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

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If 25% of the employees at a firm did not take a vacation last year,  [#permalink]

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New post Updated on: 07 Aug 2018, 06:43
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Question 3 of The e-GMAT Sets Triad

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

(I) Only 1 out of every 3 employees who took a vacation last year received a promotion.
(II) 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.

The Official Answer and the Explanation will be posted on 14th May. Till then, post your solution below and get Kudos for participation. Happy Solving! :-D
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Originally posted by EgmatQuantExpert on 13 May 2015, 07:45.
Last edited by EgmatQuantExpert on 07 Aug 2018, 06:43, edited 3 times in total.
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Re: If 25% of the employees at a firm did not take a vacation last year,  [#permalink]

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New post Updated on: 15 May 2015, 00:17
2
1
The correct answer is Option C

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

Image

From St. 1:

Image

This is clearly not sufficient.


From St. 2:

Image

Not Sufficient

Combining Statements 1 and 2:

5Y = 50

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

Sufficient.
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Originally posted by EgmatQuantExpert on 13 May 2015, 08:06.
Last edited by EgmatQuantExpert on 15 May 2015, 00:17, edited 1 time in total.
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Re: If 25% of the employees at a firm did not take a vacation last year,  [#permalink]

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New post 13 May 2015, 10:42
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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.
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Re: If 25% of the employees at a firm did not take a vacation last year,  [#permalink]

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New post 14 May 2015, 10:57
1
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
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Re: If 25% of the employees at a firm did not take a vacation last year,  [#permalink]

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New post 14 May 2015, 15:33
2
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.
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Re: If 25% of the employees at a firm did not take a vacation last year,  [#permalink]

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New post 15 May 2015, 00:06
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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
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Re: If 25% of the employees at a firm did not take a vacation last year,  [#permalink]

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New post 15 May 2015, 00:15
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:

kunals31 wrote:
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.


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?

Mechmeera wrote:
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.


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%

rohitd80 wrote:
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.



anewbeginning: You were absolutely right! :-D

I hope you guys found this discussion useful! :)

Japinder
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Re: If 25% of the employees at a firm did not take a vacation last year,  [#permalink]

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New post 15 May 2015, 00:50
EgmatQuantExpert wrote:
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:

kunals31 wrote:
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.


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?

Mechmeera wrote:
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.


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%

rohitd80 wrote:
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.



anewbeginning: You were absolutely right! :-D

I hope you guys found this discussion useful! :)

Japinder


Thanks for the pointing the mistake.
I somehow missed it.
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Re: If 25% of the employees at a firm did not take a vacation last year,  [#permalink]

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New post 21 Aug 2017, 12:41
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Re: If 25% of the employees at a firm did not take a vacation last year, &nbs [#permalink] 21 Aug 2017, 12:41
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