"Vacation"

[trey.jeffries]

Last year, the five employees of Company X took an average of 16 vacation days each. What was the average number of vacation days taken by the same employees this year?

(1) Three employees had a 50% increase in their number of vacation days, and two employees had a 50% decrease.

(2) Three employees had 10 more vacation days each, and two employees had 5 fewer vacation days each.

I received this question when taking the MGMAT CAT Math over the weekend. I think there is a logical fallacy in the question as the question asks what was the average number of vacation days TAKEN by the employees while statement (2) states "Three employees HAD 10 more vacation days each, and two employees HAD 5 fewer vacation days each."

My intepretation is that just because you have a certain number of days does not necessarily mean you have to take them. For example, if I have 25 days of vacation a year but only take 15, I will have some days left over. If statement (2) were changed to read TAKEN instead of HAD, i think it would make a lot more sense. This would raise a definite red flag in critical reasoning questions, so I think it is worth noting here as well.

Thanks!

[Ben Ku]

I think you have a good point, and I will have this problem reviewed. In real life, we know that the vacations you "have" are different from the vacations you "take."

[rajdeep115]

I had the exact same interpretation of the question. I think you guys need to change the wording of the question. It is very misguiding; it makes me a little angry that I should get penalized for some wrongly worded question :)

[jnelson0612]

I had the exact same interpretation of the question. I think you guys need to change the wording of the question. It is very misguiding; it makes me a little angry that I should get penalized for some wrongly worded question :)

Fair enough! Sorry to make you angry. :-)

[rkafc81]

hi - i'm having trouble setting up problems like this one using the methodology outlined in the Thursday's with Ron session titled "Organisation for Word Problems".

Can someone please explain how you would go about identifying the quantities, mathematical relationships and then forming a chart for this problem?

thanks!

[jlucero]

This isn't a great problem to set up algebraically, because you aren't trying to solve all of the different variables. Instead, you are trying to find a change in the total number of vacation days. If you did want to set this up algebraically, you would use the equation:

sum = average * # of employees

LY: 90 = 16 * 5

TY: S = A * 5

Notice that we are trying to answer the value of A, but statement 2 allows us to recognize the change in the total sum of the vacation days between the two years.

[rkafc81]

mm ok thanks Joe - so, how would i do this non-algebraically then?

[RonPurewal]

I had the exact same interpretation of the question. I think you guys need to change the wording of the question. It is very misguiding; it makes me a little angry that I should get penalized for some wrongly worded question :)

here's a helpful guideline:
if you think there's a "wording trick" that immediately gives you some answer (in this case E), but the alternative interpretation of the problem involves actual work, then the "wording trick" isn't a thing.

in this case:
if you are looking at the difference between "take" and "have", then you're going to think that the answer to the problem is (E) in about two seconds.
on the other hand, if you don't, then you get to do actual mathematics.

it's possible that you'll encounter this situation in the real gmat exam. if you do, then you should go with the option that involves actual mathematics.

[RonPurewal]

mm ok thanks Joe - so, how would i do this non-algebraically then?

well, one way would be to test cases. you have to have an average of 16 days for the five people -- and thus a sum of 5 x 16 = 80 days -- but you can test different cases in which those 80 days are distributed differently.
then you can literally add and subtract the requisite %'s and/or days, and then see what happens.

e.g.,
statement 1
here's one case:
before --> after
16 --> 24 (up 50%)
16 --> 24
16 --> 24
16 --> 8 (down 50%)
16 --> 8
new average is 88/5

here's another case: (you can divide 80 days up into 20, 20, 20, 10, 10)
20 --> 30
20 --> 30
20 --> 30
10 --> 5
10 --> 5
new average is 100/5
that's different; insufficient


statement 2:
try the same thing. this time, by contrast, you'll get the same "new" average every time.

[rkafc81]

awesome thanks Ron!

[jlucero]

Good stuff