• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

The average of 25 values is equal to product. . .

This topic has 4 expert replies and 0 member replies

Top Member

The average of 25 values is equal to product. . .

Post
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

The OA is D.

According to the hypothesis, the average is 0. But, how can I calculate how many of the numbers are positives?

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Vincen 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
If one of the 25 values is zero, then the PRODUCT of the 25 values will be 0
So, the AVERAGE of the 25 values is also 0
If the average is 0, then the SUM of all 25 values must be 0

At most how many numbers can be greater than zero?
We already know that one value is 0.
Can the other 24 values be greater than 0?
No. The sum of 0 and 24 positive values will always be positive.
So, we can ELIMINATE answer choice E

Can 23 values be greater than 0?
Yes. How about: {-23, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }
Here, the average = 0, and we have 23 positive values in the set.
Answer: D

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
10197 messages
Followed by:
497 members
Upvotes:
2867
GMAT Score:
800
Post
Hi Vincen,

This is a great 'concept' question - meaning that if you understand the concepts involved, then you don't have to do much math to get to the correct answer.

We're told that there are 25 numbers and that the AVERAGE of the numbers = PRODUCT of the numbers. THAT type of relationship can clearly only happen under certain circumstances. We're also told that JUST ONE of the numbers is 0. We're asked for the maximum number of those 25 values could be GREATER than 0.

Since we have a 0 in the group, we know that the product will be 0 (since anything multiplied by 0 will equal 0). To get an AVERAGE of 0, the SUM of all 25 terms must 'cancel out' and leave us with a 0. There are no limit on what the values could be, so as long as we had one NEGATIVE value to 'offset' the sum of all of the positive values, then we could hit a total sum of 0. Thus, we could have....
1 negative
1 zero
23 positives

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Vincen 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

_________________

Jeffrey Miller
Head of GMAT Instruction
jeff@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Quote:
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
Hi Vincen,
Let's take a look at your question.

Out of 25 values, one is 0.
Hence,
Product of all 25 values = 0

Since average and product of these 25 values are equal.
Therefore,
Average of 25 values = 0
For average to be equal to zero, the sum of 25 values should be equal to zero.

Sum can be zero if,
One value = 0
23 values = positive
One value = negative, that should be equal to the sum of 23 positive values.

Hence, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

  • +1 Upvote Post
  • Quote
  • Flag
Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer

Top First Responders*

1 Ian Stewart 41 first replies
2 Brent@GMATPrepNow 36 first replies
3 Scott@TargetTestPrep 33 first replies
4 Jay@ManhattanReview 30 first replies
5 GMATGuruNY 23 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

159 posts
2 image description Max@Math Revolution

Math Revolution

91 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

56 posts
4 image description Ian Stewart

GMATiX Teacher

50 posts
5 image description GMATGuruNY

The Princeton Review Teacher

35 posts
See More Top Beat The GMAT Experts