SAT Percentages Question 39 | Free SAT Prep | Aniko

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Question 39·Hard·Percentages

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In a technology company, $58\%$ of all employees belong to the Engineering division. Of the employees in Engineering, $45\%$ are classified as Software Engineers. Among Software Engineers, $10\%$ work remotely on a full-time basis. Among all employees who are not Software Engineers, $5\%$ work remotely on a full-time basis.

Which of the following is closest to the percentage of all employees who do not work remotely on a full-time basis?

For layered percentage problems, set the total to 100 so each percentage becomes an easy count, then carefully follow the group structure: find the percentage in each subgroup, apply the given percentages within those subgroups, and finally combine the results. Pay close attention to phrases like "of those" and "among all who are not..." so you always know what each percentage is taken from, and when the question asks for "do not" or "non-", compute the complement by subtracting from 100% at the end.

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Use a convenient total

Imagine there are 100 employees in total so that each percentage directly tells you how many employees are in a group (for example, $58\%$ becomes 58 employees).

Separate Software Engineers from others

First figure out what percent of all employees are Software Engineers, then how many of those are remote; after that, do the same for everyone who is not a Software Engineer.

Remember what the question is asking

After you calculate the percent of all employees who work remotely full-time, think about how to use that number to find the percent who do not work remotely full-time.

Desmos Guide

Compute the overall non-remote percentage in one expression

In Desmos, type the expression 1 - (0.580.450.10 + (1 - 0.58*0.45)*0.05). The output is the fraction of all employees who do not work remotely full-time; convert that decimal to a percentage and choose the closest answer choice.

Step-by-step Explanation

Find the percent of all employees who are Software Engineers

Treat the total number of employees as 100, so every percentage is also a number of employees out of 100.

Engineering employees: $58\%$ of all employees.
Of those, $45\%$ are Software Engineers.

So the percent of all employees who are Software Engineers is:

0.58 \times 0.45 = 0.261

This means $26.1\%$ of all employees are Software Engineers.

Find the percent of all employees who are remote Software Engineers

Among Software Engineers, $10\%$ work remotely full-time.

We just found that $26.1\%$ of all employees are Software Engineers, so the percent of all employees who are remote Software Engineers is:

0.10 \times 26.1\% = 2.61\%

So $2.61\%$ of all employees are Software Engineers who work remotely full-time.

Find the percent of all employees who are remote non–Software Engineers

Now find the employees who are not Software Engineers.

Total employees: $100\%$
Software Engineers: $26.1\%$

So non–Software Engineers make up:

100\% - 26.1\% = 73.9\%

Among these non–Software Engineers, $5\%$ work remotely full-time, so the percent of all employees who are remote non–Software Engineers is:

0.05 \times 73.9\% = 3.695\%

So $3.695\%$ of all employees are non–Software Engineers who work remotely full-time.

Combine remote workers and find those who are not remote

Add the two remote groups to get the total percent of employees who do work remotely full-time:

Remote Software Engineers: $2.61\%$
Remote non–Software Engineers: $3.695\%$

Total remote full-time:

2.61\% + 3.695\% = 6.305\%

So about $6.3\%$ of all employees work remotely full-time.

The question asks for those who do not work remotely full-time, so subtract from $100\%$ :

100\% - 6.305\% = 93.695\%

This rounds to $93.7\%$ , which matches choice D.

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Step-by-step Explanation

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Step-by-step Explanation