A set consists of 12 numbers, all are even or multiple of 5. : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 10 Dec 2016, 13:04

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A set consists of 12 numbers, all are even or multiple of 5.

Author Message
TAGS:

### Hide Tags

Intern
Joined: 09 Feb 2011
Posts: 16
Followers: 1

Kudos [?]: 40 [0], given: 0

A set consists of 12 numbers, all are even or multiple of 5. [#permalink]

### Show Tags

09 Feb 2011, 14:19
1
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

71% (02:10) correct 29% (01:23) wrong based on 146 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 35950
Followers: 6865

Kudos [?]: 90118 [0], given: 10418

A set consists of 12 numbers, all are even or multiple of 5. [#permalink]

### Show Tags

10 Feb 2011, 12:55
Expert's post
1
This post was
BOOKMARKED
loveparis wrote:
38. 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

{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).

_________________
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 162

Kudos [?]: 1671 [0], given: 376

Re: A set consists of 12 numbers [#permalink]

### Show Tags

10 Feb 2011, 13:17
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"
_________________
Senior Manager
Joined: 08 Nov 2010
Posts: 417
Followers: 7

Kudos [?]: 100 [0], given: 161

Re: A set consists of 12 numbers [#permalink]

### Show Tags

25 Feb 2011, 14:06
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,
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 35950
Followers: 6865

Kudos [?]: 90118 [1] , given: 10418

Re: A set consists of 12 numbers [#permalink]

### Show Tags

25 Feb 2011, 14:19
1
KUDOS
Expert's post
144144 wrote:
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,

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?
_________________
Senior Manager
Joined: 08 Nov 2010
Posts: 417
Followers: 7

Kudos [?]: 100 [0], given: 161

Re: A set consists of 12 numbers [#permalink]

### Show Tags

25 Feb 2011, 21:02
ye, i got it now. thanks. i didnt read the question well.

thanks.
_________________
Intern
Joined: 25 Feb 2011
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 3

Re: A set consists of 12 numbers [#permalink]

### Show Tags

25 Feb 2011, 21:39
Good question, thanks!
Manager
Joined: 26 Sep 2010
Posts: 155
Nationality: Indian
Concentration: Entrepreneurship, General Management
GMAT 1: 760 Q V
Followers: 7

Kudos [?]: 58 [0], given: 18

Re: A set consists of 12 numbers [#permalink]

### Show Tags

25 Feb 2011, 22:26
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.
_________________

You have to have a darkness...for the dawn to come.

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12907
Followers: 563

Kudos [?]: 158 [0], given: 0

Re: A set consists of 12 numbers, all are even or multiple of 5. [#permalink]

### Show Tags

09 Feb 2015, 09:35
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: A set consists of 12 numbers, all are even or multiple of 5.   [#permalink] 09 Feb 2015, 09:35
Similar topics Replies Last post
Similar
Topics:
Set A consists of 7 consecutive even numbers. Set B consists of 5 cons 3 07 Mar 2016, 08:23
9 Set J consists of 18 consecutive even numbers. If the smallest term in 7 30 Oct 2015, 07:44
Exactly 36% of the numbers in set S are even multiples of 3 1 11 Feb 2012, 15:42
10 Exactly 36% of the numbers in set S are even multiples of 3. 11 05 Feb 2012, 17:20
20 Set A consists of all even integers between 2 and 100 12 14 Mar 2011, 08:20
Display posts from previous: Sort by