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

It is currently 20 Aug 2019, 20:13

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

If P is the product of n distinct integers, is P<0?

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
G
Joined: 01 Nov 2017
Posts: 67
Location: India
Premium Member
If P is the product of n distinct integers, is P<0?  [#permalink]

Show Tags

New post Updated on: 04 Aug 2019, 11:56
3
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

17% (01:39) correct 83% (01:39) wrong based on 41 sessions

HideShow timer Statistics

If P is the product of n distinct integers, is P<0?

1. n distinct integers are consecutive numbers and their median is 4.5
2. Out of n distinct integers 5 are negative

Originally posted by raghavrf on 04 Aug 2019, 04:01.
Last edited by Bunuel on 04 Aug 2019, 11:56, edited 1 time in total.
Edited the OA.
GMAT Tutor
avatar
G
Joined: 24 Jun 2008
Posts: 1816
Re: If P is the product of n distinct integers, is P<0?  [#permalink]

Show Tags

New post 04 Aug 2019, 06:41
3
raghavrf wrote:
If P is the product of n distinct integers, is P<0?
1. n distinct integers are consecutive numbers and their median is 4.5
2. Out of n distinct integers 5 are negative


If the OA is B, there's something wrong with the question. If Statement 1 is true, then either the set contains a small number of consecutive integers, and every value is positive, so their product is positive, or the set is larger and the lower values in the set extend to zero or past zero into negative values. But if it's a set of consecutive integers, then the set would then contain zero, so the product of the values in the set would be zero. The product could never be negative, so Statement 1 is sufficient to give a "no" answer to the question.

Statement 2 is not sufficient, because if we have five negative values, and the rest of the values are positive, the product is negative, but if we have five negative values and we have zero in the set, the product is zero. So we can't be sure if the product is negative.
_________________
GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Duke & Cornell Moderator
User avatar
S
Joined: 29 May 2018
Posts: 86
Location: India
GMAT 1: 700 Q48 V38
GMAT 2: 720 Q49 V39
GPA: 4
CAT Tests
Re: If P is the product of n distinct integers, is P<0?  [#permalink]

Show Tags

New post 04 Aug 2019, 07:01
2
Statement 1: the median is 4.5 hence middle terms are 4 and 5 and there is even number of terms in the set.

terms can be 1,2,3,4,5,6,7,8 - product>0
terms can be -5,-4,-3,-2,-1,0,1,2,3,4,5- product=0

see that product will never be <0 if median is 4.5 because 0 cross-over will always be there

Sufficient

Statement 2: there are 5 negative terms out of n consecutive terms

-5,-4,-3,-2,-1 - product is <0
-5,4,-3,-2,-1,0 - product=0

Not Sufficient

Answer A

Bunuel please correct the answer
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57155
Re: If P is the product of n distinct integers, is P<0?  [#permalink]

Show Tags

New post 04 Aug 2019, 12:05
vinayakvaish wrote:
Statement 1: the median is 4.5 hence middle terms are 4 and 5 and there is even number of terms in the set.

terms can be 1,2,3,4,5,6,7,8 - product>0
terms can be -5,-4,-3,-2,-1,0,1,2,3,4,5- product=0

see that product will never be <0 if median is 4.5 because 0 cross-over will always be there

Sufficient

Statement 2: there are 5 negative terms out of n consecutive terms

-5,-4,-3,-2,-1 - product is <0
-5,4,-3,-2,-1,0 - product=0

Not Sufficient

Answer A

Bunuel please correct the answer

_____________________
Edited the OA. Thank you.
_________________
Senior Manager
Senior Manager
User avatar
G
Joined: 09 Aug 2017
Posts: 403
Re: If P is the product of n distinct integers, is P<0?  [#permalink]

Show Tags

New post 04 Aug 2019, 19:30
We know that numbers are consecutive integers.

For statement 2,

If 5 values out of n are negative than, the remaining values will be equal to or more than 0. Therefore, if the value of n is 5 then P will be negative; otherwise, P will be 0 in all other cases.
For ex. -5, -4, -3, -2, -1 then P IS NEGATIVE.
-5, -4, -3, -2, -1, 0 then P is 0.
-5. -4, -3, -2, -1, 0, 1 Then P is O.

The main problem is that we are not told whether n is 5.

quote="IanStewart"]
raghavrf wrote:
If P is the product of n distinct integers, is P<0?
1. n distinct integers are consecutive numbers and their median is 4.5
2. Out of n distinct integers 5 are negative


If the OA is B, there's something wrong with the question. If Statement 1 is true, then either the set contains a small number of consecutive integers, and every value is positive, so their product is positive, or the set is larger and the lower values in the set extend to zero or past zero into negative values. But if it's a set of consecutive integers, then the set would then contain zero, so the product of the values in the set would be zero. The product could never be negative, so Statement 1 is sufficient to give a "no" answer to the question.

Statement 2 is not sufficient, because if we have five negative values, and the rest of the values are positive, the product is negative, but if we have five negative values and we have zero in the set, the product is zero. So we can't be sure if the product is negative.[/quote]
Senior Manager
Senior Manager
User avatar
G
Joined: 09 Aug 2017
Posts: 403
Re: If P is the product of n distinct integers, is P<0?  [#permalink]

Show Tags

New post 04 Aug 2019, 19:36
According to your explanation,
terms can be -5,-4,-3,-2,-1,0,1,2,3,4,5- product=0

But in your sequence, the median is not 4.5.
We can understand this as below.
Seq.1= 2, 3, 4, 5, 6 7 >>>>P= POSITIVE
Seq.2= 1, 2, 3, 4, 5, 6, 7, 8>>>>>p= zero
Seq.3 = -1,0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 =>>>>P=ZER0.

so P will never be negative.

vinayakvaish wrote:
Statement 1: the median is 4.5 hence middle terms are 4 and 5 and there is even number of terms in the set.

terms can be 1,2,3,4,5,6,7,8 - product>0
terms can be -5,-4,-3,-2,-1,0,1,2,3,4,5- product=0

see that product will never be <0 if median is 4.5 because 0 cross-over will always be there

Sufficient

Statement 2: there are 5 negative terms out of n consecutive terms

-5,-4,-3,-2,-1 - product is <0
-5,4,-3,-2,-1,0 - product=0

Not Sufficient

Answer A

Bunuel please correct the answer
GMAT Club Bot
Re: If P is the product of n distinct integers, is P<0?   [#permalink] 04 Aug 2019, 19:36
Display posts from previous: Sort by

If P is the product of n distinct integers, is P<0?

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





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