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overlapping set

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overlapping set

by buoyant » Thu Dec 25, 2014 12:14 pm
Of the 200 employees in a certain company, 25 percent will
be relocated to City X and the remaining 75 percent will be
relocated to City Y. However, 40 percent of the employees
prefer City Y and 60 percent prefer City X. What is the highest
possible number of employees who will be relocated to the city
they prefer?
(A) 65
(B) 100
(C) 115
(D) 130
(E) 135

is there a shortcut approach to this question? I solved it in a time consuming way.

[spoiler]OA: D[/spoiler]
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by GMATGuruNY » Thu Dec 25, 2014 1:18 pm
buoyant wrote:Of the 200 employees in a certain company, 25 percent will
be relocated to City X and the remaining 75 percent will be
relocated to City Y. However, 40 percent of the employees
prefer City Y and 60 percent prefer City X. What is the highest
possible number of employees who will be relocated to the city
they prefer?
(A) 65
(B) 100
(C) 115
(D) 130
(E) 135

is there a shortcut approach to this question? I solved it in a time consuming way.

[spoiler]OA: D[/spoiler]
To MAXIMIZE the number of employees assigned to the city they prefer, we must MINIMIZE the number of disappointed employees.

X:
40% prefer X.
75% will be relocated to X.
Thus, every researcher who prefers X can be relocated to X.

Y:
60% prefer Y.
Only 25% will be relocated to Y.
Thus, at least 35% of the 200 employees will be disappointed.
Thus:
Minimum number of disappointed employees = 35% of 200 = 70.
Maximum number of employees assigned to the city they prefer = 200-70 = 130.

The correct answer is D.
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