Problem Solving

boomgoesthegmat wrote: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) 5000 - z
B) 5000 - x - y
C) 5000 - x + z
D) 5000 - x - y - z
E) 5000 - x - y + z

OA: E

Solution:

We are given an overlapping set with 2 categories: music and art. In any two-category set problem we can use the following formula:

Total number of members = # in category A + # in category B - # in both categories + # in neither category

Using the formula for the current problem we have:

5,000 = x + y - z + neither

5,000 - x - y + z = neither

Answer:E

boomgoesthegmat wrote: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) 5000 - z
B) 5000 - x - y
C) 5000 - x + z
D) 5000 - x - y - z
E) 5000 - x - y + z

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

Hi All,

While this question can be solved Algebraically, it can also be solved by TESTing VALUES and taking some basic notes:

We're given a series of facts to work with:
1) A certain high school has 5,000 students.
2) Of these students:
X are taking music,
Y are taking art, and
Z are taking BOTH music and art.

We're asked how many students are taking NEITHER music nor art?

Let's TEST
X = 2
Y = 2
Z = 1

So, we have 2 students taking music, 2 taking art and 1 taking BOTH music and art. That 1 person has been counted TWICE though (once in the music 'group' and once in the art 'group'), so what we really have is...

1 student taking JUST music
1 student taking JUST art
1 student taking BOTH music and art
Total = 3 students

We're asked for the total number of students who are taking NEITHER Course. That is 5000 - 3 = 4997. So that's the answer that we're looking for when X=2, Y=2 and Z=1. There's only one answer that matches...

Final Answer: E

GMAT assassins aren't born, they're made,
Rich