Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 04 Nov 2006
Posts: 238
Location: California

For nonzero integers a, b, c and d, is ab/cd positive?
[#permalink]
Show Tags
Updated on: 09 Aug 2013, 03:09
Question Stats:
62% (01:54) correct 38% (01:52) wrong based on 518 sessions
HideShow timer Statistics
For nonzero integers a, b, c and d, is ab/cd positive? (1) ad + bc = 0 (2) abcd = 4
Official Answer and Stats are available only to registered users. Register/ Login.
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
Posts: 114

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.
_________________
I think I can. I think I can. I think I can.



Manager
Joined: 04 Feb 2004
Posts: 68
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
Posts: 573
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
Posts: 238
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



Director
Joined: 26 Feb 2006
Posts: 870

Re: DS_For nonzero integers a, b, c and d...
[#permalink]
Show Tags
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: 684
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 !
_________________
"Education is what remains when one has forgotten everything he learned in school."



Manager
Joined: 25 Jan 2010
Posts: 104
Location: Calicut, India

Re: For non–zero integers a, b, c and d, is ab/cd positive?
[#permalink]
Show Tags
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.
_________________
If u think this post is useful plz feed me with a kudo



Manager
Joined: 30 Sep 2009
Posts: 93

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



Intern
Joined: 12 Mar 2013
Posts: 3

For nonzero integers a, b, c and d, is ab/cd positive?
[#permalink]
Show Tags
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.



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1076
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: For nonzero integers a, b, c and d, is ab/cd positive?
[#permalink]
Show Tags
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.
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Manager
Joined: 13 Aug 2012
Posts: 97

Re: For nonzero integers a, b, c and d, is ab/cd positive?
[#permalink]
Show Tags
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



SVP
Joined: 06 Sep 2013
Posts: 1764
Concentration: Finance

Re: For nonzero integers a, b, c and d, is ab/cd positive?
[#permalink]
Show Tags
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



Intern
Joined: 31 Oct 2015
Posts: 33

Re: For nonzero integers a, b, c and d, is ab/cd positive?
[#permalink]
Show Tags
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.



Intern
Joined: 26 Jun 2012
Posts: 6

Re: For nonzero integers a, b, c and d, is ab/cd positive?
[#permalink]
Show Tags
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



NonHuman User
Joined: 09 Sep 2013
Posts: 8487

Re: For nonzero integers a, b, c and d, is ab/cd positive?
[#permalink]
Show Tags
02 Feb 2018, 11:46
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: For nonzero integers a, b, c and d, is ab/cd positive? &nbs
[#permalink]
02 Feb 2018, 11:46






