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For nonzero integers a, b, c and d, is ab/cd positive? [#permalink]
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Updated on: 09 Aug 2013, 03:09
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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.



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



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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



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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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Re: DS_For nonzero integers a, b, c and d... [#permalink]
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22 Dec 2006, 15:48
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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.



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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 !
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For nonzero integers a, b, c and d, is ab/cd positive? [#permalink]
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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? [#permalink]
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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? [#permalink]
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17 Aug 2013, 01:26
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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? [#permalink]
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10 Oct 2013, 14:57
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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? [#permalink]
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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? [#permalink]
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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? [#permalink]
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02 Feb 2018, 11:46
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