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

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For non-zero integers a, b, c and d, is ab/cd positive? [#permalink] New post 20 Dec 2006, 02:25
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A
B
C
D
E

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62% (01:00) correct 38% (01:23) wrong based on 99 sessions
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, 02:09, edited 2 times in total.
Added OA.
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 [#permalink] New post 20 Dec 2006, 05:09
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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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 [#permalink] New post 21 Dec 2006, 07:12
Getting B ...

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



then AB/CD < 0

B is SUFF
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 [#permalink] New post 21 Dec 2006, 15:29
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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 [#permalink] New post 22 Dec 2006, 14:08
From 1 we get the expression as -(b^2/d^2) hence negative

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

Both are negative

Answer is D
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Re: DS_For non-zero integers a, b, c and d... [#permalink] New post 22 Dec 2006, 14:48
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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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 [#permalink] New post 24 Dec 2006, 16:51
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 non-zero integers a, b, c and d, is ab/cd positive? [#permalink] New post 03 Aug 2013, 08:26
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, 08:30, 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] New post 03 Aug 2013, 08:34
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).
Your second point is correct.

Hope it's clear.
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Re: For non-zero integers a, b, c and d, is ab/cd positive? [#permalink] New post 17 Aug 2013, 00:26
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 non-zero integers a, b, c and d, is ab/cd positive? [#permalink] New post 10 Oct 2013, 13:57
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
Re: For non-zero integers a, b, c and d, is ab/cd positive?   [#permalink] 10 Oct 2013, 13:57
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