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We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL. # How many two-element subsets of {1,2,3,4} are there that do not  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Intern Joined: 07 Sep 2016 Posts: 3 How many two-element subsets of {1,2,3,4} are there that do not [#permalink] ### Show Tags 01 Nov 2016, 01:55 1 12 00:00 Difficulty: 45% (medium) Question Stats: 53% (01:05) correct 47% (01:05) wrong based on 399 sessions ### HideShow timer Statistics How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4? (a) One (b) Two (c) Four (d) Five (e) Six _________________ Srijat Verma Will apply for MBA in 2018-19 Appearing for GMAT in 2016 Math Expert Joined: 02 Sep 2009 Posts: 52108 Re: How many two-element subsets of {1,2,3,4} are there that do not [#permalink] ### Show Tags 01 Nov 2016, 03:04 1 3 srijatverma wrote: How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4? (a) One (b) Two (c) Four (d) Five (e) Six {1,2}, {1,3}, {1,4}, {2,3}, {3,4}. Or: $$C^2_4-1=5$$. Answer: D. _________________ Intern Joined: 11 Jun 2016 Posts: 4 Re: How many two-element subsets of {1,2,3,4} are there that do not [#permalink] ### Show Tags 14 Sep 2017, 22:07 Bunuel, Could you please explain why do you deduct one? Math Expert Joined: 02 Sep 2009 Posts: 52108 Re: How many two-element subsets of {1,2,3,4} are there that do not [#permalink] ### Show Tags 14 Sep 2017, 22:23 1 1 e100 wrote: Bunuel, Could you please explain why do you deduct one? 4C2 is the number of ALL two-element subsets. We subtract one subset {2, 4} to get the desired number. _________________ Intern Joined: 25 Jan 2013 Posts: 28 Location: United States Concentration: General Management, Entrepreneurship Schools: Johnson '21 Re: How many two-element subsets of {1,2,3,4} are there that do not [#permalink] ### Show Tags 15 Sep 2017, 01:38 Why we should not delete 2, one for (4,2) also Sent from my XT1045 using GMAT Club Forum mobile app Math Expert Joined: 02 Sep 2009 Posts: 52108 Re: How many two-element subsets of {1,2,3,4} are there that do not [#permalink] ### Show Tags 15 Sep 2017, 01:46 vs224 wrote: Why we should not delete 2, one for (4,2) also Sent from my XT1045 using GMAT Club Forum mobile app A set, by definition, is a collection of elements without any order. While, a sequence, by definition, is an ordered list of terms. 4C2 = 6 is the number of different two-element subsets from {1, 2, 3, 4} without the order: {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}. Only 1 one subset, namely {2,4}, should be subtracted. _________________ Senior SC Moderator Joined: 22 May 2016 Posts: 2323 How many two-element subsets of {1,2,3,4} are there that do not [#permalink] ### Show Tags 15 Sep 2017, 11:00 srijatverma wrote: How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4? (a) One (b) Two (c) Four (d) Five (e) Six You can list the subsets in about 30 seconds. {1,2,3,4} Two-element subsets that do not contain the pair of elements 2 and 4 Element 1 paired with each possibility Element 2 paired with each possibility Element 3 - same {1,2} {1,3} {1,4} {2,3} {3,4} There are 5 subsets that satisfy the conditions of the prompt. Answer D _________________ Never look down on anybody unless you're helping them up. --Jesse Jackson Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4518 Location: United States (CA) Re: How many two-element subsets of {1,2,3,4} are there that do not [#permalink] ### Show Tags 21 Sep 2017, 13:53 srijatverma wrote: How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4? (a) One (b) Two (c) Four (d) Five (e) Six The number of 2-element subsets that can be formed from a 4-element set is 4C2 = (4 x 3)/2! = 6. Since the pair of elements 2 and 4 is only 1 of these 6 subsets, we have 6 - 1 = 5 subsets that do not contain the pair of elements. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13325 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: How many two-element subsets of {1,2,3,4} are there that do not [#permalink] ### Show Tags 07 Feb 2018, 11:41 Hi All, You can use the Combination Formula to answer this question, although we have to do a little bit of extra work at the end. Since the number of possible outcomes is so small, you could also list them all out. 4C2 = 4!/(2!2!) = 6 pairs The pairs would be 12, 13, 14, 23, 24 and 34 Since we're asked to NOT use 24, there are 5 options remaining. 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 # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: How many two-element subsets of {1,2,3,4} are there that do not  [#permalink]

### Show Tags

24 Mar 2018, 10:03
srijatverma wrote:
How many two-element subsets of {1,2,3,4} are there that do not contain the pair of elements 2 and 4?

(a) One
(b) Two
(c) Four
(d) Five
(e) Six

hi,
can anyone explain what does subset mean ? I didn't understand the question ...
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Re: How many two-element subsets of {1,2,3,4} are there that do not  [#permalink]

### Show Tags

24 Mar 2018, 10:12
1
dave13 wrote:
hi,
can anyone explain what does subset mean ? I didn't understand the question ...

Hey dave13 ,

Subset means part of the set.

Here : Set is {1,2,3,4}

Subset could be {1} , {2}, {1,2},{1,2,3}, etc. where {1} is one element subset, {1,2} is two element subset and so on.

Question is asking how many such two element subsets could be made.

Does that make sense?
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Re: How many two-element subsets of {1,2,3,4} are there that do not &nbs [#permalink] 24 Mar 2018, 10:12
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