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

It is currently 17 Nov 2019, 10:26

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

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

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59089
Ben has 30 pencils in a box. Each of the pencils is one of 5 different  [#permalink]

Show Tags

New post 27 Nov 2018, 00:06
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

57% (01:25) correct 43% (01:51) wrong based on 119 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

_________________
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8180
Ben has 30 pencils in a box. Each of the pencils is one of 5 different  [#permalink]

Show Tags

New post 28 Nov 2018, 19:42
2
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 4*6=24 balls and there are 6 balls of same color.
Now the next two will surely give you two of this left over color, so 24+2 are a MUST to be sure to pick up two of each.
thus our answer is 26.
_________________
General GMAT Forum Moderator
User avatar
V
Joined: 15 Jan 2018
Posts: 640
Concentration: General Management, Finance
GMAT 1: 720 Q50 V37
Premium Member Reviews Badge
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, 00:16
1
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.
_________________
In case you find my post helpful, please provide me with kudos. Thank you!

New to GMAT Club or overwhelmed with so many resources? Follow the GMAT Club Study Plan!
Not happy with your GMAT score? Retaking GMAT Strategies!
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5277
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Ben has 30 pencils in a box. Each of the pencils is one of 5 different  [#permalink]

Show Tags

New post Updated on: 09 Jan 2019, 01:31
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 :

for each color we have 6 pencils each
so incase of worst 4 colors 6 pencils 4*6;24
after which the next set of 26 would be the min no pencils would be 26
IMO 26

Originally posted by Archit3110 on 27 Nov 2018, 08:58.
Last edited by Archit3110 on 09 Jan 2019, 01:31, edited 1 time in total.
Manager
Manager
avatar
B
Joined: 02 Oct 2018
Posts: 62
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, 04:25
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
Manager
Manager
avatar
B
Joined: 27 Nov 2015
Posts: 121
GMAT ToolKit User
Re: Ben has 30 pencils in a box. Each of the pencils is one of 5 different  [#permalink]

Show Tags

New post 08 Jan 2019, 06:04
chetan2u wrote:
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.


Hi Chetan,

Is the answer 27 - D, or 26 - C?
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8180
Re: Ben has 30 pencils in a box. Each of the pencils is one of 5 different  [#permalink]

Show Tags

New post 08 Jan 2019, 07:06
nausherwan wrote:
chetan2u wrote:
ParthSanghavi wrote:


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.


Hi Chetan,

Is the answer 27 - D, or 26 - C?


Hi..
Answer will be 26. There was a typo, which I have corrected.
Thanks
_________________
GMAT Club Bot
Re: Ben has 30 pencils in a box. Each of the pencils is one of 5 different   [#permalink] 08 Jan 2019, 07:06
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  





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