In a certain store, the ratio of part-time workers to full-time worker

Question

In a certain store, the ratio of part-time workers to full-time workers is 2 to 5. If 4 part-time workers were hired, then the ratio would be 3 to 5. How many workers does the store have?

(A) 11

(B) 12

(C) 21

(D) 28

(E) 35

BrentGMATPrepNow · Accepted Answer

We can also use two variables (although 1 variable is typically faster)

The ratio of part-time workers to full-time workers is 2 to 5  \
Let P = number of Part-time workers
Let F = number of Full-time workers
We can write: P/F = 2/5
Cross multiply to get:  5P = 2F

If 4 part-time workers were hired, then the ratio would be 3 to 5.  
This would mean there are no P+4 part-time workers
Also, there are still F full-time workers
We can write: (P+4)/F = 3/5
Cross multiply to get: 5(P + 4) = 3F
Expand to get: 5P + 20 = 3F
Replace  5P  with  2F  to get:  2F  + 20 = 3F
Solve to get  F = 20 
So, there are presently 20 full-time employees

How many workers does the store have?  
Since F = 20, we can use the equation  5P = 2F  to help find the value of P
Replace F with 20 to get:  5P = 2(20) 
Simplify: 5P = 40
Solve to get:  P = 8

TOTAL number of workers = F + P =  20  +  8  =  28

Answer: D

Cheers,
Brent

lmuenzel · Answer

My Approach
2x+5x=7x

\frac{2}{5}

+4 part time =>  \frac{3}{5}

1x=4

(2*4) + (5*4) = 28

EMPOWERgmatRichC · Answer

Hi All,

We're told that the ratio of part-time workers to full-time workers is 2 to 5. This means that:

1) The number part-time workers MUST be a multiple of 2 
2) The number of full-time workers MUST be a multiple of 5 
3) The total number of workers must be a multiple of 7

We're also told that IF 4 part-time workers were hired, then the ratio of part-time workers to full-time workers would be 3 to 5. We're asked for the TOTAL number of workers there are NOW (meaning before 4 part-time workers are hired).

This question can be solved in a number of different ways. Since the total number of workers is a multiple of 7 - and the answers are numbers - we can TEST THE ANSWERS. To start, we can eliminate Answers A and B (since they're NOT multiples of 7).

Let's TEST Answer D: 28 total workers

IF.... there are 28 total workers 
8 are part-time and 20 are full-time 
Adding 4 more part-time workers would give us.... 
12 part-time and 20 full-time 
12:20 = 3:5 
This is an exact match for what we were told, so this MUST be the answer!

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

generis · Answer

Another approach: set up the original ratio with x, add the number given, set it equal to the new ratio, and multiplier x gives you the original actual numbers.

The ratio of part-time workers to full-time workers is 2 to 5

\frac{Part-time}{Full-time}=\frac{2x}{5x}

If 4 part-time workers were hired, then the ratio would be 3 to 5:

\frac{2x + 4}{5x}=\frac{3}{5}

5(2x + 4) = 3(5x) 
 10x + 20 = 15x 
 20 = 5x 
 x = 4

x is the multiplier for the original ratio

How many workers (TOTAL)?
Part-time = 2x = (2)(4) = 8
Full-time = 5x = (5)(4)= 20

20 + 8 = 28

Answer D

ScottTargetTestPrep · Answer

We can let the number of part-time and full-time workers be 2x and 5x, respectively. We can create the equation:

(2x + 4)/(5x) = 3/5

5(2x + 4) = 3(5x)

10x + 20 = 15x

20 = 5x

4 = x

So there are 2(4) = 8 part-time workers and 5(4) = 20 full-time workers, and therefore, there are 28 workers in the store.

Answer: D

Lowpoint · Answer

Doubt: Why are we multiplying x = 4 with 2/5 instead of 3/5? Because it says the new ratio is 3/5? So shouldn't we multiply x with 3/5 and won't it become 32 workers at store?

Bunuel · Answer

I understand the confusion. The stem states that the ratio IS 2 to 5, and then it presents a  hypothetical  scenario, stating that IF 4 part-time workers were hired, then the ratio would become 3 to 5. Therefore, in reality, these 4 employees are not hired, and when calculating the number of employees, we should use the 2 to 5 ratio.

Hope it helps.

In a certain store, the ratio of part-time workers to full-time worker

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