Aug 20 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Aug 20 09:00 PM PDT  10:00 PM PDT Take 20% off the plan of your choice, now through midnight on Tuesday, 8/20 Aug 22 09:00 PM PDT  10:00 PM PDT What you'll gain: Strategies and techniques for approaching featured GMAT topics, and much more. Thursday, August 22nd at 9 PM EDT Aug 24 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Aug 25 09:00 AM PDT  12:00 PM PDT Join a FREE 1day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today! Aug 25 08:00 PM PDT  11:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 07 Mar 2015
Posts: 2

The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
06 Nov 2015, 13:28
Question Stats:
56% (01:29) correct 44% (01:22) wrong based on 992 sessions
HideShow timer Statistics
The subsets of the set { w, x, y} are { w}, { x}, { y}, { w, x}, { w, y}, { x,y}, { w, x, y}, and { } (the empty subset). How many subsets of the set { w, x, y, z} contain w? (A) Four (B) Five (C) Seven (D) Eight (E) Sixteen
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Manager
Joined: 01 Jan 2015
Posts: 62

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
07 Nov 2015, 15:10
JDPB7 wrote: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y}, {x,y}, {w, x, y}, and { } (the empty subset).
How many subsets of the set {w, x, y, z} contain w?
(A) Four (B) Five (C) Seven (D) Eight (E) Sixteen A powerset of a set is the set of all subsets of that set. For example, the power set of {w, x, y} is {w}, {x}, {y}, {w, x}, {w, y}, {x,y}, {w, x, y}, and { } as given by the question stem. The cardinality of a powerset (the number of subsets of the powerset) is calculated by \(2^N\), where N is the number of elements in the set. Since {w, x, y} contains 3 elements, the cardinality of the powerset of that set contains \(2^3\) subsets. The powerset of the set { w, x, y, z} contains \(2^4\) subsets. The powerset of the set { x, y, z} contains \(2^3\) subsets; these 8 subsets don't have w. So the number of subsets of the set { w, x, y, z} that contain w is the total number of subsets minus number of subsets that don't contain w, 168 = 8. Correct answer choice is D.




EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14823
Location: United States (CA)

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
06 Nov 2015, 15:41
Hi JDPB7, The prompt itself literally tells you how to go about answering this question. You're asked for the total number of available subsets that contain W, and you're shown the 'definition' of what makes up a subset. With that knowledge, you should be able to list them all out (and there can't be that many, since the answers don't go any higher than 16). If you try to create the list, then how many options do you come up with? GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14823
Location: United States (CA)

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
07 Nov 2015, 14:11
Hi JDPB7, The subsets that include W are: {W}, {W, X}, {W, Y}, {W, Z}, {W, X, Y}, {W, X, Z}, {W, Y, Z} and {W, X, Y, Z) Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/



Intern
Status: Gaja!
Joined: 26 Aug 2014
Posts: 49
Location: United States (CA)
GMAT 1: 700 Q49 V36 GMAT 2: 680 Q49 V34 GMAT 3: 740 Q50 V40
GPA: 3.6
WE: Consulting (Consulting)

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
25 Dec 2015, 17:17
As an alternative approach, notice that the formula to get the the total number of subsets is \(2^n\)where n is the number of items in the set. {w, x, y, z} has 4 in total so we have \(2^4=16\) subsets. Since we want to see the number of subsets containing w, take it for granted that w is in your subset and use \(2^3\) instead. EMPOWERgmatRichC, is there a way to answer this using combination formula?



Intern
Joined: 31 Aug 2013
Posts: 9

The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
26 Dec 2015, 05:55
JDPB7 wrote: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y}, {x,y}, {w, x, y}, and { } (the empty subset).
How many subsets of the set {w, x, y, z} contain w?
(A) Four (B) Five (C) Seven (D) Eight (E) Sixteen  The number of ways of selecting 0 or more from n elements is 2^n. Hence here, once you select w , the number of ways of selecting 0 or more from x,y and z ( 3 elements) is 2^3 = 8. The same applies for { w, x, y}. If you select w here, the number of ways of selecting 0 or more from x and y = 2^2 = 4 (which aligns with the actual results) Hope it helps.



Intern
Joined: 06 Dec 2016
Posts: 2
Location: India
Concentration: General Management, Technology
GPA: 3.7
WE: Engineering (Military & Defense)

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
25 Dec 2016, 00:13
Total number of subset with 03 elements : 08 (given in the problem) Total number of subset with 04 elements ( with one element repeated) = Total number of subset with 03 elements ( As the 4th element is forced in all subsets)
Hence Answer = 08 (D)



Manager
Joined: 03 Jan 2017
Posts: 139

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
23 Mar 2017, 04:35
Be careful with the question, because this a very tricky one! Question asks us in how many sets is w present! W is present in 1 {w} set in 3 {w,...} set and 3 {w,...,...} set and one {w,x,y,z} set total 8.
Answer is D
If you would like to count all combinations of the set {w,x,y,z}. Those are: 4+2C4+3C4+1+1=16 total (E)



Manager
Joined: 26 Mar 2017
Posts: 112

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
03 Jun 2017, 02:29
its just a counting problem such as how many menus are possible thus, (w,x,y) > 2*2*2=8
_________________
I hate long and complicated explanations!



Senior Manager
Joined: 02 Apr 2014
Posts: 471
Location: India
GPA: 3.5

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
02 May 2018, 12:22
Good official question as usual !
Just count number of subsets of {x,y,z} = 2^3 = 8, as we add w to each of these subsets, we get all subsets that contain w.
General formula To get number of subsets including empty subset from a set of n numbers, nC0 + nC1 + .............. + nCn = 2^n



Intern
Joined: 22 Jan 2018
Posts: 21

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
09 May 2018, 13:58
EMPOWERgmatRichC wrote: Hi JDPB7,
The prompt itself literally tells you how to go about answering this question. You're asked for the total number of available subsets that contain W, and you're shown the 'definition' of what makes up a subset. With that knowledge, you should be able to list them all out (and there can't be that many, since the answers don't go any higher than 16).
If you try to create the list, then how many options do you come up with?
GMAT assassins aren't born, they're made, Rich Is there a way to get to 8 from a combination method? I got 16 from finding the total combinations but how do I parse out which sets contain W and which ones do not? Just divide by 2 because the set has it or doesn't have it? Obviously straightlisting works too!



Math Expert
Joined: 02 Sep 2009
Posts: 57155

The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
09 May 2018, 21:42
thinkpad18 wrote: EMPOWERgmatRichC wrote: Hi JDPB7,
The prompt itself literally tells you how to go about answering this question. You're asked for the total number of available subsets that contain W, and you're shown the 'definition' of what makes up a subset. With that knowledge, you should be able to list them all out (and there can't be that many, since the answers don't go any higher than 16).
If you try to create the list, then how many options do you come up with?
GMAT assassins aren't born, they're made, Rich Is there a way to get to 8 from a combination method? I got 16 from finding the total combinations but how do I parse out which sets contain W and which ones do not? Just divide by 2 because the set has it or doesn't have it? Obviously straightlisting works too! (Total number of sets)  (number of sets without w) = (number of sets with w) 2^4  2^3 = 8. Explained here: https://gmatclub.com/forum/thesubsets ... l#p1598828
_________________



Senior Manager
Joined: 10 Apr 2018
Posts: 271
Location: United States (NC)

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
20 Sep 2018, 13:12
Bunuel wrote: thinkpad18 wrote: EMPOWERgmatRichC wrote: Hi JDPB7,
The prompt itself literally tells you how to go about answering this question. You're asked for the total number of available subsets that contain W, and you're shown the 'definition' of what makes up a subset. With that knowledge, you should be able to list them all out (and there can't be that many, since the answers don't go any higher than 16).
If you try to create the list, then how many options do you come up with?
GMAT assassins aren't born, they're made, Rich Is there a way to get to 8 from a combination method? I got 16 from finding the total combinations but how do I parse out which sets contain W and which ones do not? Just divide by 2 because the set has it or doesn't have it? Obviously straightlisting works too! (Total number of sets)  (number of sets without w) = (number of sets with w) 2^4  2^2 = 8. Explained here: https://gmatclub.com/forum/thesubsets ... l#p1598828Hi Bunuel, I guess the highlighted portion is a typo. should it be\(2^4  2^3\) Probus
_________________
Probus
~You Just Can't beat the person who never gives up~ Babe Ruth



Math Expert
Joined: 02 Sep 2009
Posts: 57155

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
20 Sep 2018, 20:54
Probus wrote: Hi Bunuel, I guess the highlighted portion is a typo. should it be\(2^4  2^3\) Probus ___________________ Yes. Edited. Thank you.
_________________



Director
Joined: 14 Dec 2017
Posts: 517
Location: India

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
21 Sep 2018, 23:17
JDPB7 wrote: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y}, {x,y}, {w, x, y}, and { } (the empty subset).
How many subsets of the set {w, x, y, z} contain w?
(A) Four (B) Five (C) Seven (D) Eight (E) Sixteen The long method to solve this question is as below: Subset with 4 elements including w = 1 Subset with 3 elements including w = choosing 2 elements out of the remaining 3 = 3C2 = 3 Subset with 2 elements including w = choosing 1 element out of the remaining 3 = 3C1 = 3 Subset with just 1 element containing w = 1 Total Subsets =1 + 3 + 3 + 1 = 8 Answer D. Thanks, GyM
_________________



Manager
Joined: 24 Sep 2018
Posts: 140

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
26 Oct 2018, 12:03
JDPB7 wrote: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y}, {x,y}, {w, x, y}, and { } (the empty subset).
How many subsets of the set {w, x, y, z} contain w?
(A) Four (B) Five (C) Seven (D) Eight (E) Sixteen Certainly not the most efficient way, but worth giving a look: The subsets containing w of the set {w , x , y , z} {w} {w , x} {w , y} {w , z} {w , x , y} {w , y , z} {w , x , z} {w , x , y , z} Total 8 subsets.
_________________
Please award kudos, If this post helped you in someway.



Manager
Joined: 16 Jul 2018
Posts: 57

The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
01 Jan 2019, 08:43
chetan2u Gladiator59 Bunuel VeritasKarishma Hello could anyone be kind to answer the following question? So the general formula for finding subsets is 2^n, however when I try to separate the subsets of x,y,z manually I get 7 subsets rather than 8 (x),(y),(z) (x,y) (x,z) (y,z) (x,y,z) I don't get what is exactly the so called "empty subset" that is written in the stem I mean which combination is included in that subset...?



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14823
Location: United States (CA)

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
01 Jan 2019, 12:14
UNSTOPPABLE12 wrote: chetan2u Gladiator59 Bunuel VeritasKarishma Hello could anyone be kind to answer the following question? So the general formula for finding subsets is 2^n, however when I try to separate the subsets of x,y,z manually I get 7 subsets rather than 8 (x),(y),(z) (x,y) (x,z) (y,z) (x,y,z) I don't get what is exactly the so called "empty subset" that is written in the stem I mean which combination is included in that subset...? Hi UNSTOPPABLE12, Your list of the individual subsets assumes that at least one of the letters X, Y and Z exists in the set. That is NOT what the prompt states though  it asks how many subsets include "W." Those subsets would include all 7 of the ones that you listed as well as a set in which NONE of those 3 variables was included. In reference to 2^N, you can think of each variable as either "in" or "not in", so there would be (2)(2)(2) = 8 possible sets. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/



Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 748
GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
01 Jan 2019, 22:04
Hi UNSTOPPABLE12, Welcome to GMAT Club! You are absolutely right. There are \(2^n\) subsets of a set with a cardinality of n. So for a 3 element set {x,y,z} the subsets will be.. {x},{y},{z},{x,y},{x,z},{y,z},{x,y,z} and the empty set denoted by {}Note that an empty set is a subset of all sets.Hope this answers your question. Feel free to tag back if you have additional queries. Best, Gladi UNSTOPPABLE12 wrote: chetan2u Gladiator59 Bunuel VeritasKarishma Hello could anyone be kind to answer the following question? So the general formula for finding subsets is 2^n, however when I try to separate the subsets of x,y,z manually I get 7 subsets rather than 8 (x),(y),(z) (x,y) (x,z) (y,z) (x,y,z) I don't get what is exactly the so called "empty subset" that is written in the stem I mean which combination is included in that subset...?
_________________
Regards, Gladi
“Do. Or do not. There is no try.”  Yoda (The Empire Strikes Back)



Manager
Joined: 16 Jul 2018
Posts: 57

Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
Show Tags
02 Jan 2019, 05:11
Gladiator59 wrote: Hi UNSTOPPABLE12, Welcome to GMAT Club! You are absolutely right. There are \(2^n\) subsets of a set with a cardinality of n. So for a 3 element set {x,y,z} the subsets will be.. {x},{y},{z},{x,y},{x,z},{y,z},{x,y,z} and the empty set denoted by {}Note that an empty set is a subset of all sets.Hope this answers your question. Feel free to tag back if you have additional queries. Best, Gladi UNSTOPPABLE12 wrote: chetan2u Gladiator59 Bunuel VeritasKarishma Hello could anyone be kind to answer the following question? So the general formula for finding subsets is 2^n, however when I try to separate the subsets of x,y,z manually I get 7 subsets rather than 8 (x),(y),(z) (x,y) (x,z) (y,z) (x,y,z) I don't get what is exactly the so called "empty subset" that is written in the stem I mean which combination is included in that subset...? Gladiator59 Thank you for your prompt response !




Re: The subsets of the set {w, x, y} are {w}, {x}, {y}, {w, x}, {w, y},
[#permalink]
02 Jan 2019, 05:11



Go to page
1 2
Next
[ 23 posts ]



