GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Oct 2018, 21:05

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
User avatar
Joined: 04 Nov 2006
Posts: 238
Location: California
For non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

Show Tags

New post Updated on: 09 Aug 2013, 03:09
1
9
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (01:54) correct 38% (01:52) wrong based on 518 sessions

HideShow timer Statistics

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.
Added OA.
Manager
Manager
avatar
Joined: 12 Jul 2006
Posts: 114
  [#permalink]

Show Tags

New post 20 Dec 2006, 06:09
2
1
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
Manager
avatar
Joined: 04 Feb 2004
Posts: 68
Location: India
  [#permalink]

Show Tags

New post 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
Director
Director
User avatar
Joined: 30 Nov 2006
Posts: 573
Location: Kuwait
  [#permalink]

Show Tags

New post 21 Dec 2006, 16:29
1
1
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
Manager
avatar
Joined: 28 Aug 2006
Posts: 238
Location: Albuquerque, NM
  [#permalink]

Show Tags

New post 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

Answer is D
Director
Director
User avatar
Joined: 26 Feb 2006
Posts: 870
Re: DS_For non-zero integers a, b, c and d...  [#permalink]

Show Tags

New post 22 Dec 2006, 15:48
1
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
Director
avatar
Joined: 24 Aug 2006
Posts: 684
Location: Dallas, Texas
  [#permalink]

Show Tags

New post 24 Dec 2006, 17:51
2
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
Manager
User avatar
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

New post 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
Manager
avatar
Joined: 30 Sep 2009
Posts: 93
GMAT ToolKit User
Re: For non–zero integers a, b, c and d, is ab/cd positive?  [#permalink]

Show Tags

New post 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
Intern
avatar
Joined: 12 Mar 2013
Posts: 3
For non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

Show Tags

New post Updated on: 03 Aug 2013, 09:30
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.
VP
VP
User avatar
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1076
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: For non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

Show Tags

New post 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).
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 I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Manager
Manager
avatar
Joined: 13 Aug 2012
Posts: 97
Re: For non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

Show Tags

New post 17 Aug 2013, 01:26
2
2
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
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1764
Concentration: Finance
GMAT ToolKit User
Re: For non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

Show Tags

New post 10 Oct 2013, 14:57
2
2
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
Intern
avatar
Joined: 31 Oct 2015
Posts: 33
Re: For non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

Show Tags

New post 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.
Intern
Intern
avatar
B
Joined: 26 Jun 2012
Posts: 6
Re: For non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

Show Tags

New post 04 Jan 2017, 04:31
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
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8487
Premium Member
Re: For non-zero integers a, b, c and d, is ab/cd positive?  [#permalink]

Show Tags

New post 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

GMAT Club Bot
Re: For non-zero integers a, b, c and d, is ab/cd positive? &nbs [#permalink] 02 Feb 2018, 11:46
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.