by: Bunuel
13 mins
by: Bunuel
13 mins
Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
67% (01:29) correct
33%
(01:34)
wrong
based on 291
sessions
History
Date
Time
Result
Not Attempted Yet
A set consists of 12 numbers, all are even or multiple of 5. If 5 numbers are even and 8 numbers are multiple of 5, how many numbers is multiple of 10?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
loveparis
{Total} = {Even} + {Multiple of 5} - {Both} + {Nether}.
Since {Neither}=0 ("all are even or multiple of 5") then:
12 = 5 + 8 - {Both} + 0;
{Both}=1 (so 1 number is both even AND multiple of 5, so it must be a multiple of 10).
Answer: B.
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
A- Elements those are multiple of 2.
B - Elements those are multiple of 5.
\(n(A \cup B)\) - Number of elements either multiple of 2 or 5.
\(n(A)\) - Number of elements multiple of 5
\(n(B)\) - Number of elements multiple of 2.
\(n(A \cap B)\) - Number of elements multiple of both 5 and 2(or 10)
\(n(A \cup B) = n(A) + n(B) - n(A \cap B)\)
\(12 = 5+8- n(A \cap B)\)
\(n(A \cap B) = 13-12 = 1\)
Ans: "B"
B - Elements those are multiple of 5.
\(n(A \cup B)\) - Number of elements either multiple of 2 or 5.
\(n(A)\) - Number of elements multiple of 5
\(n(B)\) - Number of elements multiple of 2.
\(n(A \cap B)\) - Number of elements multiple of both 5 and 2(or 10)
\(n(A \cup B) = n(A) + n(B) - n(A \cap B)\)
\(12 = 5+8- n(A \cap B)\)
\(n(A \cap B) = 13-12 = 1\)
Ans: "B"
Guys, i understand the way u solved it, but why cant it be 5 as well?
no one told us they are not all multiples of 5 and 2... can someone point out what i am missing?
thanks,
no one told us they are not all multiples of 5 and 2... can someone point out what i am missing?
thanks,
144144
It's not clear what you mean. This is overlapping sets problem:
{Total} = {Even} + {Multiple of 5} - {Both} --> 12 = 5 + 8 - {Both} --> {Both}=1 .
Now, how can the answer be other then 1?
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
ye, i got it now. thanks. i didnt read the question well.
thanks.
thanks.
Posts: 4
Good question, thanks!
IndigoIntentions
Current Student
Joined: 26 Sep 2010
Last visit: 29 Jan 2016
Posts: 119
Nationality: Indian
Concentration: Entrepreneurship, General Management
Products:
Posts: 119
B).
Lets say x1 to x12 are the numbers. Assume that x1-x5 are even. The Q says that all numbers are even or multiple of 5. There are 8 multiples of 5 , so lets mark x12 to x6 as multiples of 5 (7 in total) and thus , we will have x5 as the even number that will be multiple of 5.
Thus,
X5 = 5m
X5 = 2n
Since 5 and 2 are primes, the Number X5 = 2.5. (p) where p = m/2 and n/5.
Also, x6 to x12 will have a format of 5.(Odd) since they are odd numbers. Thus they cant be multiple of 10 which is even.
=> x5 will be the only multiple of 10.
Lets say x1 to x12 are the numbers. Assume that x1-x5 are even. The Q says that all numbers are even or multiple of 5. There are 8 multiples of 5 , so lets mark x12 to x6 as multiples of 5 (7 in total) and thus , we will have x5 as the even number that will be multiple of 5.
Thus,
X5 = 5m
X5 = 2n
Since 5 and 2 are primes, the Number X5 = 2.5. (p) where p = m/2 and n/5.
Also, x6 to x12 will have a format of 5.(Odd) since they are odd numbers. Thus they cant be multiple of 10 which is even.
=> x5 will be the only multiple of 10.
Posts: 33
A set consists of 12 numbers, all are even or multiples of 5. If 5 numbers are even and 8 numbers are multiples of 5, how many numbers are multiples of 10?
a) 0
b) 1
c) 2
d) 3
e) 5
source gmat tutor
a) 0
b) 1
c) 2
d) 3
e) 5
source gmat tutor
bettatantalo
it is about overlapping set...
so multiples of 5 = 8 and even = 5
total 5+8=13 but the set has only 12 numbers ..
as all are part of one of the group, the overlap is 13-12=1
B
_________________
bettatantalo
Yep... Venn diagrams ("overlapping sets"). See image attached.
\(? = x\)
Using the simplifier, we have:
\(\left[ {{\text{even}}} \right] \cup \left[ {{\text{mult}}\,\,{\text{5}}} \right] = \left[ {{\text{even}}} \right] + \left[ {{\text{mult}}\,\,{\text{5}}} \right] - \left[ {{\text{x}}\,\,{\text{ = }}\,\,{\text{mult}}\,{\text{10}}} \right]\)
\(12 = 5 + 8 - x\,\,\,\,\, \Rightarrow \,\,\,\,\,x = 1\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Attachments
21Set18_6r.gif [ 12.49 KiB | Viewed 3894 times ]
bettatantalo
Merging topics.
Please read carefully and follow our rules when posting a question: https://gmatclub.com/forum/rules-for-po ... 33935.html Thank you.
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
Moderator:
Announcements
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.