BrainLab 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

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