It is currently 19 Nov 2017, 11:36

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

For how many non-empty subsets of S is the product of the elements

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Senior Manager
Senior Manager
User avatar
G
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 332

Kudos [?]: 106 [0], given: 321

Location: India
GPA: 3.64
GMAT ToolKit User Premium Member Reviews Badge
For how many non-empty subsets of S is the product of the elements [#permalink]

Show Tags

New post 13 Oct 2017, 21:05
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (00:53) correct 0% (00:00) wrong based on 2 sessions

HideShow timer Statistics

S={1,2,3,.....400}.
For how many non-empty subsets of S is the product of the elements of the subset equal to an even number?
A) 2^400-2^300
B) 2^400-2^100
C) 2^400-2^200
D) 2^200
E) 2^300
[Reveal] Spoiler: OA

_________________

Please give kudos, if you like my post

When the going gets tough, the tough gets going...

Kudos [?]: 106 [0], given: 321

Director
Director
avatar
P
Joined: 25 Feb 2013
Posts: 553

Kudos [?]: 248 [0], given: 33

Location: India
Schools: Mannheim"19 (S)
GPA: 3.82
GMAT ToolKit User Reviews Badge
For how many non-empty subsets of S is the product of the elements [#permalink]

Show Tags

New post 14 Oct 2017, 00:37
souvonik2k wrote:
S={1,2,3,.....400}.
For how many non-empty subsets of S is the product of the elements of the subset equal to an even number?
A) 2^400-2^300
B) 2^400-2^100
C) 2^400-2^200
D) 2^200
E) 2^300


For any set having \(n\) elements, number of subset \(= 2^n\)

Here we have \(400\) elements, total number of subsets \(= 2^{400}\)

Now we need a subset whose elements' product yield an even number. So from the total subset we need to remove ODD element subset

From \(1\) to \(400\) we have \(200\) elements that are odd. So number of subsets that have ONLY ODD elements \(= 2^{200}\)

Hence required No \(= 2^{400}-2^{200}\)

Option C

Kudos [?]: 248 [0], given: 33

For how many non-empty subsets of S is the product of the elements   [#permalink] 14 Oct 2017, 00:37
Display posts from previous: Sort by

For how many non-empty subsets of S is the product of the elements

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.