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 boxesAs per the three points mentioned above we have no information about point 1 and 2 hence
NOT SUFFICIENT
COmbining the two statementsWe 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?