OF the 800 students at a certain college, 250 students live on campus and are more than 20 years old. How many of the 800 students live on campus and are 20 years old or less?
1. 640 students at the college are more than 20 years old.
2. 60 students at the college are 20 years old or less and live off campus.
This question involves a lot of data points, and therefore can quickly get overwhelming!
The key to solving such questions is to represent the given information visually
One good visual representation for the given info is the Double set matrix as mentioned by GMATBLACKBELT above.
Another representation is as attached. In our concept files, we call this a TREE STRUCTURE
The question asks us about the number of students who live on campus and are <= 20 years. Let the number of such students = x
Therefore, total number of students who live ON campus = 250 + x
Total number of students who live OFF campus = 800 - (250 + x) = 550 - x
Let the number of students who live OFF campus and are >20 years = y
This means, the number of students who live OFF campus and are <= 20 years = (550 - x) - y
(Refer to Attached Picture for visual representation of this info on the Tree Structure)
We are now ready to assess if the information given in Statements 1 and 2 is sufficient to determine the value of x.Per Statement 1,
250 + y = 640
This equation gets us the value of y. We need the value of x. Clearly, Statement 1 alone is not sufficient.Per Statement 2
550 - x - y = 60
This is a linear equation in 2 variables. Since we have only equation, we will not be able to determine a unique value of x. Therefore, Statement 2 alone is not sufficient either.Combining Statements 1 and 2:
We get two linear equations in two variables. Solving both these equations together, we WILL be able to get a unique value of x.
Therefore, the correct answer choice is C - Both the statements together are sufficient to answer the question.The Important Takeaway from this discussion: VISUAL Representation of the given data is the key to simplifying questions involving two or more sets.
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