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

It is currently 11 Dec 2018, 04:01

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

Ben has 30 pencils in a box. Each of the pencils is one of 5 different

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51098
Ben has 30 pencils in a box. Each of the pencils is one of 5 different  [#permalink]

Show Tags

New post 26 Nov 2018, 23:06
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

57% (01:14) correct 43% (01:48) wrong based on 47 sessions

HideShow timer Statistics

Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?

A. 24
B. 25
C. 26
D. 27
E. 28

_________________

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

Intern
Intern
User avatar
B
Joined: 15 Jan 2018
Posts: 22
Location: India
Concentration: General Management, Finance
GMAT 1: 720 Q50 V37
WE: Information Technology (Computer Software)
Reviews Badge CAT Tests
Re: Ben has 30 pencils in a box. Each of the pencils is one of 5 different  [#permalink]

Show Tags

New post 26 Nov 2018, 23:16
Answer: C. 26
Let me 5 color be C1, C2, C3, C4, C5
In the worst case scenario, Ben selects all 6 pencils of each of the 4 colors. Total ways = 6X4 = 24
Then Ben must select at least 2 pencil from the 5th color to ensure that he selects at least 2 pencils of each color.
Therefore, minimum number of ways = 24+2 = 26. Hence, option C is the correct choice.
Director
Director
User avatar
S
Joined: 18 Aug 2017
Posts: 656
Location: India
Concentration: Sustainability, Marketing
WE: Marketing (Energy and Utilities)
CAT Tests
Re: Ben has 30 pencils in a box. Each of the pencils is one of 5 different  [#permalink]

Show Tags

New post 27 Nov 2018, 07:58
Bunuel wrote:
Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?

A. 24
B. 25
C. 26
D. 27
E. 28


GMATinsight :

Sir could you please help in solving this question ... i am not able to make the arrangement
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Manager
Manager
avatar
B
Joined: 02 Oct 2018
Posts: 54
Re: Ben has 30 pencils in a box. Each of the pencils is one of 5 different  [#permalink]

Show Tags

New post 28 Nov 2018, 03:25
Bunuel wrote:
Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?

A. 24
B. 25
C. 26
D. 27
E. 28



chetan2u

Pls Weigh in on this
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7100
Re: Ben has 30 pencils in a box. Each of the pencils is one of 5 different  [#permalink]

Show Tags

New post 28 Nov 2018, 18:42
1
ParthSanghavi wrote:
Bunuel wrote:
Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?

A. 24
B. 25
C. 26
D. 27
E. 28



chetan2u

Pls Weigh in on this



Hi ParthSanghavi,
The question is a simple one if we understand what is happening in this question.

Say there were 7 red balls and 3 blue balls. You have to pick balls one by one such that you MUST have one ball of each.
Now, this is MUST, so take the worst scenario - you keep picking the larger color, red, one after another. So you pick up 7 red and now three blue ball are left.
Now, when you pick a ball, it has to be blue. Thus, you MUST pick up 8 balls to be sure that you have a ball of each color.

Let us apply the same to this question.
We have 5 colors and 6 ball of each. There MUST be 2 of each.
So, we take worst scenario again.
We keep getting all other colors except one color, so you pick up 5*5=25 balls and there are 6 balls of same color.
Now the next two will surely give you two of this left over color, so 5*5+2 are a MUST to be sure to pick up two of each.
thus our answer is 27.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

GMAT Club Bot
Re: Ben has 30 pencils in a box. Each of the pencils is one of 5 different &nbs [#permalink] 28 Nov 2018, 18:42
Display posts from previous: Sort by

Ben has 30 pencils in a box. Each of the pencils is one of 5 different

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


Copyright

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®.