If 25% of the employees at a firm did not take a vacation last year

Question

If 25% of the employees at a firm did not take a vacation last year, what percent of the employees received a promotion?

(1) Only 1 out of every 3 employees who took a vacation last year received a promotion.
(2) The number of employees who took a vacation but did not get a promotion was 500% of the number of employees who neither took a vacation nor got a promotion.

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EgmatQuantExpert · Answer

The correct answer is Option C

The information given in the question statement can be tabulated as below:

https://s12.postimg.org/byemwu9xp/St1.png

From St. 1:

https://s24.postimg.org/pts368v05/st11.png

This is clearly not sufficient.

From St. 2:

https://s24.postimg.org/czymqn6yd/st2.png

Not Sufficient

Combining Statements 1 and 2:

5Y = 50

So, Y = 10%
Therefore, X = 40%

Sufficient.

kunals31 · Answer

According to me, the answer is C.

The question says that 25% of the employees did not take a vacation. This can be interpreted as 75% took a vacation.

So the question involves a two-variable Venn diagram.

Statement - 1 : 1 in every 3 employees who took a vacation got a promotion. So this means that people who got a promotion as well as took a vacation is 25% of the total. However, there is no information about the people who got only a promotion as well as people who got neither of the two. So, INSUFFICENT.

Statement - 2 : The people who took a vacation but did not get a promotion is 500% of the number who neither took a vacation nor got a promotion. This statement is clearly INSUFFICIENT.

Combining both the statements.

The people who took a vacation as well as got a promotion is 25%. Hence, the people who took a vacation but did not get a promotion is 50%. This means that the people who neither took a vacation nor got a promotion is 10% of the total. Thus, the people who got a promotion but did not take a vacation is (100-50-25-10)%, i.e. 15%. This means that the number of people who got a promotion is 35% of the total.

Thus, both statements considered together are SUFFICIENT.

Thus, both statements considered together are SUFFICIENT.

Nevernevergiveup · Answer

To make things simpler let us assume employees at a firm be 100.
employees who took vacation are 75.
1. this statement gives the information that the no of employees who took vacation and ( out of those1/3) who received promotion is 25. thereby it is 25% percent of the employees received a promotion. Stmt 1 is sufficient.
2.This gives the info that out of people who did not get promotion, those who attended vacation is 5 times the no of people who did not attend vacation. This does not give us enough info to solve the question.

Stmt 1 is sufficient. Answer is A

rohitd80 · Answer

This is how I approached it to get to Answer = C:

Let's assume there are 100 employees
Given - 25 No Vacay & 75 took vacay
1) 
1 in every 3 vacay employees got promoted ---->25 & 50 didn't get promotion. At this point we can't say what % of folks got promotion, so insufficient
2)
Given 50 is 500% of No Vacay folks who didn't get promoted 
So 25 folks took no vacay…some got promoted and some did not. 
Let x be the # of folks in the category of no vacay + no promo 
so, 50 = 5 * (25-x)….hence, x = 15.....Again 2 alone is not sufficient to answer 
 
1) + 2) 
So, in total how many people got promoted = 10+25 
Thus, 35% got promoted & Therefore both statements considered together are SUFFICIENT.

keats · Answer

According to me,the answer should be C. However the number of people who are promoted is coming out to be 40% of the total. Cheers :-D

EgmatQuantExpert · Answer

kunals31 : You answered the question right and your analysis was spot-on till the very last sentence. Please have a look at the red part in your solution below: The correct % of people who got a promotion is 40%. Had this been a PS question, even this mistake in the last step would have led to you marking a wrong answer choice. Mechmeera : This 25% number refers to the number of employees who took a vacation AND got a promotion. What about the employees who didn't take a vacation and got a promotion? rohitd80 : You got the answer right but please have a look at the red part in your solution below. The correct equation would have been 50 = 5x. This would have led you to the total % of promoted people = 40% anewbeginning : You were absolutely right! :-D

I hope you guys found this discussion useful!

Japinder

Nevernevergiveup · Answer

Thanks for the pointing the mistake.
I somehow missed it.

anandch1994 · Answer

I Egmat, I am unable to look at the images that have been posted. I tried refreshing and opening it in chrome as well as internet explorer. It will be really helpful if you can pst he images again

D4kshGargas · Answer

Hi, the images seem to be corrupted or unavailable. 
Can you please update the URLs? 
Thanks!

Mona2019 · Answer

EgmatQuantExpert  ,

Hi, I am unable to view the images in your explanation. Please help.

RahulRajIN1988 · Answer

Hi,
The word 'only' in the first statement is creating some confusion. The statement can mean -> Promoted = Only (1/3 rd of Vaccinated)
Statement 2 doesn't mention when they got vaccinated - last year, year before it or this year?

Wazzzaa · Answer

Let's say total number of employees = T
Employees went for vacation = 0.75T
Employees not went for vacation = 0.25T -------- (b)

1) Employees went for vacation and got promotion = 0.75T/3 = 0.25T (insufficient) ----------- (c)
 Employees went for vacation and not got promotion = 2 * 0.75T/3 = 0.5T -------- (a)

2) from (a) 0.5 T/ ( Employees did not went for vacation and did not got promotion) = 5
 Employees did not went for vacation and did not got promotion = 0.1T
 from (b), Employees did not went for vacation and got promotion = 0.25T - 0.1T = 0.15T (insufficient) ------------ (d)

From (c) and (d), Employees got promotion = 0.4T

Therefore, OPTION C, is correct.

If 25% of the employees at a firm did not take a vacation last year

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GMAT Data Sufficiency (DS) Questions

If 25% of the employees at a firm did not take a vacation last year

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