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Math Expert V
Joined: 02 Sep 2009
Posts: 56244

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1 00:00

Difficulty:   35% (medium)

Question Stats: 61% (00:59) correct 39% (01:04) wrong based on 83 sessions

### HideShow timer Statistics How many subsets of $$\{a,b,c,d\}$$ including both $$a$$ and $$c$$ (order of elements does not matter) are there?

A. 3
B. 4
C. 5
D. 6
E. 7

_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 56244

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Official Solution:

How many subsets of $$\{a,b,c,d\}$$ including both $$a$$ and $$c$$ (order of elements does not matter) are there?

A. 3
B. 4
C. 5
D. 6
E. 7

Here are the four subsets: $$\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}$$.

_________________
Intern  Joined: 11 May 2014
Posts: 2
Schools: Haas '17, IE Sept'16

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I think this question is good and helpful.
Is there a way to solve with combinatorics?
Intern  Joined: 14 May 2014
Posts: 39
GMAT 1: 700 Q44 V41 GPA: 3.11

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Bunuel wrote:
Official Solution:

How many subsets of $$\{a,b,c,d\}$$ including both $$a$$ and $$c$$ (order of elements does not matter) are there?

A. 3
B. 4
C. 5
D. 6
E. 7

Here are the four subsets: $$\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}$$.

hi, Bunuel,

can we count {a,b,c,d} as subset of {a,b,c,d}..?
Math Expert V
Joined: 02 Sep 2009
Posts: 56244

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riyazgilani wrote:
Bunuel wrote:
Official Solution:

How many subsets of $$\{a,b,c,d\}$$ including both $$a$$ and $$c$$ (order of elements does not matter) are there?

A. 3
B. 4
C. 5
D. 6
E. 7

Here are the four subsets: $$\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}$$.

hi, Bunuel,

can we count {a,b,c,d} as subset of {a,b,c,d}..?

____________________________
Yes.
_________________
Intern  Joined: 14 Oct 2015
Posts: 30
GMAT 1: 640 Q45 V33 ### Show Tags

Bunuel wrote:
riyazgilani wrote:
Bunuel wrote:
Official Solution:

How many subsets of $$\{a,b,c,d\}$$ including both $$a$$ and $$c$$ (order of elements does not matter) are there?

A. 3
B. 4
C. 5
D. 6
E. 7

Here are the four subsets: $$\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}$$.

hi, Bunuel,

can we count {a,b,c,d} as subset of {a,b,c,d}..?

____________________________
Yes.

That does not make sense. How can a "sub" set be the same as the set?? {a,b,c,d} is not a subset of {a,b,c,d}. Agree to disagree.
Math Expert V
Joined: 02 Sep 2009
Posts: 56244

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1
danjbon wrote:
Bunuel wrote:
riyazgilani wrote:

hi, Bunuel,

can we count {a,b,c,d} as subset of {a,b,c,d}..?

____________________________
Yes.

That does not make sense. How can a "sub" set be the same as the set?? {a,b,c,d} is not a subset of {a,b,c,d}. Agree to disagree.

Mathematically B is a subset of A if every member of B is a member of A. So, a set is a subset of itself.
_________________
Intern  B
Joined: 15 Dec 2014
Posts: 8
Concentration: Strategy, General Management
Schools: Rotman '18
GMAT 1: 610 Q44 V31 ### Show Tags

Buenel,

I have a (naive) question. Why (D,A,C,B) is not a subset of (A,B,C,D) - when order of elements doesn't matter ?
Math Expert V
Joined: 02 Sep 2009
Posts: 56244

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1
cricketer wrote:
Buenel,

I have a (naive) question. Why (D,A,C,B) is not a subset of (A,B,C,D) - when order of elements doesn't matter ?

A set, by definition, is a collection of elements without any order. (While, a sequence, by definition, is an ordered list of terms.)
_________________
Intern  B
Joined: 15 Dec 2014
Posts: 8
Concentration: Strategy, General Management
Schools: Rotman '18
GMAT 1: 610 Q44 V31 ### Show Tags

Bunuel wrote:
cricketer wrote:
Buenel,

I have a (naive) question. Why (D,A,C,B) is not a subset of (A,B,C,D) - when order of elements doesn't matter ?

A set, by definition, is a collection of elements without any order. (While, a sequence, by definition, is an ordered list of terms.)

Thanks a lot. Very helpful/useful concept.
Intern  Joined: 19 Jun 2016
Posts: 1
Location: India
Schools: ISB '18 (A)
GMAT 1: 710 Q50 V34 GPA: 3.5

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I think this is a poor-quality question. Useless question
Current Student B
Joined: 27 Oct 2014
Posts: 156
Location: India
GMAT 1: 760 Q50 V41 GPA: 4
WE: Consulting (Consulting)

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Can this question be re-worded to say "include both a & c"?
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Current Student S
Joined: 08 Feb 2017
Posts: 80
Concentration: Entrepreneurship, Marketing
GMAT 1: 660 Q48 V33 GMAT 2: 710 Q49 V38 GPA: 3.32

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Why we don't consider singletons? (Set of one number here).
Math Expert V
Joined: 02 Sep 2009
Posts: 56244

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Evgart wrote:
Why we don't consider singletons? (Set of one number here).

Doesn't the question say that the subsets must include at least both a and c?
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Intern  B
Joined: 26 Dec 2015
Posts: 2

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why not {a,d} and {b,d}?
Math Expert V
Joined: 02 Sep 2009
Posts: 56244

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frndabu1 wrote:
why not {a,d} and {b,d}?

Because the subsets must include both a and c. Neither {a, d} nor {b, d} include both a and c.
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Intern  B
Joined: 26 Dec 2015
Posts: 2

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Manager  B
Joined: 23 Jun 2016
Posts: 94

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the number of subsets from k elements is 2^k
here if we consider a and c together as one element (since they are always present together), won't the number of subsets: 2^3 = 8?
now a&c will always need to be present, therefore the only remaining subsets: 2^2 = 4

is above understanding correct?
Manager  S
Joined: 21 Jul 2017
Posts: 190
Location: India
GMAT 1: 660 Q47 V34 GPA: 4
WE: Project Management (Education)

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Bunuel wrote:
Official Solution:

How many subsets of $$\{a,b,c,d\}$$ including both $$a$$ and $$c$$ (order of elements does not matter) are there?

A. 3
B. 4
C. 5
D. 6
E. 7

Here are the four subsets: $$\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}$$.

Dear Bunuel,

Is there any other way to approach alike questions. What if the subsets were asked for {a, b, c, d, e, f, g}?
Manager  B
Joined: 14 Aug 2012
Posts: 85
Location: United States
GMAT 1: 620 Q43 V33 GMAT 2: 690 Q47 V38 ### Show Tags

Is this fair game on the real test? I haven't seen subsets covered anywhere. Any reference material would be helpful.... Re: M12-23   [#permalink] 04 Nov 2018, 10:34

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# M12-23

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