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

 It is currently 18 Jan 2019, 06:15

### 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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# The subsets of the set {s, t, u} consisting of the three elements s, t

Author Message
TAGS:

### Hide Tags

Intern
Joined: 24 Nov 2012
Posts: 12
The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

### Show Tags

Updated on: 09 Jan 2019, 02:51
5
00:00

Difficulty:

65% (hard)

Question Stats:

55% (01:12) correct 45% (01:25) wrong based on 62 sessions

### HideShow timer Statistics

The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

Originally posted by saxenarahul021 on 26 Nov 2012, 23:54.
Last edited by Bunuel on 09 Jan 2019, 02:51, edited 2 times in total.
Renamed the topic and edited the tags.
Math Expert
Joined: 02 Sep 2009
Posts: 52284
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

### Show Tags

27 Nov 2012, 02:02
saxenarahul021 wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

Consider the set without t: {s, u, w, x}. Each subset of this set will be subset of the original set but without t.

# of subsets of {s, u, w, x} is 2^4=16 (each out of 4 element of the set {s, u, w, x} has TWO options: either to be included in the subset or not, so total # of subsets is 2^4=16).

_________________
Manager
Joined: 28 Feb 2012
Posts: 109
GPA: 3.9
WE: Marketing (Other)
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

### Show Tags

29 Nov 2012, 00:52
Bunuel wrote:
saxenarahul021 wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

Consider the set without t: {s, u, w, x}. Each subset of this set will be subset of the original set but without t.

# of subsets of {s, u, w, x} is 2^4=16 (each out of 4 element of the set {s, u, w, x} has TWO options: either to be included in the subset or not, so total # of subsets is 2^4=16).

I am a little bit confused by your solution can you please clarify.
I agree we need to find out how many subsets are possible without t, so 4 letter could have 1 set ({SUWX} 4!/4!=1), 3 letters could have 4 sets (4!/3!=4), 2 letters could have 6 sets (4!/2!x2!=6), and 1 letter could have 4 sets. So overall 15 sets and the answer is D. Where did i go wrong?
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Math Expert
Joined: 02 Sep 2009
Posts: 52284
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

### Show Tags

29 Nov 2012, 01:59
ziko wrote:
Bunuel wrote:
saxenarahul021 wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

Consider the set without t: {s, u, w, x}. Each subset of this set will be subset of the original set but without t.

# of subsets of {s, u, w, x} is 2^4=16 (each out of 4 element of the set {s, u, w, x} has TWO options: either to be included in the subset or not, so total # of subsets is 2^4=16).

I am a little bit confused by your solution can you please clarify.
I agree we need to find out how many subsets are possible without t, so 4 letter could have 1 set ({SUWX} 4!/4!=1), 3 letters could have 4 sets (4!/3!=4), 2 letters could have 6 sets (4!/2!x2!=6), and 1 letter could have 4 sets. So overall 15 sets and the answer is D. Where did i go wrong?

You are forgetting an empty set, which is also a subset of {s, u, w, x} and do not contain t.
_________________
Manager
Joined: 28 Feb 2012
Posts: 109
GPA: 3.9
WE: Marketing (Other)
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

### Show Tags

29 Nov 2012, 04:58
I am a little bit confused by your solution can you please clarify.
I agree we need to find out how many subsets are possible without t, so 4 letter could have 1 set ({SUWX} 4!/4!=1), 3 letters could have 4 sets (4!/3!=4), 2 letters could have 6 sets (4!/2!x2!=6), and 1 letter could have 4 sets. So overall 15 sets and the answer is D. Where did i go wrong?[/quote]

You are forgetting an empty set, which is also a subset of {s, u, w, x} and do not contain t.[/quote]

Thanks Bunuel, i got it, but do you think the way of thinking was correct?
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Math Expert
Joined: 02 Sep 2009
Posts: 52284
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

### Show Tags

29 Nov 2012, 07:27
ziko wrote:
Thanks Bunuel, i got it, but do you think the way of thinking was correct?

# of subsets with 4 elements is 1: $$C^4_4=1$$;
# of subsets with 3 elements is 4: $$C^3_4=4$$;
# of subsets with 2 elements is 6: $$C^2_4=6$$;
# of subsets with 1 elements is 4: $$C^1_4=4$$;
plus 1 empty set.

1+4+6+4+1=16.
_________________
SVP
Joined: 06 Sep 2013
Posts: 1705
Concentration: Finance
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

### Show Tags

12 May 2014, 13:22
saxenarahul021 wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

I thought that the formula for number of subsets for n elements was 2^n -1

Can anybody explain why this formula does not apply in this case?

Thanks!
Cheers
J
Math Expert
Joined: 02 Sep 2009
Posts: 52284
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

### Show Tags

13 May 2014, 00:03
jlgdr wrote:
saxenarahul021 wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

I thought that the formula for number of subsets for n elements was 2^n -1

Can anybody explain why this formula does not apply in this case?

Thanks!
Cheers
J

The number of subsets of a set with n elements is 2^n, including an empty set.
_________________
CEO
Joined: 11 Sep 2015
Posts: 3331
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

### Show Tags

06 Dec 2018, 16:16
Top Contributor
saxenarahul021 wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

Take the task of building subsets and break it into stages.

Stage 1: Determine whether or not to place "t" in the subset
The question tells us that "t" cannot be in the subset.
So, we can complete stage 1 in 1 way (that is, we DO NOT place "t" in the subset

Stage 2: Determine whether or not to place "s" in the subset
We can either HAVE "s" in the subset or NOT HAVE "s" in the subset
So, we can complete stage 2 in 2 ways

Stage 3: Determine whether or not to place "u" in the subset
We can either HAVE "u" in the subset or NOT HAVE "u" in the subset
So, we can complete this stage in 2 ways

Stage 4: Determine whether or not to place "w" in the subset
We can either HAVE "w" in the subset or NOT HAVE "w" in the subset
So, we can complete this stage in 2 ways

Stage 5: Determine whether or not to place "x" in the subset
We can complete this stage in 2 ways

By the Fundamental Counting Principle (FCP), we can complete the 5 stages (and thus build all possible subsets) in (1)(2)(2)(2)(2) ways (= 16 ways)

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

RELATED VIDEOS

_________________

Test confidently with gmatprepnow.com

Director
Joined: 27 May 2012
Posts: 667
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

### Show Tags

09 Jan 2019, 02:48
1
saxenarahul021 wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

Dear Moderator,
Can we please update the OA for this question, Thank you.
_________________

- Stne

Math Expert
Joined: 02 Sep 2009
Posts: 52284
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

### Show Tags

09 Jan 2019, 02:52
stne wrote:
saxenarahul021 wrote:
The subsets of the set {s, t, u} consisting of the three elements s, t, and u are {s}, {t}, {u}, {s, t}, {s, u}, {t, u}, {s, t, u}, and the empty set { }. How many different subsets of the set {s, t, u, w, x} do not contain t as an element?

A. 4
B. 7
C. 8
D. 15
E. 16

Dear Moderator,
Can we please update the OA for this question, Thank you.

________________
Done. Thank you.
_________________
Re: The subsets of the set {s, t, u} consisting of the three elements s, t &nbs [#permalink] 09 Jan 2019, 02:52
Display posts from previous: Sort by