overlapping set: of 80 students in the eighth grade

Expert replies

buoyant: Master | Next Rank: 500 Posts; Posts: 106; Joined: Sat Mar 02, 2013 4:29 pm; Thanked: 4 times

by buoyant » Mon Jan 13, 2014 10:08 am

Of 80 students in the eighth grade, 35 played basketball and 19 made the Dean's List. How many of the students neither made the Dean's List, nor played basketball?

10 students played basketball and made the Dean's List
44 students played basketball or made the Dean's List or both

[spoiler]OA: D[/spoiler]

want to know various ways to deal with statement 2.

Like this post

Source: Beat The GMAT — Data Sufficiency | Mon Jan 13, 2014 10:08 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jan 13, 2014 12:54 pm

buoyant wrote:Of 80 students in the eighth grade, 35 played basketball and 19 made the Dean's List. How many of the students neither made the Dean's List, nor played basketball?

10 students played basketball and made the Dean's List
44 students played basketball or made the Dean's List or both

[spoiler]OA: D[/spoiler]

want to know various ways to deal with statement 2.

We can use the following equation:

Total = Basketball + Dean's list - Both + Neither.

The big idea with overlapping groups is to SUBTRACT THE OVERLAP.
When we count everyone in Group 1 (basketball) and everyone in Group 2 (Dean's list), those in BOTH groups (students who can BOTH played basketball AND made the Dean's list) get counted twice.
So that we don't double-count the students who belong to both groups, we SUBTRACT THE OVERLAP from the total.

Statement 1: 10 students played basketball and made the Dean's List
In other words, both = 10.
Since total = 80, basketball = 35, Dean's list = 19, and both = 10, we get:
80 = 35 + 19 - 10 + N
N = 36.
SUFFICIENT.

Statement 2: 44 students played basketball or made the Dean's List or both
Of the 80 students, 44 played basketball, made the Dean's list, or both played basketball and made the Dean's list.
Implication:
The remaining students neither played basketball nor made the Dean's list:
N = 80-44 = 36.
SUFFICIENT.

The correct answer is D.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Jan 14, 2014 6:54 am

buoyant wrote:Of 80 students in the eighth grade, 35 played basketball and 19 made the Dean's List. How many of the students neither made the Dean's List, nor played basketball?

(1) 10 students played basketball and made the Dean's List
(2) 44 students played basketball or made the Dean's List or both

We can use the Double Matrix Method to solve this question. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of 80 students, and the two characteristics are:
- play basketball and don't play basketball
- on Dean's list and not on Dean's list.

So, we can set up our diagram as follows:

To learn more about this technique, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Now let's continue....

Target question: How many of the students neither made the Dean's List, nor played basketball?

So, let's place a star in the box that need to find the value for.

Given: 35 played basketball and 19 made the Dean's List.
We can add this information to our diagram as follows:

As you can see, we don't yet have sufficient information to determine the value that goes in the starred box.

Statement 1: 10 students played basketball AND made the Dean's List
We can add that information to the diagram as follows:

At this point, we have enough information to determine the value that goes in every box:

So, as we can see, 36 students neither made the Dean's List, nor played basketball
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 44 students played basketball or made the Dean's List or both
This statement is referring to more than 1 box.
In fact, it's saying that each of the 44 students can be found in one of the 3 highlighted boxes below:

This means that the remaining 36 students must be in the non-highlighted box:

So, as we can see, 36 students neither made the Dean's List, nor played basketball
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

-------------------------------------------------------

Here are some additional practice questions that can be solved using the Double Matrix Method:
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
- https://www.beatthegmat.com/ds-quest-t187706.html
- https://www.beatthegmat.com/overlapping- ... 83320.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html
- https://www.beatthegmat.com/sets-t269449.html#692540
- https://www.beatthegmat.com/in-costume-f ... tml#692116

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

buoyant: Master | Next Rank: 500 Posts; Posts: 106; Joined: Sat Mar 02, 2013 4:29 pm; Thanked: 4 times

by buoyant » Tue Jan 14, 2014 12:33 pm

GMATGuruNY wrote: We can use the following equation:

Total = Basketball + Dean's list - Both + Neither.

The big idea with overlapping groups is to SUBTRACT THE OVERLAP.
When we count everyone in Group 1 (basketball) and everyone in Group 2 (Dean's list), those in BOTH groups (students who can BOTH played basketball AND made the Dean's list) get counted twice.
So that we don't double-count the students who belong to both groups, we SUBTRACT THE OVERLAP from the total.

Statement 1: 10 students played basketball and made the Dean's List
In other words, both = 10.
Since total = 80, basketball = 35, Dean's list = 19, and both = 10, we get:
80 = 35 + 19 - 10 + N
N = 36.
SUFFICIENT.

Statement 2: 44 students played basketball or made the Dean's List or both
Of the 80 students, 44 played basketball, made the Dean's list, or both played basketball and made the Dean's list.
Implication:
The remaining students neither played basketball nor made the Dean's list:
N = 80-44 = 36.
SUFFICIENT.

The correct answer is D.

Hi Mitch,
In the above, can i write the equation as :

Only B + Only D + both B and D + neither = Total ?

If above is what you mean to say, then i get how the answer is derived from statement 2.

I assume that in the equation you have mentioned [Total = Basketball + Dean's list - Both + Neither], you mean that Basketball = only basket ball+ both basket ball and dean's list and that Dean's List= only Dean's list+ both basket ball and dean's list

Am i getting this right?

Like this post

buoyant: Master | Next Rank: 500 Posts; Posts: 106; Joined: Sat Mar 02, 2013 4:29 pm; Thanked: 4 times

by buoyant » Tue Jan 14, 2014 1:05 pm

Brent@GMATPrepNow wrote: Statement 2: 44 students played basketball or made the Dean's List or both
This statement is referring to more than 1 box.
In fact, it's saying that each of the 44 students can be found in one of the 3 highlighted boxes below:

This means that the remaining 36 students must be in the non-highlighted box:

So, as we can see, 36 students neither made the Dean's List, nor played basketball
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

-------------------------------------------------------

Hi Brent,

The pictorial explanation was helpful indeed.

Could you please respond to the below thread of set problem as well ?
I tried to solve using double matrix method, but could not get the answer.

https://www.beatthegmat.com/nationwide-p ... tml#704705

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jan 14, 2014 1:30 pm

buoyant wrote:
GMATGuruNY wrote: We can use the following equation:

Total = Basketball + Dean's list - Both + Neither.

The big idea with overlapping groups is to SUBTRACT THE OVERLAP.
When we count everyone in Group 1 (basketball) and everyone in Group 2 (Dean's list), those in BOTH groups (students who can BOTH played basketball AND made the Dean's list) get counted twice.
So that we don't double-count the students who belong to both groups, we SUBTRACT THE OVERLAP from the total.

Statement 1: 10 students played basketball and made the Dean's List
In other words, both = 10.
Since total = 80, basketball = 35, Dean's list = 19, and both = 10, we get:
80 = 35 + 19 - 10 + N
N = 36.
SUFFICIENT.

Statement 2: 44 students played basketball or made the Dean's List or both
Of the 80 students, 44 played basketball, made the Dean's list, or both played basketball and made the Dean's list.
Implication:
The remaining students neither played basketball nor made the Dean's list:
N = 80-44 = 36.
SUFFICIENT.

The correct answer is D.

Hi Mitch,
In the above, can i write the equation as :

Only B + Only D + both B and D + neither = Total ?

If above is what you mean to say, then i get how the answer is derived from statement 2.

I assume that in the equation you have mentioned [Total = Basketball + Dean's list - Both + Neither], you mean that Basketball = only basket ball+ both basket ball and dean's list and that Dean's List= only Dean's list+ both basket ball and dean's list

Am i getting this right?

Given two groups B and D, each student has 2 options:
Option X: he/she is in NEITHER group
Option Y: he/she is in ONE OR BOTH groups

Here are two equations that can be used to count the students:
(Everyone in B) + (Everyone in D) - (Both B and D) + Neither = Total.
(Only B) + (Only D) + (Both B and D) + Neither = Total.
In these equations, the portions in red represent two different ways to account for all of the students in option Y.

Statement 2 indicates that the number of students in Option Y = 44.
Thus, regardless of which equation we use, the result is the same:
44 + N = 80
N = 36.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review