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

It is currently 19 Apr 2019, 10:08

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

The average of 25 values is equal to product of these values. If only

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54371
The average of 25 values is equal to product of these values. If only  [#permalink]

Show Tags

New post 26 Jan 2015, 05:45
3
10
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

51% (01:18) correct 49% (01:07) wrong based on 299 sessions

HideShow timer Statistics

Most Helpful Expert Reply
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13953
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The average of 25 values is equal to product of these values. If only  [#permalink]

Show Tags

New post 26 Jan 2015, 12:32
5
3
HI DesiGmat,

This is a great "concept" question - it really tests a person's thoroughness when dealing with "restrictions" (or lack of restrictions).

We're asked for the MAXIMUM number of terms that COULD be greater than 0, given the following restrictions:

1) There are 25 terms in total
2) One of the terms is 0
3) The average of the terms = the product of the terms

Since one of the terms is 0, the product = 0. Since we're told that the average = the product, the average ALSO = 0

Now we have to think about how we can make the average = 0 AND maximize the number of terms that are greater than 0. Notice how the question did NOT say anything about "consecutive" or "duplicates" - so we have a lot of ways to "play around" with this idea.

What if we had....
A 0, Twenty-three 1s and a -23
The product = 0 (because we have a 0 in the group)
The average = 0 + 23(1) +1(-23) = 0/25 = 0

In this situation, we have 23 numbers that are greater than 0. From a concept-standpoint, it can't be 24 though, since we need at least one negative term to offset the positives and bring the average back down to 0.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
General Discussion
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7559
Re: The average of 25 values is equal to product of these values. If only  [#permalink]

Show Tags

New post Updated on: 26 Jan 2015, 09:38
3
1
ans is D...... 23 is the answer
0 being one number means product is 0 therefore mean should be 0..
so the sum of +ive numbers should be equal to sum of -ive numbers to have total value as 0..
it is possible with different 23 +ive numbers and one -ive number, which is equal to total sum of 23 +ive numbers taken with a -ive sign...
_________________

Originally posted by chetan2u on 26 Jan 2015, 07:41.
Last edited by chetan2u on 26 Jan 2015, 09:38, edited 1 time in total.
Manager
Manager
avatar
Joined: 27 Oct 2013
Posts: 205
Location: India
Concentration: General Management, Technology
GMAT Date: 03-02-2015
GPA: 3.88
Re: The average of 25 values is equal to product of these values. If only  [#permalink]

Show Tags

New post 26 Jan 2015, 08:56
Here we go---

Given that avg of 25 values is equal to product of these values.
One of the number is 0.
So avg = 0

Now Surplus above the mean = Deficit below the mean

There can be at most 12 numbers greater than 0 to make the avg 0.

Option B is correct
Manager
Manager
avatar
Joined: 27 Oct 2013
Posts: 205
Location: India
Concentration: General Management, Technology
GMAT Date: 03-02-2015
GPA: 3.88
Re: The average of 25 values is equal to product of these values. If only  [#permalink]

Show Tags

New post 26 Jan 2015, 22:42
Ohh...
I completely missed this point....

We can have 23 1s creating the surplus above the mean = 23
and we can have -23 creating deficit below the mean = -23-----> maintaining the avg = 0

Answer is indeed D

Thank you so much.
Kudos to you.
Manager
Manager
User avatar
Joined: 03 Oct 2014
Posts: 127
Location: India
Concentration: Operations, Technology
GMAT 1: 720 Q48 V40
WE: Engineering (Aerospace and Defense)
Reviews Badge
Re: The average of 25 values is equal to product of these values. If only  [#permalink]

Show Tags

New post 26 Jan 2015, 23:20
Answer - D......

One number is 0 .....So product of all numbers will be 0.....Avg will be 0.....

Now we can have 23 numbers whose sum is equal to one large negative number to make the resultant 0....

Good question
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54371
Re: The average of 25 values is equal to product of these values. If only  [#permalink]

Show Tags

New post 02 Feb 2015, 02:23
1
1
Bunuel wrote:
The average of 25 values is equal to product of these values. If only one of the numbers is 0, at most how many numbers can be greater than zero?

A. 0
B. 12
C. 13
D. 23
E. 24

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

Since the product of these values is 0, then the average must be 0. In order to then maximize the number of positive values, there are 24 values left. If all 24 were positive, then the average could not be 0, as the sum of the values needs to be 0. But if there were one negative value that was equal to -1 times the sum of the other 23 nonzero values, then the sum of values would be 0 and a total of 23 values could be positive. Therefore, the answer is D.
_________________
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1813
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: The average of 25 values is equal to product of these values. If only  [#permalink]

Show Tags

New post 03 Feb 2015, 20:56
2
Answer = D = 23

Let the remaining values be from a1 to........... a24

Given that \(\frac{0 + (a1 + a2 + a3 + ............. + a24)}{25} = 0\)

a1 + a2 + a3 .................. + a24 = 0

a1 + a2 + a3 + ............. + a23 = -a24

So all values from a1 to a23 can be positive, whose sum would give a negative a24
_________________
Kindly press "+1 Kudos" to appreciate :)
Senior Manager
Senior Manager
User avatar
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 413
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: The average of 25 values is equal to product of these values. If only  [#permalink]

Show Tags

New post 06 Feb 2015, 12:09
Well, since one is 0 we know that the product is zero.

For the mean to be zero, we need their sum to be zero.

Out of the 25 numbers, we know the value of one: 0.
We still have 24 numbers to think about.

Now, we know for example that 10-10=0. So, we need the same number with opposite signs to get a sum of 0.

How is this possible in our case? It is possible if for the remaining 24 numbers, 23 equal to one ammount and the 24th to the same ammount with the opposite sign. L

et's say that 23 numbers have the value of 1. Then their sum would be 23, and we need a -23 to get a zero.
So, we could have the most 23 positive numbers and 1 negative number to end up with 0.
Manager
Manager
User avatar
B
Joined: 17 Nov 2014
Posts: 51
Location: India
Re: The average of 25 values is equal to product of these values. If only  [#permalink]

Show Tags

New post 27 Feb 2016, 23:36
Given The average of 25 values is equal to product of these values.
Since, one of the value is 0, Mean must be equal to 0
Total number of numbers (a1 to a25) = 25, one value is 0
Mean = a1 + a2 + a3 .................. + a24 = 0
The maximum positive values that can exist satisfying the above relation is = 23
So answer is D =23

Kindly press "+1 Kudos" to appreciate
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 5790
Location: United States (CA)
Re: The average of 25 values is equal to product of these values. If only  [#permalink]

Show Tags

New post 26 Jul 2017, 16:18
1
Bunuel wrote:
The average of 25 values is equal to product of these values. If only one of the numbers is 0, at most how many numbers can be greater than zero?

A. 0
B. 12
C. 13
D. 23
E. 24


Since the average is equal to the product and one value is zero, the product is zero. Thus, in order to have an average of zero, we need the sum to be zero also. We can have 23 numbers that are positive, one that is zero, and one that is negative with its absolute value as the sum of the 23 positive numbers.

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

GMAT Club Bot
Re: The average of 25 values is equal to product of these values. If only   [#permalink] 26 Jul 2017, 16:18
Display posts from previous: Sort by

The average of 25 values is equal to product of these values. If only

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.