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

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

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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Aug 2013, 03:09, edited 2 times in total.
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20 Dec 2006, 06:09
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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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Re: DS_For non-zero integers a, b, c and d... [#permalink]

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22 Dec 2006, 15:48
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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.
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Re: For non-zero 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 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

Hope it helps
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21 Dec 2006, 08:12
Getting B ...

if ABCD <0 (either one or three of them is negetive)

then AB/CD < 0

B is SUFF
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21 Dec 2006, 16:29
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Given : a,b,c and d are all non-zero ints.

(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

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22 Dec 2006, 15:08
From 1 we get the expression as -(b^2/d^2) hence negative

from 2 we get (-a^2b^2)/4

Both are negative

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24 Dec 2006, 17:51
a,b,c,d are all non zero.

Now we have:

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

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03 Aug 2013, 09:26
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?

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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03 Aug 2013, 09:34
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).

Hope it's clear.
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Re: For non-zero 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.

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

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Re: For non-zero 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 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.
Re: For non-zero integers a, b, c and d, is ab/cd positive?   [#permalink] 10 Nov 2015, 19:49
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