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Set S consists of the integers from -1 to 5, inclusive. If N

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Senior Manager
Joined: 20 May 2014
Posts: 282
Followers: 18

Kudos [?]: 50 [0], given: 220

Set S consists of the integers from -1 to 5, inclusive. If N [#permalink]  29 Oct 2017, 02:19
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100% (01:54) correct 0% (00:00) wrong based on 3 sessions
Set S consists of the integers from -1 to 5, inclusive. If N is the product of three distinct members of Set S, how many unique values of N are there?

[Reveal] Spoiler: OA
21

Kudos for correct solution.
Director
Joined: 03 Sep 2017
Posts: 521
Followers: 1

Kudos [?]: 344 [1] , given: 66

Re: Set S consists of the integers from -1 to 5, inclusive. If N [#permalink]  30 Oct 2017, 10:12
1
KUDOS
The maximum number of triplets out of 7 numbers is $$7C3 = \frac{7!}{4!3!} = 35$$. Then, given that there is 0 as one of the numbers, each time the triplet contains zero, the product is zero. Thus, we are over-counting the results. We have to subtract the copies from the total number.

The number of triplets which contains 0 is 15, thus there are 14 copies. The number of unique results is 35-14 = 21.
Re: Set S consists of the integers from -1 to 5, inclusive. If N   [#permalink] 30 Oct 2017, 10:12
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