It is currently 19 Nov 2017, 11:36

### 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

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

Author Message
Senior Manager
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 332

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

Location: India
GPA: 3.64
For how many non-empty subsets of S is the product of the elements [#permalink]

### Show Tags

13 Oct 2017, 21:05
1
This post was
BOOKMARKED
00:00

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
Joined: 25 Feb 2013
Posts: 553

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

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

### Show Tags

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