BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Even and Odd

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 21
Joined: Mon Apr 19, 2010 4:22 pm

Even and Odd

by pingu » Mon Apr 25, 2011 4:12 pm
Set Q contains n non-zero numbers. Does set Q contain an even number of negative numbers?
(1) n is even.
(2) The product of all the numbers in Q is 100,000

Edit: At the first look, I got confused by the word - non-zero numbers. Now I understand. Will post the OA, If needed. Thanks
Top
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 965
Joined: Thu Jan 28, 2010 12:52 am
Thanked: 156 times
Followed by:34 members
GMAT Score:720

by vineeshp » Mon Apr 25, 2011 4:35 pm
OA is B.

1) n is even . Not sufficient.
there can be 3 negative and 5 positive numbers.
There can be 4 negative and positive numbers.

2) Product is positive.
suggests that it contains an even number of negative numbers. ( 0 or 2 or 4 etc)
Vineesh,
Just telling you what I know and think. I am not the expert. :)
Top
Junior | Next Rank: 30 Posts
Posts: 21
Joined: Mon Apr 19, 2010 4:22 pm

by pingu » Mon Apr 25, 2011 4:36 pm
OA: B
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Apr 25, 2011 4:51 pm
pingu wrote:Set Q contains n non-zero numbers. Does set Q contain an even number of negative numbers?
(1) n is even.
(2) The product of all the numbers in Q is 100,000.

Edit: At the first look, I got confused by the word - non-zero numbers. Now I understand. Will post the OA, If needed. Thanks
Non-zero means not zero. In other words, positive or negative.

Statement 1: n is even.
Let Q = {-2, 50,000}.
Does set Q contain an even number of negative numbers? No.
Let Q = (-2, -50,000}.
Does set Q contain an even number of negative numbers? Yes.
Since in the first case the answer is No and in the second case the answer is Yes, insufficient.

Statement 2: The product of all the numbers in Q is 100,000.
If there are an odd number of negative numbers in Q, then the product will be negative.
Thus, the number of negative numbers in Q must be even.
Sufficient.

The correct answer is B.

I'm a bit skeptical of the trap in this question.
Nothing in the problem requires that set Q contain any negative values.
For statement 2 to be sufficient, we have to consider no negative values an even number of negative values.
Such logic typically isn't used in the real world (or on the GMAT). If my candy car contained no lollipops -- perish the thought! -- I wouldn't claim that the jar contained an even number of lollipops.
To avoid confusion, the question could be rephrased:

Does set Q contain an odd number of negative numbers?

The answer would remain the same.
Last edited by GMATGuruNY on Mon Apr 25, 2011 5:35 pm, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Junior | Next Rank: 30 Posts
Posts: 21
Joined: Mon Apr 19, 2010 4:22 pm

by pingu » Mon Apr 25, 2011 5:19 pm
Thanks a Ton. My understanding of non-zero number was wrong. I thought only numbers with out zeros are non-zero numbers. e.g. I did not consider 10, 100, 10,000

My Example Set answers the question:

Let Q = {1, 10,000}.

Does set Q contain an even number of negative numbers?

First the set Q contains NO negative numbers => Zero number of negative Numbers => Even number of negative numbers=> YES


Let Q = (-1, -10,000}.
Does set Q contain an even number of negative numbers? Yes.
Top
Senior | Next Rank: 100 Posts
Posts: 87
Joined: Sun Jul 24, 2011 10:36 am

by [email protected] » Thu Jul 28, 2011 3:59 pm
I THINK THE ANSWER IS E. THERE MAY OR MAY NOT BE NEGATIVE NUMBERS.
GMATGuruNY wrote:
pingu wrote:Set Q contains n non-zero numbers. Does set Q contain an even number of negative numbers?
(1) n is even.
(2) The product of all the numbers in Q is 100,000.

Edit: At the first look, I got confused by the word - non-zero numbers. Now I understand. Will post the OA, If needed. Thanks
Non-zero means not zero. In other words, positive or negative.

Statement 1: n is even.
Let Q = {-2, 50,000}.
Does set Q contain an even number of negative numbers? No.
Let Q = (-2, -50,000}.
Does set Q contain an even number of negative numbers? Yes.
Since in the first case the answer is No and in the second case the answer is Yes, insufficient.

Statement 2: The product of all the numbers in Q is 100,000.
If there are an odd number of negative numbers in Q, then the product will be negative.
Thus, the number of negative numbers in Q must be even.
Sufficient.

The correct answer is B.

I'm a bit skeptical of the trap in this question.
Nothing in the problem requires that set Q contain any negative values.
For statement 2 to be sufficient, we have to consider no negative values an even number of negative values.
Such logic typically isn't used in the real world (or on the GMAT). If my candy car contained no lollipops -- perish the thought! -- I wouldn't claim that the jar contained an even number of lollipops.
To avoid confusion, the question could be rephrased:

Does set Q contain an odd number of negative numbers?

The answer would remain the same.
Top
User avatar
Legendary Member
Posts: 934
Joined: Tue Nov 09, 2010 5:16 am
Location: AAMCHI MUMBAI LOCAL
Thanked: 63 times
Followed by:14 members

by [email protected] » Thu Jul 28, 2011 9:32 pm
According to me the answer should be E. As there can be no negative numbers and only positive numbers and still the product will be a positive number. The question says that set q contains all non-zero numbers and hence it can be positive or negative. please reply....
IT IS TIME TO BEAT THE GMAT

LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!

Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button.
Top
Senior | Next Rank: 100 Posts
Posts: 87
Joined: Sun Jul 24, 2011 10:36 am

by [email protected] » Sun Jul 31, 2011 12:16 pm
THE ANSWER SHOULD BE EEEEEEEEEEEEEEEEEEEEE.
FROM 1: IT CAN BE -1,-2,-3,-4 OR IT CAN BE 1,2,3,4. HENCE NOT SUFFICIENT.
FROM 2: THE NO. CAN BE BOTH NEGATIVE AND POSITIVE. ALTHOUGH FROM THIS STATEMENT WE KNOW THAT IF THERE ARE NEGATIVE NO.-- THEIR NUMBERS ARE EVEN. BUT WE DON'T KNOW THAT THE NUMBERS ARE POSITIVE OR NEGATIVE.
FROM STATEMENT 1 AND 2 NOTHING HELP.
HENCE ANSWER IS EEEEEEEEEE
Top
Legendary Member
Posts: 712
Joined: Fri Sep 25, 2015 4:39 am
Thanked: 14 times
Followed by:5 members

by Mo2men » Mon Nov 07, 2016 3:18 pm
GMATGuruNY wrote:
pingu wrote:Set Q contains n non-zero numbers. Does set Q contain an even number of negative numbers?
(1) n is even.
(2) The product of all the numbers in Q is 100,000.

Edit: At the first look, I got confused by the word - non-zero numbers. Now I understand. Will post the OA, If needed. Thanks
Non-zero means not zero. In other words, positive or negative.

Statement 1: n is even.
Let Q = {-2, 50,000}.
Does set Q contain an even number of negative numbers? No.
Let Q = (-2, -50,000}.
Does set Q contain an even number of negative numbers? Yes.
Since in the first case the answer is No and in the second case the answer is Yes, insufficient.

Statement 2: The product of all the numbers in Q is 100,000.
If there are an odd number of negative numbers in Q, then the product will be negative.
Thus, the number of negative numbers in Q must be even.
Sufficient.

The correct answer is B.

I'm a bit skeptical of the trap in this question.
Nothing in the problem requires that set Q contain any negative values.
For statement 2 to be sufficient, we have to consider no negative values an even number of negative values.
Such logic typically isn't used in the real world (or on the GMAT). If my candy car contained no lollipops -- perish the thought! -- I wouldn't claim that the jar contained an even number of lollipops.
To avoid confusion, the question could be rephrased:

Does set Q contain an odd number of negative numbers?

The answer would remain the same.
Hi Mitch,

I have another view for statement 2. Can we say that the set Q consists of positive numbers?? Hence, we have ZERO negative numbers and zero is even number and therefore it is sufficient.

Thanks
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Fri Nov 11, 2016 7:29 am
pingu wrote:Set Q contains n non-zero numbers. Does set Q contain an even number of negative numbers?
(1) n is even.
(2) The product of all the numbers in Q is 100,000
We are given that set Q contains n non-zero numbers - all numbers except for zero. We need to determine whether set Q contains an even number of negative numbers.

Statement One Alone:

n is even.

Knowing that n is even is not enough information to determine whether set Q contains an even number of negative numbers. For instance if n = 2, set Q could contain 2 negative numbers and 0 positive numbers or 1 negative number and 1 positive number. Statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The product of all the numbers in Q is 100,000.

In analyzing statement two, we may recall that when multiplying negative numbers, the ONLY WAY to produce a positive product is by multiplying together an even number of negative numbers. Since we know that the product of all the numbers in Q is 100,000, n must be even. Statement two alone is sufficient to answer the question.

Answer: B
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Fri Nov 11, 2016 7:50 am
Mo2men wrote:Hi Mitch,

I have another view for statement 2. Can we say that the set Q consists of positive numbers?? Hence, we have ZERO negative numbers and zero is even number and therefore it is sufficient.

Thanks
This line of reasoning is incorrect.
As {-2, -50,000} illustrates, Set Q can be composed of negative numbers and still satisfy the constraint in Statement 2 that the product of the numbers in Q = 100,000.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Legendary Member
Posts: 712
Joined: Fri Sep 25, 2015 4:39 am
Thanked: 14 times
Followed by:5 members

by Mo2men » Fri Nov 11, 2016 7:56 am
GMATGuruNY wrote:
Mo2men wrote:Hi Mitch,

I have another view for statement 2. Can we say that the set Q consists of positive numbers?? Hence, we have ZERO negative numbers and zero is even number and therefore it is sufficient.

Thanks
This line of reasoning is incorrect.
As {-2, -50,000} illustrates, Set Q can be composed of negative numbers and still satisfy the constraint in Statement 2 that the product of the numbers in Q = 100,000.
In all cases there is Even number:

if set Q has {-2, -50,000} so we have 2 negative numbers. Even number.

If set Q has {2, 50,000}, we have zero negative number. zero is even.

In all cases, we have EVEN number.

is the line of reasoning valid?
Top
Post new topic Post Reply
• Page 1 of 1