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.