A certain list consists of several different integers : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 00:30

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A certain list consists of several different integers

Author Message
TAGS:

### Hide Tags

Manager
Joined: 27 Feb 2010
Posts: 105
Location: Denver
Followers: 3

Kudos [?]: 341 [5] , given: 14

A certain list consists of several different integers [#permalink]

### Show Tags

28 Apr 2010, 06:28
5
KUDOS
13
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

52% (01:47) correct 48% (00:43) wrong based on 375 sessions

### HideShow timer Statistics

A certain list consist of several different integers. Is the product of all integers in the list positive?

(1) The product of the greatest and smallest of the integers in the list is positive.
(2) There is an even number of integers in the list.
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Aug 2012, 04:32, edited 1 time in total.
Intern
Joined: 23 May 2010
Posts: 5
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: Stuck with an easy number property....:( [#permalink]

### Show Tags

24 May 2010, 10:00
Ithink both statement together is not sufficient, so what is the real answer here? why do care about the existence of 0 ?
Math Expert
Joined: 02 Sep 2009
Posts: 36540
Followers: 7074

Kudos [?]: 93060 [2] , given: 10541

Re: Stuck with an easy number property....:( [#permalink]

### Show Tags

24 May 2010, 10:43
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
diemxua175 wrote:
Ithink both statement together is not sufficient, so what is the real answer here? why do care about the existence of 0 ?

A certain list consist of several different integers. Is the product of all integers in the list positive?

(1) The product of the greatest and smallest of the integers in the list is positive.
Two cases:
A. all integers in the list are positive: in this case product of all integers would be positive;
OR
B. all integers in the list are negative: now, if there is even number of integers, then product of all integers would be positive BUT if there is odd number of integers, then product of all integers would be negative.

Not sufficient.

(2) There is an even number of integers in the list.

(1)+(2) Now if we have scenario A (from 1) then answer is YES. If we have scenario B, then as there are even number of integers (from 2) the product of all integers still would be positive, so answer is still YES. Sufficient.

Hope it's clear.
_________________
Intern
Joined: 20 Oct 2010
Posts: 7
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: Stuck with an easy number property....:( [#permalink]

### Show Tags

23 Feb 2011, 17:06
Dear Bunuel:

I am sorry still i am not clear.

Can you explain how are you sure From ST 1 that all are either - or +? We just know smallest and largest number's multiplication is positive. if we combine ST 1 & 2, it may be

(i.e, lets say 6 even numbers)

- - - - + - = -
+ + - - + + = +
Math Expert
Joined: 02 Sep 2009
Posts: 36540
Followers: 7074

Kudos [?]: 93060 [7] , given: 10541

Re: Stuck with an easy number property....:( [#permalink]

### Show Tags

23 Feb 2011, 17:26
7
KUDOS
Expert's post
1
This post was
BOOKMARKED
moniralinda wrote:
Dear Bunuel:

I am sorry still i am not clear.

Can you explain how are you sure From ST 1 that all are either - or +? We just know smallest and largest number's multiplication is positive. if we combine ST 1 & 2, it may be

(i.e, lets say 6 even numbers)

- - - - + - = -
+ + - - + + = +

(1) says: The product of the greatest and smallest of the integers in the list is positive.

Product of two multiple to be positive they must have the same sign:

So either: smallest * greatest = negative * negative and in this case as both the smallest and the greatest are negative then ALL integers in the list are negative OR smallest * greatest = positive * positive and in this case as both the smallest and the greatest are positive then ALL integers in the list are positive.

Hope it's clear.
_________________
Intern
Joined: 20 Oct 2010
Posts: 7
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: Stuck with an easy number property....:( [#permalink]

### Show Tags

23 Feb 2011, 19:01
Ohh.... Genius...Thanks a lot! Now I understood how come all have the same sign...Thank u sooo much.
Senior Manager
Joined: 21 Mar 2010
Posts: 314
Followers: 5

Kudos [?]: 30 [0], given: 33

Re: Stuck with an easy number property....:( [#permalink]

### Show Tags

24 Feb 2011, 22:50
great question! Kudos are due

Completely missed it!
Intern
Joined: 01 Nov 2011
Posts: 7
Followers: 0

Kudos [?]: 9 [2] , given: 14

Re: Product of integers - Gmatprep [#permalink]

### Show Tags

04 Jan 2012, 01:09
2
KUDOS
Hi Janealams,

1. The above DS question is a Yes/No type Question.
2. Question Stem: Products of all integers in a list positive?
=> [a, b, c, r,t,d] or [1, 2, -9, -3] - a few random numbers in a set
3. Statement I: The product of Greatest and smallest integer in the List is +ve
=> Case 1: all integers in the list are +ve: [1, 2, 3, 4] => 4*1 = 4 = +ve -- YES
=> Case 2: all integers in the list are -ve: [-1, -2, -3,-4] - => (-4)*(-1) = 4 = +ve -- YES
=> Case 3: few integers in the list are -ve: [-1, 2, 3,4] - => (4)*(-1) = 4 = -ve -- NO
Hence Statement I is Not Sufficient.
4. Statement 2: There is an even number of Integers in the list
=> We know from number properties that -ve no multiplied even number of times is +ve
and +ve no multiplied even number of times is +ve
Ex: -2 * -2 * -3*-7 = +ve and 2 * 7 * 9 *10 = +ve
This statement provides only information about the Integers in the Set and this cant be helpful in determining the
Question stem. So NO - In Sufficient.
5. Now Taking I and II together.
=> We know that from I - All numbers in set are either +ve or -ve and from II that there are even number of Integers.
Hence we can use the above information to get the value if the product of all Integers is +ve or not.

Do let me know, if you need further explanation.

Thanks,
Arvind.
_________________

"Simplicity is the Ultimate Sophistication"

Current Student
Joined: 30 Oct 2011
Posts: 203
Followers: 0

Kudos [?]: 29 [0], given: 88

A certain list consists of several different integers [#permalink]

### Show Tags

04 Jan 2012, 01:55
- Edited -
- Edited -
- Edited -
- Edited -

Last edited by BrainFog on 11 Mar 2015, 01:56, edited 1 time in total.
Manager
Joined: 29 Jul 2011
Posts: 107
Location: United States
Followers: 5

Kudos [?]: 58 [0], given: 6

Re: Product of integers - Gmatprep [#permalink]

### Show Tags

04 Jan 2012, 13:07
Stem rephrase: There are even number of negative numbers or all are positive.

1. Not sufficient information on the middle numbers, insufficient
2. Even numbers does not mean even negatives or all positives, insufficient

Together, no overlapping information, so insufficient. E
_________________

I am the master of my fate. I am the captain of my soul.
Please consider giving +1 Kudos if deserved!

DS - If negative answer only, still sufficient. No need to find exact solution.
PS - Always look at the answers first
CR - Read the question stem first, hunt for conclusion
SC - Meaning first, Grammar second
RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

Current Student
Joined: 30 Oct 2011
Posts: 203
Followers: 0

Kudos [?]: 29 [0], given: 88

A certain list consists of several different integers [#permalink]

### Show Tags

04 Jan 2012, 16:13
- Edited -
- Edited -
- Edited -
- Edited -

Last edited by BrainFog on 11 Mar 2015, 01:57, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 36540
Followers: 7074

Kudos [?]: 93060 [0], given: 10541

Re: Product of integers - Gmatprep [#permalink]

### Show Tags

13 Jan 2012, 05:46
Janealams wrote:
I don't have much time left in the exam I would really appreciate explanation to following question!

_________________
Intern
Joined: 26 Jul 2010
Posts: 24
Followers: 0

Kudos [?]: 132 [0], given: 8

Re: A certain list consists of several different integers [#permalink]

### Show Tags

04 May 2012, 18:37
Quote:
(1)+(2) Now if we have scenario A (from 1) then answer is YES. If we have scenario B, then as there are even number of integers (from 2) the product of all integers still would be positive, so answer is still YES. Sufficient.

Hi, I have one question here. Statement 2 says, there are even number of integers in the list. How can we assume all are negative or positive? What if, (-,-,-,+). This will result in negative.

Math Expert
Joined: 02 Sep 2009
Posts: 36540
Followers: 7074

Kudos [?]: 93060 [1] , given: 10541

Re: A certain list consists of several different integers [#permalink]

### Show Tags

04 May 2012, 20:48
1
KUDOS
Expert's post
pgmat wrote:
Quote:
(1)+(2) Now if we have scenario A (from 1) then answer is YES. If we have scenario B, then as there are even number of integers (from 2) the product of all integers still would be positive, so answer is still YES. Sufficient.

Hi, I have one question here. Statement 2 says, there are even number of integers in the list. How can we assume all are negative or positive? What if, (-,-,-,+). This will result in negative.

Answer to the question is C, not E.

(1)+(2): From statement (1) we have that either all integers are negative or all integers are positive (check this: a-certain-list-consists-of-several-different-integers-126040.html#p878206). Statement (2) says that there are even number of elements in the set. So in either of cases the product will be positive.

Hope it's clear.
_________________
Senior Manager
Status: swimming against the current
Joined: 24 Jul 2009
Posts: 252
Location: Chennai, India
Followers: 4

Kudos [?]: 91 [1] , given: 30

Re: A certain list consists of several different integers [#permalink]

### Show Tags

05 May 2012, 09:04
1
KUDOS
Statement 2 is insufficient, because it says there are even number of items.

But from the first statement the numbers are either on the negative side of the number line or positive side of the number line.
only then multiplying the larger and smaller will lead to a positive number.

Ignoring the positive side, because odd number of items or even number of items will lead to a positive outcome.

But for the negative side of the number line to become postive there should be an even number of multiples.
_________________

Gonna make it this time

Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 547
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 61 [0], given: 562

Re: Product of integers - Gmatprep [#permalink]

### Show Tags

26 Jan 2013, 06:49
Janealams wrote:
arvindravulavaru wrote:
Hi Janealams,

1. The above DS question is a Yes/No type Question.
2. Question Stem: Products of all integers in a list positive?
=> [a, b, c, r,t,d] or [1, 2, -9, -3] - a few random numbers in a set
3. Statement I: The product of Greatest and smallest integer in the List is +ve
=> Case 1: all integers in the list are +ve: [1, 2, 3, 4] => 4*1 = 4 = +ve -- YES
=> Case 2: all integers in the list are -ve: [-1, -2, -3,-4] - => (-4)*(-1) = 4 = +ve -- YES
=> Case 3: few integers in the list are -ve: [-1, 2, 3,4] - => (4)*(-1) = 4 = -ve -- NO
Hence Statement I is Not Sufficient.
4. Statement 2: There is an even number of Integers in the list
=> We know from number properties that -ve no multiplied even number of times is +ve
and +ve no multiplied even number of times is +ve
Ex: -2 * -2 * -3*-7 = +ve and 2 * 7 * 9 *10 = +ve
This statement provides only information about the Integers in the Set and this cant be helpful in determining the
Question stem. So NO - In Sufficient.
5. Now Taking I and II together.
=> We know that from I - All numbers in set are either +ve or -ve and from II that there are even number of Integers.
Hence we can use the above information to get the value if the product of all Integers is +ve or not.

Do let me know, if you need further explanation.

Thanks,
Arvind.

Thanks Arvind for your explanation. One point I was missing that if the smallest and the greatest integers have same signs mean the numbers in between have the same sign too. Thanks again much appreciated!

i missed the same.. tricky stuffs u c
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : http://gmatclub.com/forum/end-of-my-gmat-journey-149328.html#p1197992

Director
Joined: 29 Nov 2012
Posts: 898
Followers: 14

Kudos [?]: 1044 [0], given: 543

Re: Product of integers - Gmatprep [#permalink]

### Show Tags

01 Jul 2013, 23:02
arvindravulavaru wrote:
Hi Janealams,

1. The above DS question is a Yes/No type Question.
2. Question Stem: Products of all integers in a list positive?
=> [a, b, c, r,t,d] or [1, 2, -9, -3] - a few random numbers in a set
3. Statement I: The product of Greatest and smallest integer in the List is +ve
=> Case 1: all integers in the list are +ve: [1, 2, 3, 4] => 4*1 = 4 = +ve -- YES
=> Case 2: all integers in the list are -ve: [-1, -2, -3,-4] - => (-4)*(-1) = 4 = +ve -- YES
=> Case 3: few integers in the list are -ve: [-1, 2, 3,4] - => (4)*(-1) = 4 = -ve -- NO
Hence Statement I is Not Sufficient.

Thanks,
Arvind.

Isn't this case incorrect as the stem says the product of the largest and smallest integer is positive? Is there an example where the list of largest and smallest is positive and the product of the integers can be negative?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 36540
Followers: 7074

Kudos [?]: 93060 [0], given: 10541

Re: Product of integers - Gmatprep [#permalink]

### Show Tags

01 Jul 2013, 23:11
fozzzy wrote:
arvindravulavaru wrote:
Hi Janealams,

1. The above DS question is a Yes/No type Question.
2. Question Stem: Products of all integers in a list positive?
=> [a, b, c, r,t,d] or [1, 2, -9, -3] - a few random numbers in a set
3. Statement I: The product of Greatest and smallest integer in the List is +ve
=> Case 1: all integers in the list are +ve: [1, 2, 3, 4] => 4*1 = 4 = +ve -- YES
=> Case 2: all integers in the list are -ve: [-1, -2, -3,-4] - => (-4)*(-1) = 4 = +ve -- YES
=> Case 3: few integers in the list are -ve: [-1, 2, 3,4] - => (4)*(-1) = 4 = -ve -- NO
Hence Statement I is Not Sufficient.

Thanks,
Arvind.

Isn't this case incorrect as the stem says the product of the largest and smallest integer is positive? Is there an example where the list of largest and smallest is positive and the product of the integers can be negative?

Yes, this solution is not clear.

Proper solution is here: a-certain-list-consists-of-several-different-integers-126040.html#p729037
_________________
Director
Joined: 29 Nov 2012
Posts: 898
Followers: 14

Kudos [?]: 1044 [0], given: 543

Re: A certain list consists of several different integers [#permalink]

### Show Tags

01 Jul 2013, 23:23
Thanks!

A certain list consist of several different integers. Is the product of all integers in the list positive?

(1) The product of the greatest and smallest of the integers in the list is positive.

all positive 1,2,3,4 largest is 4, smallest is 1 product positive. When we multiply all the numbers the result is positive YES

all negative -1,-2,-3,-4 largest is -1 smallest is -4 product is positive When we multiply all the numbers YES

third scenario -1,-2,-3 Largest -1, smallest -3 product is positive but in this case when we multiply all the numbers we get negative result so its NO

(2) There is an even number of integers in the list.

no constraint here it could be 1,2,3,4 in this case YES

-1,2,3,4 product is negative so answer is NO

Combined 1+2 we have the case highlighted in Blue so its sufficient! Answer C
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 36540
Followers: 7074

Kudos [?]: 93060 [0], given: 10541

Re: A certain list consists of several different integers [#permalink]

### Show Tags

01 Jul 2013, 23:25
fozzzy wrote:
Thanks!

A certain list consist of several different integers. Is the product of all integers in the list positive?

(1) The product of the greatest and smallest of the integers in the list is positive.

all positive 1,2,3,4 largest is 4, smallest is 1 product positive. When we multiply all the numbers the result is positive YES

all negative -1,-2,-3,-4 largest is -1 smallest is -4 product is positive When we multiply all the numbers YES

third scenario -1,-2,-3 Largest -1, smallest -3 product is positive but in this case when we multiply all the numbers we get negative result so its NO

(2) There is an even number of integers in the list.

no constraint here it could be 1,2,3,4 in this case YES

-1,2,3,4 product is negative so answer is NO

Combined 1+2 we have the case highlighted in Blue so its sufficient! Answer C

Yes, that's correct.
_________________
Re: A certain list consists of several different integers   [#permalink] 01 Jul 2013, 23:25

Go to page    1   2    Next  [ 25 posts ]

Similar topics Replies Last post
Similar
Topics:
5 A certain list consists of 400 different numbers. Is the average...... 2 22 May 2016, 22:36
A certain list consists of several different integers. Is 7 26 Jun 2011, 04:27
A certain list consists of serveral different integers. is 3 13 May 2011, 09:07
3 A certain list consist of several different integers. Is the 10 08 Apr 2010, 23:15
19 A certain list consists of five different integers. Is the 12 20 Jul 2007, 02:19
Display posts from previous: Sort by