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# There are X people at a dance, where X is an integer

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There are X people at a dance, where X is an integer [#permalink]  09 May 2018, 09:13
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There are $$X$$ people at a dance, where $$X$$ is an integer greater than 1. The number of different pairs of people who can be partnered up for the waltz is $$Z$$. Which of the following could be the value of $$Z$$ ?

A. 2

B. 6

C. 9

D. 14

E. 20
[Reveal] Spoiler: OA

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Manager
Joined: 27 Feb 2017
Posts: 188
Followers: 1

Kudos [?]: 77 [0], given: 15

Re: There are people at a dance, where is an integer greater tha [#permalink]  09 May 2018, 13:22
Active Member
Joined: 07 Jan 2018
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Kudos [?]: 769 [1] , given: 88

Re: There are X people at a dance, where X is an integer [#permalink]  10 May 2018, 03:15
1
KUDOS
A pair of people is required. Z is the number of unique pair of people for the dance
number of total people $$> 1$$

There are two spots in a pair
Here we chose $$2$$ people out of 2 people Hence $$2c2$$ $$= 1$$. Not in the option

Let us try $$3$$
$$3c2 = 3$$. Not in the option

Let us try $$4$$
$$4c2 = 6$$. This is the correct option
B
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Manager
Joined: 27 Feb 2017
Posts: 188
Followers: 1

Kudos [?]: 77 [0], given: 15

Re: There are X people at a dance, where X is an integer [#permalink]  11 May 2018, 13:08
amorphous wrote:
A pair of people is required. Z is the number of unique pair of people for the dance
number of total people $$> 1$$

There are two spots in a pair
Here we chose $$2$$ people out of 2 people Hence $$2c2$$ $$= 1$$. Not in the option

Let us try $$3$$
$$3c2 = 3$$. Not in the option

Let us try $$4$$
$$4c2 = 6$$. This is the correct option
B

so how did we eliminate the other options? And is there an easier and quicker way to do this rather than trial and error? I also had a hard time understanding the wording of the question
Active Member
Joined: 07 Jan 2018
Posts: 694
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Kudos [?]: 769 [1] , given: 88

Re: There are X people at a dance, where X is an integer [#permalink]  11 May 2018, 19:49
1
KUDOS
Since this is a select one multiple choice ans there cannot be more than 1 ans choice. If in the process of solving the problem we get our ans, no need to work with other options.
There can be other methods for solving the ans for eg. you can formulate a eqn $$x(x-1) = 2a$$; where a is the ans options
make the left side equivalent to the right side for correct ans such as $$x(x-1) = 4*3$$ for option B try it with different options only B is correct
Realize that this is not a time consuming question. If you understand the logic the question should not take more than 1'30 min to answer
Wording of questions can be confusing, ets regularly uses this technique to make test-takers chose wrong answers. Get familiar with gre language. Give attention to sign words such as only, not, must be, could be, if, approximately and so on
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Re: There are X people at a dance, where X is an integer   [#permalink] 11 May 2018, 19:49
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