jose.mario.amaya wrote:At company X, 44% of the employees that own laptops do not own cellphone, and 30% of the employees that own cellphone do not own laptops. If the number of employees without laptops is 40% less than the employees with laptops, then what percent of the company's employees neither own a laptop nor a cellphone ??
A. 17.5
B. 22.5
C. 24
D. 26
E. 28
B
This is an EITHER/OR problem.
Every employee EITHER owns a laptop OR doesn't.
Every employee EITHER owns a cell or OR doesn't.
To organize the data, draw a GROUP GRID:
In the grid above, L = laptop, NL = no laptop, C = cell, NC = no cell.
44% of the employees who own a laptop do not own a cellphone.
Thus, 56% of laptop owners have BOTH:
.56L = LC.
30% of the employees who own a cellphone do not own a laptop.
Thus, 70% of cell owners have BOTH:
.7C = LC.
Since .56L = LC and .7C = LC, we get:
.56L = .7C
56L = 70C
4L = 5C
L/C = 5/4.
Let L = 50 and C = 40.
Since 70% of cell owners have both a laptop and a cell, LC = .7(40) = 28.
Enter these values into the grid and calculate any other values that can be determined:
The number of employees without laptops is 40% less than the employees with laptops.
Since L = 50, NL = 50 - .4(50) = 30.
Complete the grid:
Of the 80 total employees, 18 have neither a laptop nor a cell:
18/80 * 100 = 22.5%.
The correct answer is
B.
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