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Senior Manager
Joined: 04 Nov 2006
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For non-zero integers a, b, c and d, is ab / cd positive? [#permalink]
 20 Dec 2006, 03:25
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For non-zero integers a, b, c and d, is ab / cd
positive?
(1) ad + bc = 0
(2) abcd = -4
(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question
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Manager
Joined: 12 Jul 2006
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Agree with D.
S1: One of ad or bc has to be negative for them to add to zero.
S2: One or three of abcd has to be negative for their product to be negative.
_________________
I think I can. I think I can. I think I can.
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Manager
Joined: 04 Feb 2004
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Getting B ...
if ABCD <0 (either one or three of them is negetive)
then AB/CD < 0
B is SUFF
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Director
Joined: 30 Nov 2006
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My answer is D
Given : a,b,c and d are all non-zero ints.
asked: ab/cd > 0 ?
(1) ad + bc = 0
---------------------
ad = - bc --> one of abcd has a different sign that the others
ex: all +ve and one is -ve or all -ve and one is +ve
So, is ab/cd > 0 ? NO
statement 1 is sufficient
(2) abcd = -4
------------------
abcd = -ve # --> one abcd also has a different sign than the others
So, is ab/cd > 0 ? NO
statement 2 is sufficient
Thus, the answer is D
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Manager
Joined: 28 Aug 2006
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From 1 we get the expression as -(b^2/d^2) hence negative
from 2 we get (-a^2b^2)/4
Both are negative
Answer is D
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Director
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Re: DS_For non-zero integers a, b, c and d... [#permalink]
22 Dec 2006, 15:48
mm007 wrote: For non-zero integers a, b, c and d, is ab/cd positive?
(1) ad + bc = 0
(2) abcd = -4
should be D.
i. one of the integer is -ve so ab/cd is -ve. sufficient
ii. either one or three of the integers is/are -ve, so ab/cd is again -ve. sufficient.
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Director
Joined: 24 Aug 2006
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Location: Dallas, Texas
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a,b,c,d are all non zero.
Now we have:
ad + bc =0
multiply it by bd we get (since bd non zero):
ab(d^2) + (b^2)cd=0
Therefore: ab/cd = -(b^2)/(d^2)
or ab/cd <0 --------------------------- sufficient
abcd = -4
or (ab/cd)* (cd)^2 = -4
or ab/cd = -4/(cd)^2
or ab/cd <0 ...................................sufficient
D !
_________________
"Education is what remains when one has forgotten everything he learned in school."
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