A certain high school has 5,000 students. Of these students, x are taking music, y are taking...

[AAPL]

Official Guide

A certain high school has 5,000 students. Of these students, x are taking music, y are taking art, and z are taking both music and art. How many students are taking neither music nor art?

A. 5,000 - z
B. 5,000 - x - y
C. 5,000 - x + z
D. 5,000 - x - y - z
E. 5,000 - x - y + z

OA E

[Jay@ManhattanReview]

Official Guide

A certain high school has 5,000 students. How many students are taking neither music nor art?

A. 5,000 - z
B. 5,000 - x - y
C. 5,000 - x + z
D. 5,000 - x - y - z
E. 5,000 - x - y + z

OA E

Given that of these students, x are taking music, y are taking art, and z are taking both music and art, the no. of students taking art, music or both = x + y – z

Thus, the no. of students taking neither music nor art = 5,000 – x – y + z

The correct answer: E

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

Official Guide

A certain high school has 5,000 students. Of these students, x are taking music, y are taking art, and z are taking both music and art. How many students are taking neither music nor art?

A. 5,000 - z
B. 5,000 - x - y
C. 5,000 - x + z
D. 5,000 - x - y - z
E. 5,000 - x - y + z

OA E

We can use the following formula:

Total students = # taking music + # taking art - # taking both + # taking neither

5,000 = x + y - z + neither

5,000 - x - y + z = neither

Answer: E