A corporation recently expanded both its sales department and its tech

Question

A corporation recently expanded both its sales department and its technical department. Immediately  before  expansion, the number of employees in the sales department was exactly 60% of the number of employees in the technical department. Immediately  after  the expansion, the sales department had exactly 12 employees, and the technical department had exactly 15 employees.

Select for  Sales  and  Technical  percent increases in the number of employees that the sales department and the technical department, respectively could have experienced during expansion, such that the percent increases are jointly consistent with the information provided. Make only 2 selections, one in each column.

egmat · Accepted Answer

A simple question indeed on the surface – appears to be a word problem question with ratios and percent increase.

But the key to solving this question is making this inference:
 
 The presented information of 60% simplifies to 3:5 ratio and that implies that one quantity is a multiple of 3 and the other is a multiple of 5.

This processing is at the heart of solving this question.

Now after this step, one should take care of processing in the most efficient way, rejecting the combinations that are not possible.

So, this question is one of those easy wins – that you should be able to solve in less than 1.5’ if you do the processing in the most efficient way!

https://www.youtube.com/watch?v=wc5MeM_3gqI

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=82990 Before the expansion, we are told that the number of employees in the sales department (S) was 60% of the number of employees in the technical department (T). This gives us S = 0.6T or S/T = 3/5. Since after the expansion, the number of employees in the sales and technical departments was 12 and 15 respectively, the number of employees in the departments before the expansion should have been less. Based on the ratio, the possible values could have been: (S, T) (3, 5) (6, 10) (9, 15) ____________ After the expansion, the number of employees in sales was 12, and in technical, 15. If the values were (3, 5), the sales department would have had a 300% increase (from 3 to 12), but since this option isn't available, we discard this. If the values were (6, 10), the sales department would have a 100% increase (from 6 to 12) and the technical department a 50% increase (from 10 to 15). This matches the available options. Done! GMAT-Club-Forum-6liosdpf.png

chetan2u · Answer

Before expansion: 
 Let the number of employees in technical department be x, then those in sales department = 0.6x
S:T = 0.6x:x = 3x:5x. 
Thus, the minimum number can be S = 3 and T=5
 After expansion: 
 S=12 and T=15
 So S changes from 3 to 12, a 400% increase. No option

Next
 Before expansion: 
 S:T = 0.6x:x = 3x:5x =3*2:5*2 = 6:10 
 After expansion: 
 S=12 and T=15
So, S changes from 6 to 12, a 100% increase. The answer is a part of option, so let us test for T.
T changes from 10 to 15, an increase of 50%, again in the option.

Answer 
100% and 50%

sayan640 · Answer

chetan2u  
I think you should have written 300% increase...(12-3)/3 *100 = 300%

Posted from my mobile device

agrasan · Answer

We can solve this question algebrically

Let's say s and t be number of employees in sales and technical departments

s = 0.6*t ----------- (1)

After expansion, they are 12 and 15.
Let x and y be expansion rates

e*(1+x) = 12
t*(1+y) = 15

Using eq(1)

12/(1+x) = 0.6*(15/(1+y))

By simplifying, we get:
3x = 4y + 1

Clearly,  x = 100% and y = 50%

bot00078 · Answer

In This Question, I just took x=10, is it fine?

Bunuel · Answer

What does x represent? Is it the number of employees in the technical department? If yes, then you can’t just assume T = 10 from the start because that’s exactly what the question is testing. You need to figure out which values of S and T, consistent with S/T = 3/5, lead to the final numbers 12 and 15.

When you test possible multiples of 3 and 5, you see that (S, T) = (6, 10) fits perfectly, since the increases become 100% and 50%, which match the available choices. So while T = 10 works, it isn’t something you “pick” freely, it’s the value that turns out to satisfy the given conditions.

A corporation recently expanded both its sales department and its tech

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A corporation recently expanded both its sales department and its tech

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