How many people in a group of 50 own neithe

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!

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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

Hi All,

We're told that there are 50 people in a group . We're asked for the number of people who own NEITHER a fax machine NOR a laser printer. This question can be solved in a number of different ways depending on how you choose to organize the given information. To start, the phrasing of the prompt hints that this is an Overlapping Sets question, so there will be 4 different sub-groups that we'll need to consider:
A) Those with a fax machine but NOT a laser pointer
B) Those with a laser pointer but NOT a fax machine
C) Those with BOTH a fax machine AND a laser pointer
D) Those with NO fax machine AND NO a laser pointer

We're asked to figure out the number of people in the 4th sub-group.

1) The total number of people in the group who own a fax machine OR a laser printer OR BOTH is less than 50.

Fact 1 tells us that the total number of people in the first 3 sub-groups is LESS than 50, so the 4th group must be at least 1 (but could be as high as 50). Unfortunately, we don't know the exact numbers, so we cannot answer the question.
Fact 1 is INSUFFICIENT

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

Fact 2 tells us the exact number of people in the 3rd sub-group, so we know that the remaining 50 - 15 = 35 people are in the other 3 sub-groups. Unfortunately, we don't know the exact numbers, so we cannot answer the question.
Fact 2 is INSUFFICIENT

Combined, we still only know the value of the 3rd sub-group, so the 4th sub-group can have between 1 and 35 people (but we still don't know exactly how many).
Combined, INSUFFICIENT

Final Answer: E

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