GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Mar 2019, 19:17

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 24 Apr 2012
Posts: 50
Concentration: Strategy
WE: Project Management (Consulting)
The Natural Woman, a women's health food store, offers its  [#permalink]

### Show Tags

Updated on: 27 Aug 2014, 04:31
3
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:48) correct 27% (02:00) wrong based on 139 sessions

### HideShow timer Statistics

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 will to win, the desire to succeed, the urge to reach your full potential..."

http://gmatclub.com/forum/powerscore-cr-notes-hope-that-someone-find-it-kudosofiable-174638.html#p1384561

Originally posted by royQV on 27 Aug 2014, 01:31.
Last edited by Bunuel on 27 Aug 2014, 04:31, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 53831
Re: The Natural Woman, a women's health food store, offers its  [#permalink]

### Show Tags

27 Aug 2014, 04:34
4
2
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.
_________________
##### General Discussion
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13797
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The Natural Woman, a women's health food store, offers its  [#permalink]

### Show Tags

17 May 2015, 14:02
1
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

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 Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Intern Joined: 21 May 2018 Posts: 11 GMAT 1: 770 Q50 V45 Re: The Natural Woman, a women's health food store, offers its [#permalink] ### Show Tags 30 May 2018, 07:59 Can I ask why the following is wrong? Total possible blends = 4! = 24 Blends with 1 ingredient = 4!/3! = 4 Blends with 2 or more ingredients = 24-4 = 20 Why is the answer 11 and not 20? I understand the method of adding up blends with 2,3,4 ingredients, but why is my method wrong? Thank you! EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13797 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The Natural Woman, a women's health food store, offers its [#permalink] ### Show Tags 30 May 2018, 12:54 1 Hi strawberrycupcake, Your first calculation (4!) is the total number of ways to ARRANGE ALL 4 ingredients (meaning that all 4 are used). However, that is not what the question asks us for - it's asking for the number of combinations of AT LEAST 2 of the ingredients. Besides using 'brute force' to just list out all of the possibilities, you could use the Combination Formula 3 times and then add up the individual results: 4c2 + 4c3 + 4c4 = 6 + 4 + 1 = 11 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
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Intern
Joined: 10 Jul 2016
Posts: 45
Re: The Natural Woman, a women's health food store, offers its  [#permalink]

### Show Tags

05 Mar 2019, 15:45
Bunuel wrote:
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.

Hi Bunuel, why are we adding the number of bins and not multiplying it?
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13797
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: The Natural Woman, a women's health food store, offers its  [#permalink]

### Show Tags

05 Mar 2019, 15:55
1
Hi siddharthsinha123,

We're asked the total number of bins, but the bins do NOT all contain the same number of ingredients. As such, while we can use the Combination formula to find the number of options for 2 ingredients, 3 ingredients and 4 ingredients, we're ultimately adding up 3 different sub-totals... so we have to use addition (and not multiplication) to get to that total.

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 Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Intern Joined: 12 Feb 2019 Posts: 2 Re: The Natural Woman, a women's health food store, offers its [#permalink] ### Show Tags 12 Mar 2019, 00:46 Hi, I would like to ask which part of the problem indicates, that each ingredient can be used only once in the mix. The only part that could do this is last sentence in brackets, but I can't really get a grasp on it. And if there is no such assumption we have an infinite number of possible answers. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13797 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The Natural Woman, a women's health food store, offers its [#permalink] ### Show Tags 12 Mar 2019, 11:35 Hi ascone, When working through a PS question on the GMAT, if you interpret the question a certain way and find that "your answer" is not among the 5 choices, then you have to reconsider how you interpret the question. This prompt does NOT say anything about the possible 'ratios' of the ingredients in the blends, it just asks for the number of possible blends that use 2 (or more) ingredients. For example: -If one blend uses ingredients A, B and C, then that is DIFFERENT from one that uses just A and B. -If a blend uses '1 part A' and '1 part B', then that mixture is the SAME as one that uses '2 parts A and 1 part B.' Thinking in those terms, can you determine all of the possible blends? 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
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Re: The Natural Woman, a women's health food store, offers its   [#permalink] 12 Mar 2019, 11:35
Display posts from previous: Sort by