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
How many people in a group of 50 own neithe
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 83
- Joined: Mon Jul 24, 2017 8:16 am
- Followed by:1 members
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
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 = njjjinapinch 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
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.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7243
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
We see that we have an overlapping set problem with two categories: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.
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
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
let
no. of people who own fax machine be f.
no. of people who own printer be p.
no. of people who own both be b.
no. of people who own none be n.
so f+p+b+n = 50.
1) f+p+b < 50.
this gives us n>0, but not the exact value of n.
So statement 1) alone is not sufficient.
2) b=15.
no info about n can be extracted from this.
So statement 2) alone is also not sufficient.
Combine 1) and 2)
f+p+b < 50
b=15
this gives f+p < 35.
we can't find n using this.
So both statements combined are also not sufficient.
Hence option E is correct.
no. of people who own fax machine be f.
no. of people who own printer be p.
no. of people who own both be b.
no. of people who own none be n.
so f+p+b+n = 50.
1) f+p+b < 50.
this gives us n>0, but not the exact value of n.
So statement 1) alone is not sufficient.
2) b=15.
no info about n can be extracted from this.
So statement 2) alone is also not sufficient.
Combine 1) and 2)
f+p+b < 50
b=15
this gives f+p < 35.
we can't find n using this.
So both statements combined are also not sufficient.
Hence option E is correct.