GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 16 Oct 2018, 05:45

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.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 09 Feb 2011
Posts: 15
A set consists of 12 numbers, all are even or multiple of 5.  [#permalink]

Show Tags

New post 09 Feb 2011, 15:19
1
4
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

66% (01:31) correct 34% (01:36) wrong based on 202 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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49911
A set consists of 12 numbers, all are even or multiple of 5.  [#permalink]

Show Tags

New post 10 Feb 2011, 13:55
1
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).

Answer: B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1836
Re: A set consists of 12 numbers  [#permalink]

Show Tags

New post 10 Feb 2011, 14:17
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"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 342
WE 1: Business Development
GMAT ToolKit User
Re: A set consists of 12 numbers  [#permalink]

Show Tags

New post 25 Feb 2011, 15:06
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,
_________________

GMAT Club Premium Membership - big benefits and savings

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49911
Re: A set consists of 12 numbers  [#permalink]

Show Tags

New post 25 Feb 2011, 15:19
1
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?
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 342
WE 1: Business Development
GMAT ToolKit User
Re: A set consists of 12 numbers  [#permalink]

Show Tags

New post 25 Feb 2011, 22:02
ye, i got it now. thanks. i didnt read the question well.

thanks.
_________________

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 25 Feb 2011
Posts: 4
Re: A set consists of 12 numbers  [#permalink]

Show Tags

New post 25 Feb 2011, 22:39
Good question, thanks!
Manager
Manager
avatar
Joined: 26 Sep 2010
Posts: 132
Nationality: Indian
Concentration: Entrepreneurship, General Management
GMAT ToolKit User Reviews Badge
Re: A set consists of 12 numbers  [#permalink]

Show Tags

New post 25 Feb 2011, 23:26
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.

Intern
Intern
avatar
S
Joined: 26 Apr 2018
Posts: 39
A set consists of 12 numbers, all are even or multiples of 5. If 5 num  [#permalink]

Show Tags

New post 21 Sep 2018, 10:04
1
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
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6956
Re: A set consists of 12 numbers, all are even or multiples of 5. If 5 num  [#permalink]

Show Tags

New post 21 Sep 2018, 10:39
2
bettatantalo wrote:
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


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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

GMATH Teacher
User avatar
S
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 360
Re: A set consists of 12 numbers, all are even or multiples of 5. If 5 num  [#permalink]

Show Tags

New post 21 Sep 2018, 12:11
bettatantalo wrote:
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


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
21Set18_6r.gif [ 12.49 KiB | Viewed 354 times ]


_________________

Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount!

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49911
Re: A set consists of 12 numbers, all are even or multiple of 5.  [#permalink]

Show Tags

New post 22 Sep 2018, 02:36
bettatantalo wrote:
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


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 Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Bot
Re: A set consists of 12 numbers, all are even or multiple of 5. &nbs [#permalink] 22 Sep 2018, 02:36
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.