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A certain high school has 5,000 (OG2016)

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boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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A certain high school has 5,000 (OG2016)

Post Fri May 06, 2016 12:30 pm
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

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Post Thu Dec 14, 2017 6:00 am
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

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Post Wed May 11, 2016 11:47 pm
You could also just pick numbers.

Suppose x = 100, y = 50, and z = 10.

Since z is counted in both x and y, we have 90 taking just music, 40 taking just art, and 10 taking both.

5000 - 90 - 40 - 10 = 4860 = E.

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Post Sat May 07, 2016 7:50 pm
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
Music = x,
Art = y
Both Music and Art = z

Therefore people who take atleast one = x + y - z
People who have taken none = 5000 - (x + y - z) = 5000 - x - y + z

Correct Option: E

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Post Mon May 09, 2016 10:46 am
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

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800_or_bust Master | Next Rank: 500 Posts Default Avatar
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Post Mon May 09, 2016 11:31 am
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
In lieu of solving, I'll just post a reminder that you have to add the members of the combined set to avoid double counting. With that said, the answer should be fairly intuitive.

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