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

It is currently 23 Oct 2019, 21:27

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
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

New post Updated on: 27 Aug 2014, 04:31
6
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

73% (01:47) correct 27% (02:03) wrong based on 176 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..."

Useful Links:

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.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58465
Re: The Natural Woman, a women's health food store, offers its  [#permalink]

Show Tags

New post 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.

Answer: D.

Hope it's clear.
_________________
General Discussion
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15321
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

New post 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
AD
BC
BD
CD

3 ingredient blends:
ABC
ABD
ACD
BCD

4 ingredient blends:
ABCD

Total blends = 6+4+1 = 11

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Intern
Intern
avatar
B
Joined: 21 May 2018
Posts: 17
Location: Singapore
GMAT 1: 770 Q50 V45
Re: The Natural Woman, a women's health food store, offers its  [#permalink]

Show Tags

New post 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
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15321
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

New post 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
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Intern
Intern
avatar
S
Joined: 10 Jul 2016
Posts: 44
GMAT ToolKit User Reviews Badge
Re: The Natural Woman, a women's health food store, offers its  [#permalink]

Show Tags

New post 05 Mar 2019, 15:45
1
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.

Answer: D.

Hope it's clear.


Hi Bunuel, why are we adding the number of bins and not multiplying it?
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15321
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

New post 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
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Intern
Intern
avatar
B
Joined: 12 Feb 2019
Posts: 2
Re: The Natural Woman, a women's health food store, offers its  [#permalink]

Show Tags

New post 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
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15321
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

New post 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
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
GMAT Club Bot
Re: The Natural Woman, a women's health food store, offers its   [#permalink] 12 Mar 2019, 11:35
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne