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# The Natural Woman, a women's health food store, offers its

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Joined: 24 Apr 2012
Posts: 51
Concentration: Strategy
WE: Project Management (Consulting)
The Natural Woman, a women's health food store, offers its [#permalink]

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27 Aug 2014, 00:31
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:14) correct 24% (01:44) wrong based on 111 sessions

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The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 4 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least two ingredients? (Also assume that each bin can hold one and only one blend.)

(A) 1
(B) 4
(C) 7
(D) 11
(E) 10
[Reveal] Spoiler: OA

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Last edited by Bunuel on 27 Aug 2014, 03:31, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 02 Sep 2009
Posts: 43380
Re: The Natural Woman, a women's health food store, offers its [#permalink]

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27 Aug 2014, 03:34
2
KUDOS
Expert's post
royQV wrote:
The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 4 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least two ingredients? (Also assume that each bin can hold one and only one blend.)

(A) 1
(B) 4
(C) 7
(D) 11
(E) 10

The number of bins with 2 different ingredients = $$C^2_4=6$$;
The number of bins with 3 different ingredients = $$C^3_4=4$$;
The number of bins with 4 different ingredients = 1 ($$C^4_4=1$$).

The total number of bins with at least two ingredients = 6 + 4 + 1 = 11.

Hope it's clear.
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Re: The Natural Woman, a women's health food store, offers its [#permalink]

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17 May 2015, 13:02
1
KUDOS
Expert's post
Hi All,

The answers to this question are relatively small, so if you don't see the "math" approach to solving this question, then you can 'brute force' the solution by "mapping out" all of the possibilities...

We're told that there are 4 ingredients (we'll call them A, B, C and D); we're told that each 'mix' must include AT LEAST 2 ingredients...

2 ingredient blends:
AB
AC
BC
BD
CD

3 ingredient blends:
ABC
ABD
ACD
BCD

4 ingredient blends:
ABCD

Total blends = 6+4+1 = 11

[Reveal] Spoiler:
D

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Re: The Natural Woman, a women's health food store, offers its [#permalink]

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20 Nov 2017, 03:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The Natural Woman, a women's health food store, offers its   [#permalink] 20 Nov 2017, 03:31
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