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The employees in a company ordered pizza or spaghetti. One-half of the employees ordered pizza, 35 of the employees ord

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by Max@Math Revolution » Tue Jul 21, 2020 2:13 am
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[GMAT math practice question]

The employees in a company ordered pizza or spaghetti. One-half of the employees ordered pizza, 3/5 of the employees ordered spaghetti, and 30% of the employees order both pizza and spaghetti. Six employees ordered neither. How many employees work for the company?

A. 15
B. 20
C. 25
D. 30
E. 35
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Re: The employees in a company ordered pizza or spaghetti. One-half of the employees ordered pizza, 35 of the employees

by Max@Math Revolution » Thu Jul 23, 2020 1:15 am
=>
7.21ps(a).png
Assume a + b + c + d = 100%.
We have a + c = 50%, a + b = 60% and a = 30%.
Substituting a = 30% into the other 2 equations gives us, a + c = 50%, 30% + c = 50%, c = 20% and a + b = 60%, 30% + b = 60%, b = 30%.
We have d = 20% since a + b + c + d = 100% and a + b + c = 80%.
Since 6 employees make up 20% of the total employees we have 6e = 20100. Cross multiplying gives us 20e = 600, and the total number of employees = 30.

Therefore, D is the correct answer.
Answer: D
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