• Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • 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
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • 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

How many people in a group of 50 own neithe

This topic has 2 expert replies and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
Joined
24 Jul 2017
Posted:
83 messages

How many people in a group of 50 own neithe

Post Mon Jul 24, 2017 9:34 am
How many people in a group of 50 own neither a fax machine nor a laser printer?

(1) The total number of people in the group who own a fax machine or a laser printer or both is less than 50.
(2) The total number of people in the group who own both a fax machine and a laser printer is 15.

Official Guide question
Answer: E

  • +1 Upvote Post
  • Quote
  • Flag
Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

GMAT/MBA Expert

Post Wed Jul 26, 2017 3:27 pm
jjjinapinch wrote:
How many people in a group of 50 own neither a fax machine nor a laser printer?

(1) The total number of people in the group who own a fax machine or a laser printer or both is less than 50.
(2) The total number of people in the group who own both a fax machine and a laser printer is 15.
We see that we have an overlapping set problem with two categories:

1) Own a fax machine

2) Own a laser printer

We can also create a few variables.

F = total number of people who own a fax machine

L = total number of people who own a laser printer

B = number of people who own both a laser printer and a fax machine

N = number of people who own neither a laser printer nor a fax machine

We are given that the group consists of 50 people. Thus, we can create the following equation:

50 = F + L - B + N

Note that we subtract B in the equation because those who own both a laser printer and a fax machine were double-counted, once in F and again in L.

We must determine the value of N.

Statement One Alone:

The total number of people in the group who own a fax machine or a laser printer or both is less than 50.

Using the information in statement one, we can create the following inequality:

F + L - B < 50

We see that we can determine that N > 0; however, we cannot determine the value of N. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The total number of people in the group who own both a fax machine and a laser printer is 15.

Using the information in statement two, we know that B = 15. This is not enough information to determine the value of N. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two, and the given information, we know the following:

50 = F + L - B + N

F + L - B < 50

B = 15

We see that this is not enough information to determine the value of N.

Answer: E

_________________
Scott Woodbury-Stewart Founder and CEO

  • +1 Upvote Post
  • Quote
  • Flag
Post Mon Jul 24, 2017 10:26 pm
jjjinapinch wrote:
How many people in a group of 50 own neither a fax machine nor a laser printer?

(1) The total number of people in the group who own a fax machine or a laser printer or both is less than 50.
(2) The total number of people in the group who own both a fax machine and a laser printer is 15.

Official Guide question
Answer: E
Say # of people who own ONLY fax machine = f, # of people who own ONLY laser printer = p, # of people who own BOTH fax machine and printer = b, and # of people who own NONE = n

Thus, we have 50 = f + p + b + n

We have to get the value of n.

Statement 1: The total number of people in the group who own a fax machine or a laser printer or both is less than 50.

=> f + p + b < 50.

From this, we get that n > 0; however, we cannot get the unique value of n. Insufficient.

Statement 2: The total number of people in the group who own both a fax machine and a laser printer is 15.

=> b = 15.

However, we cannot get the value of n. Insufficient.

Statement 1 & 2:

Even after combining both the statements, we cannot get the value n. Insufficient.

The correct answer: D

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Bangkok | Abu Dhabi | Rome | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

  • +1 Upvote Post
  • Quote
  • Flag

Best Conversation Starters

1 Roland2rule 174 topics
2 lheiannie07 110 topics
3 ardz24 64 topics
4 LUANDATO 56 topics
5 swerve 46 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

150 posts
2 image description Jeff@TargetTestPrep

Target Test Prep

145 posts
3 image description Rich.C@EMPOWERgma...

EMPOWERgmat

116 posts
4 image description GMATGuruNY

The Princeton Review Teacher

103 posts
5 image description Scott@TargetTestPrep

Target Test Prep

98 posts
See More Top Beat The GMAT Experts