Problem Solving

Hi LUANDATO,

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

BTGmoderatorLU wrote: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

The OA is D.

Experts, can you help me to solve this PS question, please? I don't have it clear. Thanks.

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 a total of 28 workers in the store.

Answer: D

BTGmoderatorLU wrote: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

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