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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: 2764
Location: New York City
Followers: 9

Kudos [?]: 354 [0], given: 4

A, B, C, D are non zero numbers such that a/b = c/d and a/d [#permalink]  06 Nov 2007, 09:54
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?
SVP
Joined: 29 Aug 2007
Posts: 2496
Followers: 58

Kudos [?]: 562 [0], given: 19

Re: abs value variables [#permalink]  06 Nov 2007, 10:30
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.
Manager
Joined: 01 Nov 2007
Posts: 69
Followers: 1

Kudos [?]: 3 [0], given: 0

Yes

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

and a^2 = b^2
lal = lbl

D
Manager
Joined: 01 Nov 2007
Posts: 83
Followers: 0

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

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|
SVP
Joined: 04 May 2006
Posts: 1936
Schools: CBS, Kellogg
Followers: 19

Kudos [?]: 449 [0], given: 1

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
Director
Joined: 09 Aug 2006
Posts: 765
Followers: 1

Kudos [?]: 72 [0], given: 0

Re: abs value variables [#permalink]  09 Nov 2007, 23:41
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.

Re: abs value variables   [#permalink] 09 Nov 2007, 23:41
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