enigma123 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

The best way to solve questions containing four different items is to draw a matrix box. As per the question:

Total employees relocated to X = 25% of 200 = 50

Total employees relocated to Y = 75% of 200 = 150

Total employees who prefer city X = 60% of 200 = 120

Total employees who prefer city Y = 40% of 200 = 80

This can be represented in a matrix box as shown below:

Attachment:

Matrix_1.png [ 2.51 KiB | Viewed 2877 times ]
So we need to maximize the cells marked with green i.e.

employees who prefer city X and gets relocated to city X + employees who prefer city Y and gets relocated to city Y.

Maximum possible value of

Prefer X - Relocate X cell is 50. Then the only possible value for

Prefer X - Relocate Y cell is 70 because the total employees who prefer city X is 120.

As

Prefer X - Relocate X cell is 50, so

Prefer Y - Relocate X cell has to be 0 because total employees actually relocated to city X is 50. And if

Prefer Y - Relocate X is 0 then

Prefer Y - Relocate Y has to be 80 because total employees who preferred city Y is 80.

So now the completed matrix box looks like this:

Attachment:

Matrix_2.png [ 2.85 KiB | Viewed 2878 times ]
So total sum of green cells (employees who will be relocated to the city they prefer) = 50 + 80 = 130

Hence the correct answer is D

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