If 65 percent of a certain firm’s employees are full-time and if there

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

PS36090.02

nick1816 · Accepted Answer

percent of a certain firm’s employees that are full-time = 65% of total employees

percent of a certain firm’s employees that are part-time = 100-65= 35% of total employees

(65-35)% of total employees = 5100

total employees =  5100*\frac{100}{30 } = 17000

Bunuel · Answer

All is correct except the difference between 65% and 35% is not 15 percentage points, it's 30 percentage points. So, if 30% of the total is 5,100, then the total equals 5,100/30 *100 = 17,000.

Answer: E.

lacktutor · Answer

Let x be the total employees in the firm
-->  \frac{65x}{100} = 5100 + \frac{35x}{100}

\frac{30x}{100}= 5100

x= \frac{5100*100}{30} = 17000

Answer (E)

BrentGMATPrepNow · Answer

Let x = the TOTAL number of employees

65 percent of a certain firm’s employees are full-time  
This also means that 35 percent of the employees are  part-time

So,  0.65x  = the number of full-time employees
And  0.35x  = the number of part-time employees

There are 5,100 more full-time employees than part-time employees  
In other words: (the number of full-time employees) = (the number of part-time employees) + 5100
Substitute to get:  0.65x  = ( 0.35x ) + 5100
Subtract 0.35x from both sides of the equation to get: 0.3x = 5100
Divide both sides by 0.3 to get: x = 17,000

Answer: E

Cheers, 
Brent

CrackverbalGMAT · Answer

SOLUTION:
A NEW OG 2021 QUESTION

Its a question testing on basic application skills in percentage.

Let there be 100 employees.

Number of full time employees = 65

Number of part time employees = 100-65=35

The difference between full time and part time employees = 5100

=> 65-35 = 30 represents 5100

=>100(total employees) is represented by =(5100/30 )*100

=17000 (OPTION E)

Hope this helps

Devmitra Sen(Math)

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=DhKLWF0-7MI

avigutman · Answer

I would build a 4-way ratio for this one. Full-time : Part-time : Total : Difference
Insert 65 and 100 into first and third columns, respectively, then reduce by the common factor of 5, so you get 13 and 20.
Now you can insert 7 into the second column, and finally you can insert 6 (13-7) into the last column.
Now we're ready for the actual number that they provided: 5,100 goes into the fourth column, and they want the third column.
Looking at our ratio, the third column is twenty-sixths, or ten-thirds as big as the fourth column.
What's ten-thirds of 5,100? Well, 1/3 of 51 is 17, so 1/3 of 5,100 is 1,700, so ten-thirds of 5,100 is 17,000.
Big takeaway for this category of question: don't rush to use the actual number that they provide. First, take your time to set up all the ratio columns that would be useful, and insert your inferences in the world of ratios.
Only then, as a final step, bring in the information from the world of actual numbers.
Reason: working with a ratio (a simplified model of reality) is a lot easier than working with the actual numbers.

Abhishek_Relan · Answer

Since 65 percent of the firm’s employees work full time, that means 35 percent of the firm’s employees are part time and also according to question there are 5100 more full time employees than part time employees.

Couldn't 15% more full-time employees result in 5100, which would result in 34000 employees in the firm?

Posted from my mobile device

Abhishek_Relan · Answer

In fact, you are correct, but what I meant was that 65% of the employees are full-time and 35% are part-time, so why not assume that the company will have 50-50% of its employees working full-time and part-time? In response to the question, since 65% of the employees work full-time, this would mean that 65%-50%=15% extra of employees would be working full-time which would amount to 5100 employees and hence answer would come out to be 34,000 rather than 17,000.

habenae · Answer

Understood the reasoning to lead to the correct answer E (17 000).

However, cannot understand why the path that I chose wouldn't lead to the same answer.

Chosen path:

Let x be ''number of Full-time employees'' and y be ''number of Part-time employees''

(1) x/(x+y) = .65;

(2) x = y+5100;

substitute (2) in (1)

I find total employees x + y = 11050.

PLEASE help on how this path is incorrect

Bunuel · Answer

Your set-up is correct and leads to the correct answer of 17,000:
 
x/(x + x - 5,100) = 0.65

x = 1.3x - 3,315

0.3x = 3,315

x = 11,050

x + y = 11,050 + 11,050 - 5,100 = 17,000

P.S. That said, this is not the most efficient way to solve the problem, as it involves two variables and ugly math.

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