Question: If 65 percent of a certain firm’s employees are full-time and if there are 5,100 more full-time employees than part-time employees, how many employees does the firm have?

(A) 8,250
(B) 10,200
(C) 11,050
(D) 16,500
(E) 17,000

Correct Answer: E

Solution and Explanation:
Approach Solution 1:

Let x equal the complete number of staff members.

Full-time employees make up 65% of a certain company's workforce.
This also indicates that 35% of the workforce is part-time workers.

Therefore, 0.65 times equals the number of employees working full time.
And the number of employees working part-time is equal to 0.35x.

There are 5,100 more people working full-time jobs than part-time jobs at this company.
To put it another way, the number of full-time workers corresponds to the sum of the full-time workers and the part-time workers plus 5,100.
Replace with to obtain: 0.65x = (0.35x) + 5100
When 0.35x is subtracted from both sides of the equation, the result is 0.3x equals 5100.
By dividing each side by 0.3, we get the following result: x = 17,000

E is the correct answer.

Approach Solution 2:

This is a question evaluating fundamental application skills in percentage, and it's rather straightforward.
Let there be a hundred workers in total.
65 people are employed here on a full-time basis.
The number of employees working half time equals 100 minus 65, or 35
The difference between employees working full time and those working part time is equal to 5,100.

=> 65 – 35 = 30 symbolizes 5100
=(5100/30)*100 is the mathematical representation of 100 (total employees).
=17000 (OPTION E)

Approach Solution 3:

Let x be the total employees in the firm
=> 65x / 100 = 5100 + 35x / 100
30x / 100= 5100
X = (5100∗100) / 30 = 17000

E is the correct choice.

“If 65 percent of a certain firm’s employees are full-time and if there" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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