [0], given: 19

Manager
Joined: 01 Nov 2007
Posts: 68

Kudos [?]: 9 [0], given: 0

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06 Nov 2007, 11:56
Yes

We get d^2 = c^2
ldl = lcl (Not in the answer choices)

and a^2 = b^2
lal = lbl

D

Kudos [?]: 9 [0], given: 0

Manager
Joined: 01 Nov 2007
Posts: 82

Kudos [?]: 6 [0], given: 0

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09 Nov 2007, 19:56
from a/d=b/c you can re-write as a/b=d/c which is also equal to c/d

so if a/b=d/c=c/d and since |c|=|d| is not in the answers |a|=|b|

Kudos [?]: 6 [0], given: 0

SVP
Joined: 04 May 2006
Posts: 1890

Kudos [?]: 1354 [0], given: 1

Schools: CBS, Kellogg

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09 Nov 2007, 22:34
try A first
if |a|=|c|, then must be |b| = |d|, that is, B is also correct. It is not possible.
=> A and B can not be both correct. Eliminated

Try C
if |a| = |d|, then must be |b| = |c|, that is E must also be true. Eliminated

=> Only D remains

Kudos [?]: 1354 [0], given: 1

Director
Joined: 09 Aug 2006
Posts: 754

Kudos [?]: 240 [0], given: 0

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10 Nov 2007, 00:41
bmwhype2 wrote:
A, B, C, D are non zero numbers such that a/b = c/d and a/d = b/c

Which must be true?

|a| = |c|
|b| = |d|
|a| = |d|
|b| = |a|
|b| = |c|

How can i solve this quickly?

The only way I could solve the above was as follows:
Stem gives us ad = bc & ac = bd
ad - bc = ac - bd
ad + bd - bc - ac = 0
d(a+b) - c(a+b) = 0
The roots are d = c or a = -b
The only way for a = -b to work in the stem is if |a| = |b|
Eg:
If d = 2, c = 2 then c/d = 1
Stem tells us that c/d = a/b, therefore if a is 1 then b has to be |-1|, it cannot be -1.

Kudos [?]: 240 [0], given: 0

Re: abs value variables   [#permalink] 10 Nov 2007, 00:41
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