Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43894

Question Stats:
66% (00:32) correct 34% (00:43) wrong based on 125 sessions
HideShow timer Statistics



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re M1223 [#permalink]
Show Tags
15 Sep 2014, 23:47
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: \(\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}\). Answer: B
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 11 May 2014
Posts: 2

Re M1223 [#permalink]
Show Tags
15 Jan 2015, 10:22
I think this question is good and helpful. Is there a way to solve with combinatorics?



Current Student
Joined: 14 May 2014
Posts: 45
GPA: 3.11

Re: M1223 [#permalink]
Show Tags
24 Jul 2015, 08:27
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: \(\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}\).
Answer: B hi, Bunuel, can we count {a,b,c,d} as subset of {a,b,c,d}..?



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: M1223 [#permalink]
Show Tags
24 Jul 2015, 08:31
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: \(\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}\).
Answer: B hi, Bunuel, can we count {a,b,c,d} as subset of {a,b,c,d}..? ____________________________ Yes.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 14 Oct 2015
Posts: 37

Re: M1223 [#permalink]
Show Tags
29 Oct 2015, 07:54
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: \(\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}\).
Answer: B 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
Joined: 02 Sep 2009
Posts: 43894

Re: M1223 [#permalink]
Show Tags
29 Oct 2015, 10:42
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 15 Dec 2014
Posts: 8
Location: Canada
Concentration: Strategy, General Management

Re: M1223 [#permalink]
Show Tags
19 Jan 2016, 08:21
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
Joined: 02 Sep 2009
Posts: 43894

Re: M1223 [#permalink]
Show Tags
19 Jan 2016, 08:25
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.)
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 15 Dec 2014
Posts: 8
Location: Canada
Concentration: Strategy, General Management

Re: M1223 [#permalink]
Show Tags
19 Jan 2016, 08:31
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
GPA: 3.5

Re M1223 [#permalink]
Show Tags
10 Oct 2016, 21:28
I think this is a poorquality question. Useless question



Manager
Joined: 27 Oct 2014
Posts: 156
Location: India
GPA: 4
WE: Consulting (Consulting)

Re: M1223 [#permalink]
Show Tags
15 Jul 2017, 11:40
Can this question be reworded to say " include both a & c"?
_________________
If you found this post useful, hit Kudos! :D



HBS Thread Master
Joined: 08 Feb 2017
Posts: 53
Concentration: Entrepreneurship, Marketing
GMAT 1: 660 Q48 V33 GMAT 2: 710 Q49 V38
GPA: 3.32

Re: M1223 [#permalink]
Show Tags
23 Jul 2017, 08:36
Why we don't consider singletons? (Set of one number here).



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: M1223 [#permalink]
Show Tags
23 Jul 2017, 19:49



Intern
Joined: 26 Dec 2015
Posts: 2

Re: M1223 [#permalink]
Show Tags
14 Aug 2017, 07:19
why not {a,d} and {b,d}?



Math Expert
Joined: 02 Sep 2009
Posts: 43894

Re: M1223 [#permalink]
Show Tags
14 Aug 2017, 07:24



Intern
Joined: 26 Dec 2015
Posts: 2

Re: M1223 [#permalink]
Show Tags
14 Aug 2017, 07:45
Great! careful reading!!!



Manager
Joined: 23 Jun 2016
Posts: 140

Re: M1223 [#permalink]
Show Tags
07 Nov 2017, 11:11
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?










