Problem Solving

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 a great candidate for a technique called the Double Matrix Method. It can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria are:
- own laptop (L) and don't own laptop (~L)
- own cellphone (C) and don't own cellphone (~C)

Since the question concerns percents only, let's say there are 100 employees in this population.
So, we get:


Aside: To learn more about this technique, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Let's say that x employees have laptops. This means that 100 - x employees don't have laptops. So we get:


The number of employees without laptops is 40% less than the employees with laptops.
In other words, the number of employees without laptops = 60% of the number of employees with laptops.
We can write: 100 - x = 0.6x
Simplify: 100 = 1.6x
x = 62.5
In other words, 62.5 employees have laptops.
This means that 37.5 employees don't have laptops. We get:


44% of the employees that own laptops do not own a cellphone
We now know that 62.5 employees have laptops, so 44% of 62.5 employees do not own a cellphone
44% of 62.5 = 27.5, so we get:


30% of the employees that own cellphone do not own laptops.
Let's let y = the total number of employees that own cellphone
We get:


If 30% of the employees that own a cellphone do not own laptops, then 70% of the employees that own a cellphone do own laptops.
So, 70% of y = the number of employees that own a cellphone and own a laptop.
Since we already know that 35 employees own a cellphone and own a laptop, so we can write 0.7y = 35
Solve to get y = 50
So, 50 employees own a cellphone, which means 50 employees don't own a cellphone. We get:



From here, we can fill in the remaining boxes:


Looks like 22.5 employees (out of 100 employees) own neither a laptop nor a cellphone.

Answer: B

Cheers,
Brent

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Once you're familiar with the Double Matrix Method, you can attempt these additional practice questions:

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Easy Data Sufficiency questions
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Medium Data Sufficiency questions
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Difficult Data Sufficiency questions
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