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Last year, the five employees of company X took an average [#permalink]
22 Jan 2010, 11:41

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Difficulty:

35% (medium)

Question Stats:

57% (01:38) correct
42% (00:39) wrong based on 82 sessions

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 thier number of vacation days and two employees has a 50% decrease (2) Three employees had 10 more vacation days each , and two employees has 5 fewer vacation days each.

5 employees 16 average vacation days Find: average this year

The easy one first:

2) Average = (e1 + e2 + e3 + e4 + e5) / 5 = (e1 + e2 + e3 + e4 + e5 + 10 + 10 + 10 -5 -5) / 5 = (e1 + e2 + e3 + e4 + e5 + 20) / 5 From the knowns, we know (e1 +... e5) / 5 = 16, so e1+...e5 = 80 Thus, new average = 80 + 20 / 5 = 20 So 2 alone is sufficient.

The hard one: 1) Average = (e1 + e2 + e3 + e4 + e5) / 5 Because the option gives you a percent increase, you can only find an answer IF e1 through e5 are all the same value (I.e. 16). However, as you are not given this information, 1 alone is not sufficient. For example, take (4 + 8 + 16 + 20 + 32) / 5 = 16. A 50% increase in e1, e2, and e3 (6+12+24) is different than a 50% increase in e3, e4, and e5 (24+30+48).
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________________________________________________________________________ Andrew http://www.RenoRaters.com

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 thier number of vacation days and two employees has a 50% decrease 2) Three employees had 10 more vacation days each , and two employees has 5 fewer vacation days each.

OA is B

(1) \frac{x+y}{5}=16, where x is the # vacations days taken by the three employees mentioned and y is the the # of days taken by two employees mentioned. --> Question: \frac{1.5x+0.5y}{5}=?, can not be determined. Not sufficient.

(2) \frac{x+y}{5}=16 --> x+y=80, where x is the # vacations days taken by the three employees mentioned and y is the the # of days taken by two employees mentioned. --> Question: \frac{(x+3*10)+(y-2*5)}{5}=? --> \frac{(x+y)+20}{5}=\frac{80+20}{5}=20. Sufficient.

Answer: B.

One thing to mention here: stem says that vacation days were "taken" by employees and statements say that employees "had" (more, less) vacation days. What if they were given these vacation days but they didn't take them? But as the credited OA is B, then we should assume that all the vacation days that were given to the employees were used. Though kind of strange to "assume" something in GMAT.
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1) Three employees had a 50% increase in thier number of vacation days and two employees has a 50% decrease 2) Three employees had 10 more vacation days each , and two employees has 5 fewer vacation days each.

given 5 employees 16 days average so 80 days leave last year

stmt 1 doesn't tell for which employess 50% increase and for which employess 50% decrease in vacation days

so not sufficient

stmt 2 if 3 employees had 10 more vacation days each then total vacation days is increased 80+3*10=>110

and if 2 employee vacation days decreased by 5 days each then total vacation days will come down to 110-2*5 =>100 days

so average vac. days for emp. this year will be 100/5 => 20 days

I evaluated statement 1 intuitively: the 50% increase could be referring to those with the most vacation days, so the average would increase likewise, it could refer to those with the least vacation days, in which case the average would decrease no way to tell, so 1 = insufficient

statement 2: 5x16 = 80 (total) take away 3x10 and add 2x5: 100 100/5 = 20 sufficient

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 thier number of vacation days and two employees has a 50% decrease 2) Three employees had 10 more vacation days each , and two employees has 5 fewer vacation days each.

Clearly B...

We have Sum of all vacations taken by 5 employess = 16x5=80 S1. gives % increases of 3 employees and % decrease of 2 employees... This isn't sufficient. INSUFF... S2: This can gives us the average as we need to add 10 and subtract 5 from 80 and then divide by 5... SUFF
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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 thier number of vacation days and two employees has a 50% decrease 2) Three employees had 10 more vacation days each , and two employees has 5 fewer vacation days each.

OA is B

(1) \frac{x+y}{5}=16, where x is the # vacations days taken by the three employees mentioned and y is the the # of days taken by two employees mentioned. --> Question: \frac{1.5x+0.5y}{5}=?, can not be determined. Not sufficient.

(2) \frac{x+y}{5}=16 --> x+y=80, where x is the # vacations days taken by the three employees mentioned and y is the the # of days taken by two employees mentioned. --> Question: \frac{(x+3*10)+(y-2*5)}{5}=? --> \frac{(x+y)+20}{5}=\frac{80+20}{5}=20. Sufficient.

Answer: B.

One thing to mention here: stem says that vacation days were "taken" by employees and statements say that employees "had" (more, less) vacation days. What if they were given these vacation days but they didn't take them? But as the credited OA is B, then we should assume that all the vacation days that were given to the employees were used. Though kind of strange to "assume" something in GMAT.

Hi . .Can you pls explain the variables x and y and how you arrived at the equations ?

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 thier number of vacation days and two employees has a 50% decrease (2) Three employees had 10 more vacation days each , and two employees has 5 fewer vacation days each.

OA is B

(1) \frac{x+y}{5}=16, where x is the # vacations days taken by the three employees mentioned and y is the the # of days taken by two employees mentioned. --> Question: \frac{1.5x+0.5y}{5}=?, can not be determined. Not sufficient.

(2) \frac{x+y}{5}=16 --> x+y=80, where x is the # vacations days taken by the three employees mentioned and y is the the # of days taken by two employees mentioned. --> Question: \frac{(x+3*10)+(y-2*5)}{5}=? --> \frac{(x+y)+20}{5}=\frac{80+20}{5}=20. Sufficient.

Answer: B.

One thing to mention here: stem says that vacation days were "taken" by employees and statements say that employees "had" (more, less) vacation days. What if they were given these vacation days but they didn't take them? But as the credited OA is B, then we should assume that all the vacation days that were given to the employees were used. Though kind of strange to "assume" something in GMAT.

Hi . .Can you pls explain the variables x and y and how you arrived at the equations ?

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

Say x is the total # vacations days taken last year by the three employees mentioned and y is the total # of days taken last year by two employees mentioned.

Now, since we are told that "last year the five employees of company X took an average of 16 vacation days each", then (total # of vacation days)/(# of employees)=(x+y)/5=16.

Next, the first statement says that "the three employees had a 50% increase in their number of vacation days", so those three had 1.5x vacation days this year, and the other two had 0.5y vacation days this year. We need the new average for this year, so the value of (1.5x+0.5y)/5.