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

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Question Stats: 43% (01:55) correct 57% (02:20) wrong based on 116 sessions

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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 27 Nov 2012, 00:54.
Last edited by Bunuel on 09 Jan 2019, 03:51, edited 2 times in total.
Renamed the topic and edited the tags.
Math Expert V
Joined: 02 Sep 2009
Posts: 58395
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

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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).

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Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

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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?
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Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

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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.
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Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

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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?
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Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

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

Yes, your approach is 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.
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Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

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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 V
Joined: 02 Sep 2009
Posts: 58395
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

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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.
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Joined: 12 Sep 2015
Posts: 4015
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

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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.

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Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

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2
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.
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- Stne
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Joined: 02 Sep 2009
Posts: 58395
Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

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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.
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Re: The subsets of the set {s, t, u} consisting of the three elements s, t  [#permalink]

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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

When the answer choices are relatively small, we might also consider the straightforward strategy of listing and counting

We get:
{ }
{s}
{u}
{w}
{x}
{su}
{sw}
{sx}
{uw}
{ux}
{wx}
{suw}
{sux}
{swx}
{uwx}
{suwx}

Cheers,
Brent
_________________ Re: The subsets of the set {s, t, u} consisting of the three elements s, t   [#permalink] 01 Feb 2019, 16:01
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