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Manager  Joined: 04 Nov 2006
Posts: 218
Location: California
For non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

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Question Stats: 63% (01:53) correct 37% (01:45) wrong based on 410 sessions

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For non-zero integers a, b, c and d, is ab/cd positive?

(1) ad + bc = 0

(2) abcd = -4

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.
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  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
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
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

Director  Joined: 26 Feb 2006
Posts: 693
Re: DS_For non-zero integers a, b, c and d...  [#permalink]

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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.
Director  Joined: 24 Aug 2006
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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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Re: For non–zero integers a, b, c and d, is ab/cd positive?  [#permalink]

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(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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Manager  Joined: 30 Sep 2009
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Re: For non–zero integers a, b, c and d, is ab/cd positive?  [#permalink]

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1) ad + bc = 0
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.
Intern  Joined: 12 Mar 2013
Posts: 3
For non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

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For non-zero 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 non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

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mohitvarshney wrote:
For non-zero 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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Manager  Joined: 13 Aug 2012
Posts: 90
Re: For non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

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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 non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

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mm007 wrote:
For non-zero 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
Intern  Joined: 31 Oct 2015
Posts: 26
Re: For non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

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Q: a, b, c, d are non-zero 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 non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

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For non-zero 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 non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

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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 .

Posted from my mobile device Re: For non-zero integers a, b, c and d, is ab/cd positive?   [#permalink] 15 Sep 2019, 02:58
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