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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
84% (02:00) correct
16%
(01:53)
wrong
based on 1734
sessions
History
Date
Time
Result
Not Attempted Yet
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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
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Posts: 3,651
blog
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.
Attachments
Picture2.png [ 24.83 KiB | Viewed 33752 times ]
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reto
Retired Moderator
Joined: 29 Apr 2015
Last visit: 24 Aug 2018
Posts: 716
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE:Asset Management (Finance: Investment Banking)
Schools: LBS MIF '19
Posts: 716
blog
Set up a 3x3 table to solve this:
Attachment:
Table.jpg [ 25.25 KiB | Viewed 32190 times ]
Target value is marked with question mark.
Grey values are values derived from the question stem.
Orange value is derived from statement 1. With this you can calculate "Off Campus / > 20Yrs" = 390. However this does not lead us to the question mark. > IS
Blue Value is derived from statement 2. With this on its own, you cannot find "?". > IS
Together you will be able to find "?" in the table. 640 + X = 800 and X - 60 = ?
General Discussion
Posts: 1,138
blog
C. Use a double set matrix
We find that the number of On campus under 20 yrs old =100.
C
from stat 1 all you can tell is the number of 20 plus yr olds who live off campus
from stat 2 all you can tell is the number of less than 20s who live off campus
together, you can find the number of total students who live off campus, and therefore, the number that live on campus . as you already know the number who live on campus that are 20 plus, the difference between the total and that number will be the number of less than 20s who live on campus.
from stat 1 all you can tell is the number of 20 plus yr olds who live off campus
from stat 2 all you can tell is the number of less than 20s who live off campus
together, you can find the number of total students who live off campus, and therefore, the number that live on campus . as you already know the number who live on campus that are 20 plus, the difference between the total and that number will be the number of less than 20s who live on campus.
Quote:
niks18 Bunuel amanvermagmat gmatbusters chetan2u
I have a query regarding approach by reto. In actual mock I was confused in forming such a table by
not knowing what to label rows and columns. Do the labels need to be mutually exclusive, eg. If a column
is labelled football then next column can not be baseball, it has to be those not playing football. In simpler
words, the two events CAN NOT occur together at any point of time. (mutually exclusive)
Can this problem be also solved using venn diagrams?
Posts: 1,926
the two events CAN NOT occur together at any point of time. (mutually exclusive)
YES
Can this problem be also solved using venn diagrams?
YES
Posted from my mobile device
YES
Can this problem be also solved using venn diagrams?
YES
adkikani
Posted from my mobile device
GMAT 1: 750 Q49 V42
Posts: 469
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