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For nonzero integers a, b, c and d, is ab/cd positive?
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Updated on: 09 Aug 2013, 03:09
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63% (01:53) correct 37% (01:45) wrong based on 410 sessions
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For nonzero integers a, b, c and d, is ab/cd positive? (1) ad + bc = 0 (2) abcd = 4
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Originally posted by mm007 on 20 Dec 2006, 03:25.
Last edited by Bunuel on 09 Aug 2013, 03:09, edited 2 times in total.
Added OA.



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.
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Manager
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Location: India

Getting B ...
if ABCD <0 (either one or three of them is negetive)
then AB/CD < 0
B is SUFF



Director
Joined: 30 Nov 2006
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Location: Kuwait

My answer is D
Given : a,b,c and d are all nonzero 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



Manager
Joined: 28 Aug 2006
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Location: Albuquerque, NM

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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Re: DS_For nonzero integers a, b, c and d...
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22 Dec 2006, 15:48
mm007 wrote: For nonzero 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.



Director
Joined: 24 Aug 2006
Posts: 590
Location: Dallas, Texas

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 !
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Re: For non–zero integers a, b, c and d, is ab/cd positive?
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01 Dec 2011, 21:22
(1) SUFFICIENT: This statement can be rephrased as ad = <bc. For the signs of ad and bc to be opposite one another, either precisely one or three of the four integers must be negative. The answer to our rephrased question is "no," and, therefore, we have achieved sufficiency. (2) SUFFICIENT: For the product abcd to be negative, either precisely one or three of the four integers must be negative. The answer to our rephrased question is "no," and, therefore, we have achieved sufficiency. The correct answer is D.
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Re: For non–zero integers a, b, c and d, is ab/cd positive?
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07 Dec 2011, 00:02
1) ad + bc = 0 ad=bc therefore a=(bc/d) >replacing in the question For ab/cd to be +ve we get (b^2/d^2) > ve
(2) abcd = –4 here we can have either one integer to be ve or three integer to be ve therefore (ab/cd ) will be ve in any case.
Hence D as both are sufficient to prove the statement to be false.



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For nonzero integers a, b, c and d, is ab/cd positive?
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Updated on: 03 Aug 2013, 09:30
For nonzero integers a, b, c and d, is ab/cd positive?
(1) ad + bc = 0 (2) abcd = 4
I dont agree with the OA.
IMO B.
Statement 1 : ad = bc 1) If all integers a,b,c & d are ve/+ve, then statement 1 holds true and ab/bc is positive. 2) If any one integer is ve & other 3 integers are positive, statement 1 holds true and ab/bc is negative.
Let me know where my thinking is wrong?
Originally posted by mohitvarshney on 03 Aug 2013, 09:26.
Last edited by Zarrolou on 03 Aug 2013, 09:30, edited 1 time in total.
Merging similar topics.



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Re: For nonzero integers a, b, c and d, is ab/cd positive?
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03 Aug 2013, 09:34
mohitvarshney wrote: For nonzero integers a, b, c and d, is ab/cd positive?
(1) ad + bc = 0 (2) abcd = 4
I dont agree with the OA.
IMO B.
Statement 1 : ad = bc 1) If all integers a,b,c & d are ve/+ve, then statement 1 holds true and ab/bc is positive. 2) If any one integer is ve & other 3 integers are positive, statement 1 holds true and ab/bc is negative.
Let me know where my thinking is wrong? If \(a,b,c,d\) are all positive or negative (1) does not hold true,as \(positive+positive>0\) and \(negative + negative < 0\) ( and not equal 0). Your second point is correct. Hope it's clear.
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Re: For nonzero integers a, b, c and d, is ab/cd positive?
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17 Aug 2013, 01:26
From statement 1, we know that \(ad+bc=0\) \(=>\) \(ad=bc\) \(=>\) \(\frac{a}{b}=\frac{c}{d}\) \(=>\) \(\frac{a*b}{b*b}=\frac{c*d}{d*d}\) \(=>\) \(\frac{ab}{b^2}=\frac{cd}{d^2}\) \(=>\) \(\frac{ab}{cd}=\frac{b^2}{d^2}\) Thus from 1, we come to know that ab/cd is negative since \(b^2\) and \(d^2\) are positive
From statement 2, \(abcd=4\) Now the only way this can happen is if one of the term is negative. And if one of the term is negative, then ab/cd has to be negative.
Hence the answer D



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Re: For nonzero integers a, b, c and d, is ab/cd positive?
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10 Oct 2013, 14:57
mm007 wrote: For nonzero integers a, b, c and d, is ab/cd positive?
(1) ad + bc = 0
(2) abcd = 4 So this question is basically testing negatives and positives (Remember >0). First Statement ad = bc. Now we could rearrange this to be a/c = b/d. Now replacing in the original statement we would have (b/d)(b/d) . Since this is basically the same fraction but with different signs then the result HAS to be negative. Therefore this statement is Sufficient Second Statement abcd = 4. Now here, we see that the result is ve. So actually, we can either have 1 negative or 3 negatives. But either choice will give us ab/cd <0. Because the only thing we need is to have an odd number of negative signed numbers. I suggest to try it with different combinations and see it for yourself Hence answer is (D) Hope it helps



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Re: For nonzero integers a, b, c and d, is ab/cd positive?
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10 Nov 2015, 19:49
Q: a, b, c, d are nonzero integers. Is ab/cd positive?
St1: ad + cb = 0, ad = cb. One of the four elements is of an opposite sign, therefore either one or three elements are negative and ab/cd = ve. Sufficient.
St2: abcd = 4, ab = 4/cd, ab/cd = 4/cd^2, therefore ab/cd is negative.



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Re: For nonzero integers a, b, c and d, is ab/cd positive?
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04 Jan 2017, 04:31
For nonzero integers a, b, c and d, is ab/cd positive?
(1) ad + bc = 0
(2) abcd = 4
1) a=1 b=1 c=1 d=1 ad+bc=0 ab/cd is +ve a=2 b=3 c=2 d=3 ad+bc=0 ab/cd is ve two solutions so wrong not sufficient 2) a=1 b=1 c=1 d=4 abcd=4 ab/cd is ve a=1 b=1 c=1 d=4 abcd=4 ab/cd is ve sufficient so answer is B not D Please correct me if i am wrong



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Re: For nonzero integers a, b, c and d, is ab/cd positive?
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15 Sep 2019, 02:58
If ad+bc =0 , square of both sides should also be zero which gives us ad^2 + bc^2 + 2abcd = 0 Since ad^2 and bc^2 can’t be zero , Hence abcd<0 , which means three of them have same sign and one opposite Condition A will suffice , Condition B directly states the above Both are sufficient .
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Re: For nonzero integers a, b, c and d, is ab/cd positive?
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15 Sep 2019, 02:58






