The 250 students enrolled at ABC University are taking undergraduate, graduate courses, or both. How many students...

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Source: Princeton Review

The 250 students enrolled at ABC University are taking undergraduate courses, graduate courses, or both. How many students are taking graduate courses?

1) 200 students are taking undergraduate courses
2) 50 students are taking both undergraduate and graduate courses

The OA is C
Source: — Data Sufficiency |

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Total students = 250
Let the number of students taking undergraduate courses = a
Let the number of students taking graduate courses = b
For 2 overlapping sets, total = set 1 + set 2 - both + none
i.e 250 = a + b - both +0

Target question => How many students are taking graduate courses? i.e find the value of b

Statement 1 => 200 students are taking undergraduate courses
a = 200 but the value of ''b'' and ''both'' is unknown so statement 1 is NOT SUFFICIENT

Statement 2 => 50 students are taking both undergraduate and graduate courses
both student = 50 but the value of a and b is unknown so statement 2 is NOT SUFFICIENT

Combining both statements together =>
From statement 1 =>
a = 200
From statement 2 => both = 50
From question stem => total = a + b - both + none
250 = 200 + b - 50 + 0
250 = 150 + b
b = 250 - 150 = 100
Both statements combined together ARE SUFFICIENT

Answer = C