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

It is currently 17 Aug 2018, 18:02

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

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

Show Tags

New post Updated on: 27 Aug 2014, 04:31
2
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (01:28) correct 23% (01:27) wrong based on 147 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.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47977
Re: The Natural Woman, a women's health food store, offers its  [#permalink]

Show Tags

New post 27 Aug 2014, 04:34
4
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12189
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
_________________

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
Intern
avatar
B
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

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: 12189
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
_________________

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 &nbs [#permalink] 30 May 2018, 12:54
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  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.