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oquiella: Master | Next Rank: 500 Posts; Posts: 164; Joined: Tue May 12, 2015 9:06 am; Thanked: 3 times

by oquiella » Sun Sep 27, 2015 6:10 pm

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

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Source: Beat The GMAT — Problem Solving | Sun Sep 27, 2015 6:10 pm

Bullzi: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Thu May 28, 2015 1:13 am; Thanked: 5 times

by Bullzi » Sun Sep 27, 2015 7:14 pm

Hello,
This is how I could approach, I'll let the experts confirm if this approach is right..

Listing the combinations or using 4C2 to pick 2 out of 4,
12 21 31 41
13 23 32 42
14 24 34 43
and canceling out duplicates, we have 6 distinct values of which the only combination that has 2 and 4 is 24 removing which we have 5 values. So, I'll go with Option D

Thanks
Bullzi

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GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Sep 27, 2015 9:38 pm

Hi Bullzi,

Your approach is great, although it has some redundant elements to it. If you're going to use the Combination Formula, then you don't have to list out all of the duplicate elements.

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.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Sep 28, 2015 11:06 am

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

Always check the answer choices before solving a math question on the GMAT.
Given the very small answer choices, students should consider just listing all of the possible subsets.

They are:
(1,2)
(1,3)
(1,4)
(2,3)
(3,4)

The answer is D Five

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Sep 28, 2015 11:07 am

Listing and counting is often a useful approach on the GMAT. Here's a free video on this topic: https://www.gmatprepnow.com/module/gmat- ... /video/773

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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gmatbeater1989: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Wed Oct 07, 2015 12:04 pm

by gmatbeater1989 » Mon Nov 23, 2015 11:37 am

oquiella 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

4C2 - 1 = 5 (D)

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