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A number of ties are individually packaged in unmarked boxes. What is 08 Mar 2018, 21:19
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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.
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A number of ties are individually packaged in unmarked boxes. What is 08 Mar 2018, 21:21
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Bunuel
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.
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Check other Worst Case Scenario Questions from our Special Questions Directory to understand the concept better.
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A number of ties are individually packaged in unmarked boxes. What is 09 Mar 2018, 01:21
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Bunuel
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.
Show more

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
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A number of ties are individually packaged in unmarked boxes. What is 09 Mar 2018, 01:51
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Bunuel
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.
Show more


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
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A number of ties are individually packaged in unmarked boxes. What is 09 Jun 2018, 06:33
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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?
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A number of ties are individually packaged in unmarked boxes. What is 09 Jun 2018, 06:34
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Bunuel
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
Show more


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?
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A number of ties are individually packaged in unmarked boxes. What is 09 Jun 2018, 06:58
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nitishatomar
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?
Show more
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)

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A number of ties are individually packaged in unmarked boxes. What is 09 Jun 2018, 07:10
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nitishatomar
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?
Show more
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.
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A number of ties are individually packaged in unmarked boxes. What is 09 Jun 2018, 07:11
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nitishatomar
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)

Show more

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.
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A number of ties are individually packaged in unmarked boxes. What is 09 Jun 2018, 07:15
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Bunuel
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
Show more

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?
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A number of ties are individually packaged in unmarked boxes. What is 09 Jun 2018, 09:31
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Akash720
nitishatomar
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.
Show more
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
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A number of ties are individually packaged in unmarked boxes. What is 09 Jun 2018, 21:23
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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
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A number of ties are individually packaged in unmarked boxes. What is 02 Dec 2022, 12:13
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A

Given 5 distinct colors, if you open 10 boxes and do not get 3 ties with the same color, you will get 2 ties of each color. Once you open 11th box, you will get the third copy for one of the colors.
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