NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 01:15 It is currently 26 Apr 2024, 01:15
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If abcd is not equal to zero ,is abcd <0 ?

User avatar
meetthedevil
Intern
Intern
Joined: 15 Mar 2016
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
If abcd is not equal to zero ,is abcd <0 ? [#permalink] New post   27 Jun 2016, 09:19
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
Hide Show timer Statistics
Hi Mike,

I tried solving the below DS question and solved as given below. Could you please explain where I am going wrong, as the correct answer to this question is C.

If abcd is not equal to zero ,is abcd <0 ?

1) a/b > c/d

2) b/a > d/c

Statement 1:

a/b > c/d --> Multiplying both sides by b --> a > cb/d --> Multiplying both sides by d --> ad > bc --> Multiplying both sides by bc --> abcd > (cd)^2

Since Square of any number is positive, hence (cd)^2 is > 0, Therefore abcd > 0. Statement 1 is sufficient.


Statement 2:

b/a > d/c --> Multiplying both sides by a --> b > ad/c --> Multiplying both sides by c --> bc > ad --> Multiplying both sides by ad --> abcd > (ad)^2

Since Square of any number is positive, hence (ad)^2 is > 0, Therefore abcd > 0. Statement 2 is sufficient.

Hence answer is D.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
S
14101992
Manager
Manager
Joined: 22 Jun 2016
Posts: 187
Own Kudos [?]: 566 [1]
Given Kudos: 10
Send PM
Reviews Badge
Re: If abcd is not equal to zero ,is abcd <0 ? [#permalink] New post   27 Jun 2016, 09:45
1
Kudos
Hey meetthedevil,
Consider a case a=1, b=2, c=1 and d=4.
As per statement 1, a/b>c/d ---> 1/2 > 1/4 ---> True
As per statement 2, b/a>d/c ---> 2/1 > 4/1 ---> Not True

Hence, we know there can be examples like the above one that will make the answer D wrong. In inequalities, do not multiply L.H.S denominator to R.H.S numerator or vice-versa without carefully looking at the conditions given in the questions. The negatives and positive values can play a huge role in inequality questions.

----------------------------------------

P.S. Don't forget to give kudos :)
User avatar
G
mikemcgarry
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4452
Own Kudos [?]: 28573 [0]
Given Kudos: 130
Re: If abcd is not equal to zero ,is abcd <0 ? [#permalink] New post   27 Jun 2016, 11:37
Expert Reply
meetthedevil wrote:
Hi Mike,

I tried solving the below DS question and solved as given below. Could you please explain where I am going wrong, as the correct answer to this question is C.

If abcd is not equal to zero ,is abcd <0 ?

1) a/b > c/d

2) b/a > d/c

Statement 1:

a/b > c/d --> Multiplying both sides by b --> a > cb/d --> Multiplying both sides by d --> ad > bc --> Multiplying both sides by bc --> abcd > (cd)^2

Since Square of any number is positive, hence (cd)^2 is > 0, Therefore abcd > 0. Statement 1 is sufficient.


Statement 2:

b/a > d/c --> Multiplying both sides by a --> b > ad/c --> Multiplying both sides by c --> bc > ad --> Multiplying both sides by ad --> abcd > (ad)^2

Since Square of any number is positive, hence (ad)^2 is > 0, Therefore abcd > 0. Statement 2 is sufficient.

Hence answer is D.

Dear meetthedevil,
I'm happy to respond. :-)

I would say this is a flawed question. :-) You see, the statements are not compatible with each other. If the inequality a/b > c/d is true, then it is impossible for the inequality b/a > d/c to be true. The question would not be flawed if the inequalities were "greater than or equal to," as opposed to simply "greater than."

The problem with your approach is as follows. Suppose we know ad > bc. Now, we want to multiply both sides of the inequality by bc. But, is bc positive or negative? If we multiply by a positive, then the direction of the inequality remains the same. If bc is negative, then we reverse the order of the inequality. Because we don't know whether bc is positive or negative, we don't know which way the inequality points after we multiply.

To 14101992, I would say: the point is not to pick numbers that make some statements true and some statements false. On GMAT DS, we have to assume that the statements themselves are true, and we have to pick numbers consistent with this. Unfortunately, in this flawed question, there is no way to pick one set of numbers that would satisfy both statements.

Does all this make sense?

Mike :-)
User avatar
S
14101992
Manager
Manager
Joined: 22 Jun 2016
Posts: 187
Own Kudos [?]: 566 [1]
Given Kudos: 10
Send PM
Reviews Badge
Re: If abcd is not equal to zero ,is abcd <0 ? [#permalink] New post   27 Jun 2016, 12:29
1
Kudos
mikemcgarry

Take a condition where a and b are positive and one of c and d is negative. So, we will have a/b>c/d and b/a>d/c.
For ex. a=1, b=1, c=-1 and d=1. So, 1/1>-1/1 (True) and 1/1>1/(-1) is also true.

This will give us that abcd<0 is possible only if statement 1 and 2 both are true.

Hope this makes sense! :p

---------------------------------

P.S. Don't forget to give Kudos :)
User avatar
G
mikemcgarry
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4452
Own Kudos [?]: 28573 [0]
Given Kudos: 130
Re: If abcd is not equal to zero ,is abcd <0 ? [#permalink] New post   27 Jun 2016, 13:23
Expert Reply
14101992 wrote:
mikemcgarry

Take a condition where a and b are positive and one of c and d is negative. So, we will have a/b>c/d and b/a>d/c.
For ex. a=1, b=1, c=-1 and d=1. So, 1/1>-1/1 (True) and 1/1>1/(-1) is also true.

This will give us that abcd<0 is possible only if statement 1 and 2 both are true.

Hope this makes sense! :p

---------------------------------

P.S. Don't forget to give Kudos :)

Dear 14101992,
Yes, that's a brilliant solution. I can't believe I overlooked that. Kudos.
Mike :-)
User avatar
L
Mo2men
RSM Erasmus Moderator
Joined: 26 Mar 2013
Posts: 2461
Own Kudos [?]: 1360 [0]
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
Send PM
Reviews Badge
Re: If abcd is not equal to zero ,is abcd <0 ? [#permalink] New post   27 Jun 2016, 20:17
meetthedevil wrote:
Hi Mike,

I tried solving the below DS question and solved as given below. Could you please explain where I am going wrong, as the correct answer to this question is C.

If abcd is not equal to zero ,is abcd <0 ?

1) a/b > c/d

2) b/a > d/c

Statement 1:

a/b > c/d --> Multiplying both sides by b --> a > cb/d --> Multiplying both sides by d --> ad > bc --> Multiplying both sides by bc --> abcd > (cd)^2

Since Square of any number is positive, hence (cd)^2 is > 0, Therefore abcd > 0. Statement 1 is sufficient.


Statement 2:

b/a > d/c --> Multiplying both sides by a --> b > ad/c --> Multiplying both sides by c --> bc > ad --> Multiplying both sides by ad --> abcd > (ad)^2

Since Square of any number is positive, hence (ad)^2 is > 0, Therefore abcd > 0. Statement 2 is sufficient.

Hence answer is D.


You can see alternative approaches in link below:

if-abcd-is-not-equal-to-zero-is-abcd-215779.html
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92922
Own Kudos [?]: 619089 [0]
Given Kudos: 81596
Send PM
CAT Tests Forum Quiz Mode
Re: If abcd is not equal to zero ,is abcd <0 ? [#permalink] New post   09 May 2018, 02:17
Expert Reply
meetthedevil wrote:
Hi Mike,

I tried solving the below DS question and solved as given below. Could you please explain where I am going wrong, as the correct answer to this question is C.

If abcd is not equal to zero ,is abcd <0 ?

1) a/b > c/d

2) b/a > d/c

Statement 1:

a/b > c/d --> Multiplying both sides by b --> a > cb/d --> Multiplying both sides by d --> ad > bc --> Multiplying both sides by bc --> abcd > (cd)^2

Since Square of any number is positive, hence (cd)^2 is > 0, Therefore abcd > 0. Statement 1 is sufficient.


Statement 2:

b/a > d/c --> Multiplying both sides by a --> b > ad/c --> Multiplying both sides by c --> bc > ad --> Multiplying both sides by ad --> abcd > (ad)^2

Since Square of any number is positive, hence (ad)^2 is > 0, Therefore abcd > 0. Statement 2 is sufficient.

Hence answer is D.


Discussed here: if-abcd-is-not-equal-to-zero-is-abcd-215779.html

TOPIC IS LOCKED AND ARCHIVED.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: If abcd is not equal to zero ,is abcd <0 ? [#permalink]
09 May 2018, 02:17
Moderators:
Bunuel
Math Expert
92918 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts
GMATBusters
GMAT Tutor
1905 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions