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

It is currently 22 Oct 2018, 14:06

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

A number of ties are individually packaged in unmarked boxes. What is

  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: 50042
A number of ties are individually packaged in unmarked boxes. What is  [#permalink]

Show Tags

New post 08 Mar 2018, 21:19
1
3
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

33% (01:27) correct 67% (01:28) wrong based on 74 sessions

HideShow timer Statistics

A number of ties are individually packaged in unmarked boxes. What is the maximum number of boxes that must be opened if boxes are opened at random until there are three open boxes containing ties of the same color?

(1) There are five distinct colors of ties.

(2) There are 25 boxes.

_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50042
Re: A number of ties are individually packaged in unmarked boxes. What is  [#permalink]

Show Tags

New post 08 Mar 2018, 21:21
Bunuel wrote:
A number of ties are individually packaged in unmarked boxes. What is the maximum number of boxes that must be opened if boxes are opened at random until there are three open boxes containing ties of the same color?

(1) There are five distinct colors of ties.

(2) There are 25 boxes.


Check other Worst Case Scenario Questions from our Special Questions Directory to understand the concept better.
_________________

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

CEO
CEO
User avatar
P
Joined: 08 Jul 2010
Posts: 2569
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: A number of ties are individually packaged in unmarked boxes. What is  [#permalink]

Show Tags

New post 09 Mar 2018, 01:21
Bunuel wrote:
A number of ties are individually packaged in unmarked boxes. What is the maximum number of boxes that must be opened if boxes are opened at random until there are three open boxes containing ties of the same color?

(1) There are five distinct colors of ties.

(2) There are 25 boxes.


Question: How many boxes need to be opened to get three ties of same color?

To answer the question we need
1) The number of colors available
2) How many boxes of each color
3) How many boxes in total

Statement 1: There are five distinct colors of ties.
As per the three points mentioned above we have no information about point 2 and 3 hence
NOT SUFFICIENT

Statement 2: There are 25 boxes
As per the three points mentioned above we have no information about point 1 and 2 hence
NOT SUFFICIENT

COmbining the two statements

We still don't know if each color has equal number of boxes hence

NOT SUFFICIENT

Answer: option E
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Manager
Manager
avatar
B
Joined: 11 Feb 2017
Posts: 192
Re: A number of ties are individually packaged in unmarked boxes. What is  [#permalink]

Show Tags

New post 09 Mar 2018, 01:51
Bunuel wrote:
A number of ties are individually packaged in unmarked boxes. What is the maximum number of boxes that must be opened if boxes are opened at random until there are three open boxes containing ties of the same color?

(1) There are five distinct colors of ties.

(2) There are 25 boxes.



A) 5 distinct colors but it can be just 5 boxes only , so we can never find 3 of same color

insuff

B) 25 boxes but if all have same color then 3 boxes will do work and if there are 25 colors then its impossible

insuff


If 5 colors are there in 25 boxes
So , let us say colors r

R,B,G,Y,P
R has 10 box
B has 11 box
Y has 2 box
G and P has 1 box

so answer will be different for each color

Insuff



E answer
Intern
Intern
avatar
Joined: 19 May 2018
Posts: 6
Re: A number of ties are individually packaged in unmarked boxes. What is  [#permalink]

Show Tags

New post 09 Jun 2018, 06:33
Hi,

I found this question in Veritas Prep question bank. They chose option 1: That choice A is sufficient. The reason given is:
Statement (1) gives that there are five distinct colors of ties. Some students may feel that this is insufficient if they are thinking about this in terms of probability. However, if you think about it in terms of scenarios, it should be clear that this is sufficient.

If there are five different colors of ties, consider the worst case scenario. You open one of each color (for a total of five). Then you open a second of each color (for a total of ten). You then only need to open one more box in order to be guaranteed to have a third of any color. It doesn’t matter what that color is – you have two of each color already. So by opening the 11th box you are guaranteed to have three same-colored ties. Notice that even though there are other numbers of boxes that could yield three ties of the same color (you could, for example, open three in a row that are of the same color), that because the question is asking for a “worst case scenario”, this means that you can be done. Statement (1) is sufficient. Eliminate (B), (C), and (E).

Do you think this is right?
Intern
Intern
avatar
Joined: 19 May 2018
Posts: 6
Re: A number of ties are individually packaged in unmarked boxes. What is  [#permalink]

Show Tags

New post 09 Jun 2018, 06:34
1
GMATinsight wrote:
Bunuel wrote:
A number of ties are individually packaged in unmarked boxes. What is the maximum number of boxes that must be opened if boxes are opened at random until there are three open boxes containing ties of the same color?

(1) There are five distinct colors of ties.

(2) There are 25 boxes.


Question: How many boxes need to be opened to get three ties of same color?

To answer the question we need
1) The number of colors available
2) How many boxes of each color
3) How many boxes in total

Statement 1: There are five distinct colors of ties.
As per the three points mentioned above we have no information about point 2 and 3 hence
NOT SUFFICIENT

Statement 2: There are 25 boxes
As per the three points mentioned above we have no information about point 1 and 2 hence
NOT SUFFICIENT

COmbining the two statements

We still don't know if each color has equal number of boxes hence

NOT SUFFICIENT

Answer: option E



Hi,

I found this question in Veritas Prep question bank. They chose option 1: That choice A is sufficient. The reason given is:
Statement (1) gives that there are five distinct colors of ties. Some students may feel that this is insufficient if they are thinking about this in terms of probability. However, if you think about it in terms of scenarios, it should be clear that this is sufficient.

If there are five different colors of ties, consider the worst case scenario. You open one of each color (for a total of five). Then you open a second of each color (for a total of ten). You then only need to open one more box in order to be guaranteed to have a third of any color. It doesn’t matter what that color is – you have two of each color already. So by opening the 11th box you are guaranteed to have three same-colored ties. Notice that even though there are other numbers of boxes that could yield three ties of the same color (you could, for example, open three in a row that are of the same color), that because the question is asking for a “worst case scenario”, this means that you can be done. Statement (1) is sufficient. Eliminate (B), (C), and (E).

Do you think this is right?
Senior Manager
Senior Manager
User avatar
G
Joined: 17 Jan 2017
Posts: 295
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Premium Member CAT Tests
Re: A number of ties are individually packaged in unmarked boxes. What is  [#permalink]

Show Tags

New post 09 Jun 2018, 06:58
nitishatomar wrote:
Hi,

I found this question in Veritas Prep question bank. They chose option 1: That choice A is sufficient. The reason given is:
Statement (1) gives that there are five distinct colors of ties. Some students may feel that this is insufficient if they are thinking about this in terms of probability. However, if you think about it in terms of scenarios, it should be clear that this is sufficient.

If there are five different colors of ties, consider the worst case scenario. You open one of each color (for a total of five). Then you open a second of each color (for a total of ten). You then only need to open one more box in order to be guaranteed to have a third of any color. It doesn’t matter what that color is – you have two of each color already. So by opening the 11th box you are guaranteed to have three same-colored ties. Notice that even though there are other numbers of boxes that could yield three ties of the same color (you could, for example, open three in a row that are of the same color), that because the question is asking for a “worst case scenario”, this means that you can be done. Statement (1) is sufficient. Eliminate (B), (C), and (E).

Do you think this is right?

This is right. We have five distinct colors and they are asking to open boxes till we have 3 boxes of same color then definitely we have atleast 15 boxes to open at least. And the maximum number of boxes we can open will never exceed 11. Hence (A)

Sent from my XT1562 using GMAT Club Forum mobile app
_________________

Only those who risk going too far, can possibly find out how far one can go

Intern
Intern
avatar
Joined: 19 May 2018
Posts: 6
Re: A number of ties are individually packaged in unmarked boxes. What is  [#permalink]

Show Tags

New post 09 Jun 2018, 07:10
Akash720 wrote:
nitishatomar wrote:
Hi,

I found this question in Veritas Prep question bank. They chose option 1: That choice A is sufficient. The reason given is:
Statement (1) gives that there are five distinct colors of ties. Some students may feel that this is insufficient if they are thinking about this in terms of probability. However, if you think about it in terms of scenarios, it should be clear that this is sufficient.

If there are five different colors of ties, consider the worst case scenario. You open one of each color (for a total of five). Then you open a second of each color (for a total of ten). You then only need to open one more box in order to be guaranteed to have a third of any color. It doesn’t matter what that color is – you have two of each color already. So by opening the 11th box you are guaranteed to have three same-colored ties. Notice that even though there are other numbers of boxes that could yield three ties of the same color (you could, for example, open three in a row that are of the same color), that because the question is asking for a “worst case scenario”, this means that you can be done. Statement (1) is sufficient. Eliminate (B), (C), and (E).

Do you think this is right?

This is right. We have five distinct colors and they are asking to open boxes till we have 3 boxes of same color then definitely we have atleast 15 boxes to open at least. And the maximum number of boxes we can open will never exceed 11. Hence (A)



Ok, but the 'expert's answer on this thread has been 'E'. Also, my reasoning which goes against option A can be structured as:

If we take only option A, I.E., we only know that there are 5 distinct colors and not about the number of boxes in total, then, let's say that the ties can be grouped into T1, T2, T3, T4 and T5 (on the basis of color)

Now, suppose I start opening the boxes and find that I have opened 11 boxes in succession with ties from the color group - T1. This is because I CAN ASSUME that there might be infinite number of boxes to open and the ratio of the groups hasn't been provided. For e.g. it could be T1 - 11, T2 - 1 , T3 -4, T4-5, T5-1 or one of the innumerable other combinations. I'm unable to understand why 11 HAS to be the maximum.
Intern
Intern
avatar
Joined: 19 May 2018
Posts: 6
Re: A number of ties are individually packaged in unmarked boxes. What is  [#permalink]

Show Tags

New post 09 Jun 2018, 07:11
Akash720 wrote:
nitishatomar wrote:
Hi,

I found this question in Veritas Prep question bank. They chose option 1: That choice A is sufficient. The reason given is:
Statement (1) gives that there are five distinct colors of ties. Some students may feel that this is insufficient if they are thinking about this in terms of probability. However, if you think about it in terms of scenarios, it should be clear that this is sufficient.

If there are five different colors of ties, consider the worst case scenario. You open one of each color (for a total of five). Then you open a second of each color (for a total of ten). You then only need to open one more box in order to be guaranteed to have a third of any color. It doesn’t matter what that color is – you have two of each color already. So by opening the 11th box you are guaranteed to have three same-colored ties. Notice that even though there are other numbers of boxes that could yield three ties of the same color (you could, for example, open three in a row that are of the same color), that because the question is asking for a “worst case scenario”, this means that you can be done. Statement (1) is sufficient. Eliminate (B), (C), and (E).

Do you think this is right?

This is right. We have five distinct colors and they are asking to open boxes till we have 3 boxes of same color then definitely we have atleast 15 boxes to open at least. And the maximum number of boxes we can open will never exceed 11. Hence (A)



Ok, but the 'expert's answer on this thread has been 'E'. Also, my reasoning which goes against option A can be structured as:

If we take only option A, I.E., we only know that there are 5 distinct colors and not about the number of boxes in total, then, let's say that the ties can be grouped into T1, T2, T3, T4 and T5 (on the basis of color)

Now, suppose I start opening the boxes and find that I have opened 11 boxes in succession with ties from the color group - T1. This is because I CAN ASSUME that there might be infinite number of boxes to open and the ratio of the groups hasn't been provided. For e.g. it could be T1 - 11, T2 - 1 , T3 -4, T4-5, T5-1 or one of the innumerable other combinations. I'm unable to understand why 11 HAS to be the maximum.
Intern
Intern
avatar
Joined: 19 May 2018
Posts: 6
Re: A number of ties are individually packaged in unmarked boxes. What is  [#permalink]

Show Tags

New post 09 Jun 2018, 07:15
GMATinsight wrote:
Bunuel wrote:
A number of ties are individually packaged in unmarked boxes. What is the maximum number of boxes that must be opened if boxes are opened at random until there are three open boxes containing ties of the same color?

(1) There are five distinct colors of ties.

(2) There are 25 boxes.


Question: How many boxes need to be opened to get three ties of same color?

To answer the question we need
1) The number of colors available
2) How many boxes of each color
3) How many boxes in total

Statement 1: There are five distinct colors of ties.
As per the three points mentioned above we have no information about point 2 and 3 hence
NOT SUFFICIENT

Statement 2: There are 25 boxes
As per the three points mentioned above we have no information about point 1 and 2 hence
NOT SUFFICIENT

COmbining the two statements

We still don't know if each color has equal number of boxes hence

NOT SUFFICIENT

Answer: option E


Hi,

I found this question in Veritas Prep question bank. They chose option 1: That choice A is sufficient. The reason given is:
Statement (1) gives that there are five distinct colors of ties. Some students may feel that this is insufficient if they are thinking about this in terms of probability. However, if you think about it in terms of scenarios, it should be clear that this is sufficient.

If there are five different colors of ties, consider the worst case scenario. You open one of each color (for a total of five). Then you open a second of each color (for a total of ten). You then only need to open one more box in order to be guaranteed to have a third of any color. It doesn’t matter what that color is – you have two of each color already. So by opening the 11th box you are guaranteed to have three same-colored ties. Notice that even though there are other numbers of boxes that could yield three ties of the same color (you could, for example, open three in a row that are of the same color), that because the question is asking for a “worst case scenario”, this means that you can be done. Statement (1) is sufficient. Eliminate (B), (C), and (E).

Do you think this is right?
Senior Manager
Senior Manager
User avatar
G
Joined: 17 Jan 2017
Posts: 295
Location: India
GPA: 4
WE: Information Technology (Computer Software)
Premium Member CAT Tests
Re: A number of ties are individually packaged in unmarked boxes. What is  [#permalink]

Show Tags

New post 09 Jun 2018, 09:31
nititron wrote:
Akash720 wrote:
nitishatomar wrote:
Hi,

I found this question in Veritas Prep question bank. They chose option 1: That choice A is sufficient. The reason given is:
Statement (1) gives that there are five distinct colors of ties. Some students may feel that this is insufficient if they are thinking about this in terms of probability. However, if you think about it in terms of scenarios, it should be clear that this is sufficient.

If there are five different colors of ties, consider the worst case scenario. You open one of each color (for a total of five). Then you open a second of each color (for a total of ten). You then only need to open one more box in order to be guaranteed to have a third of any color. It doesn’t matter what that color is – you have two of each color already. So by opening the 11th box you are guaranteed to have three same-colored ties. Notice that even though there are other numbers of boxes that could yield three ties of the same color (you could, for example, open three in a row that are of the same color), that because the question is asking for a “worst case scenario”, this means that you can be done. Statement (1) is sufficient. Eliminate (B), (C), and (E).

Do you think this is right?

This is right. We have five distinct colors and they are asking to open boxes till we have 3 boxes of same color then definitely we have atleast 15 boxes to open at least. And the maximum number of boxes we can open will never exceed 11. Hence (A)



Ok, but the 'expert's answer on this thread has been 'E'. Also, my reasoning which goes against option A can be structured as:

If we take only option A, I.E., we only know that there are 5 distinct colors and not about the number of boxes in total, then, let's say that the ties can be grouped into T1, T2, T3, T4 and T5 (on the basis of color)

Now, suppose I start opening the boxes and find that I have opened 11 boxes in succession with ties from the color group - T1. This is because I CAN ASSUME that there might be infinite number of boxes to open and the ratio of the groups hasn't been provided. For e.g. it could be T1 - 11, T2 - 1 , T3 -4, T4-5, T5-1 or one of the innumerable other combinations. I'm unable to understand why 11 HAS to be the maximum.

Question is how many maximum number of boxes can be opened till we have 3 open boxes of same color tie.

Therefore if you open 3 boxes of same color T1(As mentioned by you) then we need to stop there as we have 3 boxes of same color tie in open and 3 is not the maximum number.

Thanks,
Akash
_________________

Only those who risk going too far, can possibly find out how far one can go

Intern
Intern
avatar
B
Joined: 18 Oct 2017
Posts: 1
Re: A number of ties are individually packaged in unmarked boxes. What is  [#permalink]

Show Tags

New post 09 Jun 2018, 21:23
A number of ties are individually packaged in unmarked boxes. What is the maximum number of boxes that must be opened if boxes are opened at random until there are three open boxes containing ties of the same color?

(1) There are five distinct colors of ties.

(2) There are 25 boxes.

Statement 1:

Suppose there are 5 colors R, B, G, Y, P.

The maximum number is 11 because of the following
1st 5 opens : R, B, G, Y, P or any other order with out repeating any colors,
2nd 5 opens : R, B, G, Y, P or any other order with out repeating any colors,
The 11th opening must be one of the 5 colors already opened twice and hence we have three boxes of the same color. (sufficient)

Statement 2: there is no information about number of colors.(not sufficient)

Hence answer is A
GMAT Club Bot
Re: A number of ties are individually packaged in unmarked boxes. What is &nbs [#permalink] 09 Jun 2018, 21:23
Display posts from previous: Sort by

A number of ties are individually packaged in unmarked boxes. What is

  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®.