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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Is the product of all of the elements in Set S negative? [#permalink]

Show Tags

17 Jan 2012, 17:57

2

This post received KUDOS

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

51% (01:27) correct
49% (00:21) wrong based on 227 sessions

HideShow timer Statistics

Is the product of all of the elements in Set S negative?

(1) All of the elements in Set S are negative. (2) There are 5 negative numbers in Set S.

--- I understand the official answer, but I am having trouble with an explanation by the MGMAT book given for Statement 2.

The book says that statement 2 is insufficient: "However, if any of the elements in Set S equals zero, then the product of the elements in Set S will be zero, which is NOT negative."

What? I thought that statement two is telling us that there are basically five negative elements in Set S, and if 0 is not positive or negative, then why are we even considering 0 as an element in Set S?

Is the product of all of the elements in Set S negative?

(1) All of the elements in Set S are negative. (2) There are 5 negative numbers in Set S.

--- I understand the official answer, but I am having trouble with an explanation by the MGMAT book given for Statement 2.

The book says that statement 2 is insufficient: "However, if any of the elements in Set S equals zero, then the product of the elements in Set S will be zero, which is NOT negative."

What? I thought that statement two is telling us that there are basically five negative elements in Set S, and if 0 is not positive or negative, then why are we even considering 0 as an element in Set S?

Is the product of all of the elements in Set S negative?

First of all, in order the product of all of the elements in Set S to be negative: A. there should be odd number of negative terms in set S AND B. zero shouldn't be in set S. Note that we are not concerned about positive terms at all. Also note that if even one of the condition fails, the product of all of the elements will not be negative: it'll be either zero (in case zero is in the set) or positive (if there is no zero in the set but number of negative terms is even: 0, 2, 4, ...)

(1) All of the elements in Set S are negative --> the second condition is met: there is no zero in the set. Though we don't know whether the first condition is met: if number of all these negative terms is even, then the product will be positive but if number of all these negative terms is odd, then the product will be negative. Not sufficient.

(2) There are 5 negative numbers in Set S --> the first condition is met: there is odd number of negative terms in the set. But again we don't know whether the second condition is met: if zero is in the set, then the product will be zero but if it is not, then the product will negative. Not sufficient.

(1)+(2) From (1) the second condition is met and from (2) the first condition is met, hence the product is odd (there are only 5 terms in the set and all are negative --> product=negative). Sufficient.

Re: Is the product of all of the elements in Set S negative? [#permalink]

Show Tags

17 Jan 2012, 18:45

I'm still stuck on Statement 2. It says that "There are 5 negative numbers in the set."

If we know for sure that there are 5 negative numbers in the set, although zero is an integer, it is neither positive or negative. Then why are considering zero to possibly be in the set of 5 numbers if it is not negative?
_________________

"Continuos effort - not strength or intelligence - is the key to unlocking our potential." - Winston Churchill

I'm still stuck on Statement 2. It says that "There are 5 negative numbers in the set."

If we know for sure that there are 5 negative numbers in the set, although zero is an integer, it is neither positive or negative. Then why are considering zero to possibly be in the set of 5 numbers if it is not negative?

"There are 5 negative numbers in the set" means that number of negative terms in the set is 5, but it doesn't necessarily mean that there is ONLY 5 terms in the set. There can be more than 5 terms in the set: 6, 7, 100, ... (out of which 5 are negative) and one of these other terms can be zero, for example: {-1, -2, -3, -4, -5, 0}.

Re: Is the product of all of the elements in Set S negative? [#permalink]

Show Tags

12 Jul 2014, 19:56

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.
_________________

From Stmt 1 : We can get to know if all numbers are negative then if there were an even set of negative numbers their product would be positive , else if there were an odd set of negative numbers their product would be negative. Statement 1 lacks this information on the number of negative numbers ( ' All of the elements in Set S are negative' is too broad ) . Hence insufficient.

From Stmt 2 : It only tells us there are 5 negative numbers in the set , but what about other numbers in the set , there could be a 0 also in the set . Then the product of all elements in the set would be 0 and not negative . Hence Stmt 2 is also insufficient .

When we combine Stmt 1 and Stmt 2 , we now are aware of both the number of elements ( 5 elements ) and all elements are negative . Hence we will be able to get a definitive answer. Answer is C

Some Test Takers will read this question and naturally "see" all of the possibilities. That can be a dangerous way of dealing with this Test though, since if you "miss" any of the possibilities or don't properly note a given detail, then you'll get the question wrong and not even know it. As such, proper note-taking is a MUST; you should get in the habit of finding a way to PROVE that you're correct. Here, we can TEST VALUES.

The prompt asks us if the PRODUCT of all the numbers in Set S is NEGATIVE. This is a YES/NO question. We are NOT told how many numbers are in the set, nor if they're positive, negative or 0.

Fact 1: All of the elements in Set S are NEGATIVE.

IF the set is... {-1, -2] Then the product is positive and the answer to the question is NO.

IF the set is.... {-1, -2, -3} Then the product is negative and the answer to the question is YES. Fact 1 is INSUFFICIENT

Fact 2: There are 5 negative numbers in Set S.

This does NOT tell us the total number of items in Set S (nor what those additional numbers might be)

IF the set is... {-1, -2, -3, -4, -5} Then the product is negative and the answer to the question is YES.

IF the set is... {-1, -2, -3, -4, -5, 0} Then the product is 0 and the answer to the question is NO. Fact 2 is INSUFFICIENT.

Combined, we know: ALL of the elements in Set S are NEGATIVE There are 5 NEGATIVE numbers. This mean that there are only 5 numbers AND that they're all negative, so the product MUST be negative and the answer to the question is ALWAYS YES. Combined, SUFFICIENT.

Re: Is the product of all of the elements in Set S negative? [#permalink]

Show Tags

13 Mar 2015, 23:39

rdevorse wrote:

Is the product of all of the elements in Set S negative?

(1) All of the elements in Set S are negative. (2) There are 5 negative numbers in Set S.

--- I understand the official answer, but I am having trouble with an explanation by the MGMAT book given for Statement 2.

The book says that statement 2 is insufficient: "However, if any of the elements in Set S equals zero, then the product of the elements in Set S will be zero, which is NOT negative."

What? I thought that statement two is telling us that there are basically five negative elements in Set S, and if 0 is not positive or negative, then why are we even considering 0 as an element in Set S?

The approach is 1. if all of the elements is set are negative, we don't know whether there are even or odd number of elements . Product might be or might not be -ve ,Not sufficient 2. If there are 5 elements in set S,Answer is sufficient but if there are 6 elements in set and 6th element is 0, product is 0. Hence Not sufficient.

I+II

Tells there are 5 elements in Set S ,All are negative OA=C

Re: Is the product of all of the elements in Set S negative? [#permalink]

Show Tags

19 Mar 2016, 19:47

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.
_________________

Re: Is the product of all of the elements in Set S negative? [#permalink]

Show Tags

20 Apr 2016, 15:29

I dont understand why after both statements, Its Data sufficient. The first statement gives us there are all negative elements in the set and second statement combined gives us that 5 of them are negative. So the S={-1,-2,-3,-4,-5,-x,-y,... } How does this make the both statements sufficient together?

Apologise but then i feel they are not sufficient together.

I dont understand why after both statements, Its Data sufficient. The first statement gives us there are all negative elements in the set and second statement combined gives us that 5 of them are negative. So the S={-1,-2,-3,-4,-5,-x,-y,... } How does this make the both statements sufficient together?

Apologise but then i feel they are not sufficient together.

When combined we have that there are 5 negative integers in the set. Therefore their product is negative. Please read the solutions provided above for better understanding.
_________________

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...