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

Question

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.

VivekSri · Accepted Answer

We can easily solve this question by set theory.
Remember for set theory put all the variable in the set. This will solve the question easily

Posted from my mobile device

Vinit800HBS · Answer

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!

chetan2u · Answer

We require to solve only for the data asked to solve this within a minute. Remember, time saved here will give you extra time for some harder question

•  Exactly 175 samples contained Microorganism X but not Microorganism Y, and exactly 4% of those contained Microorganism Z.  
4% of 175 or 7 samples contain Only X and Z
96% of 175 or 175-7 or 168 samples contain Only X

• Exactly 145 samples contained Microorganism Y but not Microorganism X, and exactly 20% of those contained Microorganism Z. 
20% of 145 or 29 samples contain Only Y and Z

•  Exactly 60 samples contained both Microorganism X and Microorganism Y, and exactly 15% of those contained Microorganism Z. 
15% of 60 or 9 samples contain all three

Both X and Z = Only (X and Z) + All = 7+T=16
Both Y and Z = Only (Y and Z) + All = 29+T=38

ashdank94 · Answer

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

sayan640 · Answer

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

demawtf · Answer

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.

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

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards