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## 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
Joined
24 Jul 2017
Posted:
83 messages

#### How many people in a group of 50 own neithe

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

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
891 messages
Followed by:
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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.

_________________
Scott Woodbury-Stewart Founder and CEO

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
Joined
22 Aug 2016
Posted:
1026 messages
Followed by:
22 members
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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
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

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