LUANDATO wrote:In Jackson School, 150 students study Spanish or Physics or Both. If 50 of these students do not study Spanish, how many of these students study both Spanish and Physics?
1) Of the 150 students, 30 do not study physics.
2) A total of 120 students study physics.
This is an EITHER/OR group problem.
Every student EITHER studies Spanish OR does not.
Every student EITHER studies physics OR does not.
For an EITHER/OR group problem, use a DOUBLE-MATRIX to organize the data.
In a double-matrix, the entries in any given row or column must add up to the TOTAL of that row or column.
Let S = Spanish, NS = not Spanish, P = physics, NP = not physics.
Here is the matrix:
150 students study Spanish, physics or both.
50 of these students do not study Spanish.
Because every student studies Spanish, physics or both, the center box -- which represents the number who study NEITHER subject -- must be given a value of 0.
The following matrix is yielded:
Statement 1: Of the 150 students, 30 do not study physics.
The following matrix is yielded:
Inserting the remaining values, we get:
Thus, the number who study both subjects = 70.
SUFFICIENT.
Statement 2: A total of 120 students study physics.
The following matrix is yielded:
Inserting the remaining values, we get:
Thus, the number who study both subjects = 70.
SUFFICIENT.
The correct answer is
D.
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