Last visit was: 20 Sep 2024, 09:50 It is currently 20 Sep 2024, 09:50
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Set A contains 16 even integers, and set B contains 22 integers that

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 95690
Own Kudos [?]: 660570 [4]
Given Kudos: 87331
Send PM
CAT Tests Forum Quiz Mode
Set A contains 16 even integers, and set B contains 22 integers that [#permalink] Set A contains 16 even integers, and set B contains 22 integers that   11 Mar 2020, 04:02
4
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

82% (01:38) correct 18% (02:12) wrong based on 357 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
Set A contains 16 even integers, and set B contains 22 integers that are all multiples of 3. If 7 of the integers fall into both sets A and B, how many integers are in exactly one of the two sets?

A. 21
B. 22
C. 23
D. 24
E. 25
ShowHide Answer
Official Answer
D
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8065
Own Kudos [?]: 4336 [2]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: Set A contains 16 even integers, and set B contains 22 integers that [#permalink] Set A contains 16 even integers, and set B contains 22 integers that   11 Mar 2020, 08:55
2
Bookmarks
Bunuel
Set A contains 16 even integers, and set B contains 22 integers that are all multiples of 3. If 7 of the integers fall into both sets A and B, how many integers are in exactly one of the two sets?

A. 21
B. 22
C. 23
D. 24
E. 25

Set A= 16 even integers
Set B = 22 integers
set a & b overlap = 7 integers
so not in both ; 22+16-(2*7) ; 24
IMO D
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6040
Own Kudos [?]: 4837 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: Set A contains 16 even integers, and set B contains 22 integers that [#permalink] Set A contains 16 even integers, and set B contains 22 integers that   11 Mar 2020, 10:29
Bunuel
Set A contains 16 even integers, and set B contains 22 integers that are all multiples of 3. If 7 of the integers fall into both sets A and B, how many integers are in exactly one of the two sets?

A. 21
B. 22
C. 23
D. 24
E. 25
( 16 - 7) + ( 22 - 7) = 9 + 15 => 24 , Answer must be (D)
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19491
Own Kudos [?]: 23313 [1]
Given Kudos: 287
Location: United States (CA)
Send PM
Re: Set A contains 16 even integers, and set B contains 22 integers that [#permalink] Set A contains 16 even integers, and set B contains 22 integers that   14 Mar 2020, 09:40
1
Kudos
Expert Reply
Bunuel
Set A contains 16 even integers, and set B contains 22 integers that are all multiples of 3. If 7 of the integers fall into both sets A and B, how many integers are in exactly one of the two sets?

A. 21
B. 22
C. 23
D. 24
E. 25

The 16 integers in set A include the 7 integers in both sets. So 16 - 7 = 9 integers are in set A only. Similarly, the 22 integers in set B include the 7 integers that are in both sets. So 22 - 7 = 15 integers are in set B only. Thus, the number of integers that are in exactly one set will be 9 + 15 = 24.

Answer: D
User avatar
L
BrentGMATPrepNow
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6799
Own Kudos [?]: 31373 [1]
Given Kudos: 799
Location: Canada
Send PM
Re: Set A contains 16 even integers, and set B contains 22 integers that [#permalink] Set A contains 16 even integers, and set B contains 22 integers that   21 Feb 2022, 17:55
1
Bookmarks
Expert Reply
Top Contributor
Bunuel
Set A contains 16 even integers, and set B contains 22 integers that are all multiples of 3. If 7 of the integers fall into both sets A and B, how many integers are in exactly one of the two sets?

A. 21
B. 22
C. 23
D. 24
E. 25

Let's combine the two sets make one population, and then use the Double Matrix Method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of integers, and the two characteristics are:
- In Set A or not in set A
- In Set B or not in set B

So we start with something like this:


Given: Set A contains 16 even integers. Set B contains 22 integers. 7 of the integers fall into both sets A and B
Add this information to our diagram to get:

Important: Since we're combining the integers from set A and set B, we can conclude that there are ZERO integers that are in neither set. That's why we have 0 in the bottom-right box

From here, we can complete the matrix as follows:


Question: How many integers are in exactly one of the two sets?
On the diagram we can see that there are 9 integers that are in set A but not in set B, and there are 15 integers that are in set B but not in set A.
Total = 9 + 15 = 24

Answer: D

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video:



EXTRA PRACTICE QUESTION


More questions to practice with:
EASY: https://gmatclub.com/forum/of-the-120-p ... 15386.html
MEDIUM: https://gmatclub.com/forum/in-a-certain ... 21716.html
HARD: https://gmatclub.com/forum/a-group-of-2 ... 24888.html
KILLER: https://gmatclub.com/forum/a-certain-hi ... 32899.html
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 15317
Own Kudos [?]: 68202 [0]
Given Kudos: 442
Location: Pune, India
Send PM
Re: Set A contains 16 even integers, and set B contains 22 integers that [#permalink] Set A contains 16 even integers, and set B contains 22 integers that   18 Aug 2023, 05:05
Expert Reply
Bunuel
Set A contains 16 even integers, and set B contains 22 integers that are all multiples of 3. If 7 of the integers fall into both sets A and B, how many integers are in exactly one of the two sets?

A. 21
B. 22
C. 23
D. 24
E. 25

Set A has 16 integers
Set B has 22 integers
Both = 7

Only Set A = 16 - 7 = 9
Only Set B = 22 - 7 = 15

Number of integers in exactly one set = 9 + 15 = 24

Answer (D)

Check this video on how to handle two overlapping sets:
https://youtu.be/HRnuURqGhmg
GMAT Club Bot
gmatclubot
Re: Set A contains 16 even integers, and set B contains 22 integers that [#permalink]
18 Aug 2023, 05:05
Moderator:
Bunuel
Math Expert
95690 posts