A researcher collected a total of 500 samples of river water from vari

I struggled to do this in under 2 mins, are there any fast ways to do this?

 
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Hi ashdank94,

Though the best way to solve such questions is to use Venn Diagram for overlapping sets, there is a faster way but only for this question.

The first question asks to find the number for BOTH X and Y. So, we can look at the relevant pieces of information and look for statements that mention X and Y.

• Exactly 175 samples contained Microorganism X but not Microorganism Y, and exactly 4% of those contained Microorganism Z.
• Exactly 145 samples contained Microorganism Y but not Microorganism X, and exactly 20% of those contained Microorganism Z.
• Exactly 60 samples contained both Microorganism X and Microorganism Y, and exactly 15% of those contained Microorganism Z.

Thus, 4% of 175 = 7 and 15% of 60 = 9 have both X and Y. The answer is 16.

Now,
The second question asks to find the number for BOTH Y and Z. So, we can look at the relevant pieces of information and look for statements that mention Y and Z.

• Exactly 175 samples contained Microorganism X but not Microorganism Y, and exactly 4% of those contained Microorganism Z.
• Exactly 145 samples contained Microorganism Y but not Microorganism X, and exactly 20% of those contained Microorganism Z.
• Exactly 60 samples contained both Microorganism X and Microorganism Y, and exactly 15% of those contained Microorganism Z.

Thus, 20% of 145 = 29 and 15% of 60 = 9 have both Y and Z. The answer is 38.

This approach avoids calculating all the other numbers unnecessarily. But remember, this approach is relevant for ONLY THIS QUESTION. For other questions, we might have to calculate all the other numbers before actually answering the question.

Hope that helps!­

Please find the venn diagram atteched herewith. It can be easily solved by looking at the venn diagram.­

A researcher collected a total of 500 samples of river water from various locations along a certain river and tested the samples for the presence of Microorganisms X, Y, and Z, with the following results:

• Exactly 175 samples contained Microorganism X but not Microorganism Y, and exactly 4% of those contained Microorganism Z.
• Exactly 145 samples contained Microorganism Y but not Microorganism X, and exactly 20% of those contained Microorganism Z.
• Exactly 60 samples contained both Microorganism X and Microorganism Y, and exactly 15% of those contained Microorganism Z.

Based on the information provided, select for Both X and Z the total number of samples that contained both Microorganism X and Microorganism Z, and select for Both Y and Z the total number of samples that contained both Microorganism Y and Microorganism Z. Make only two selections, one in each column.