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Last year, the five employees of company X took an average

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Last year, the five employees of company X took an average [#permalink] New post 22 Jan 2010, 11:41
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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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Aug 2012, 00:28, edited 2 times in total.
Edited the question.
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Re: Statistics [#permalink] New post 22 Jan 2010, 12:18
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GMAT10 wrote:
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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Re: Statistics [#permalink] New post 22 Jan 2010, 12:08
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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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Re: Statistics [#permalink] New post 15 Feb 2010, 05:39
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

so ans is B
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Re: Statistics [#permalink] New post 17 Feb 2010, 07:18
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
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Re: Statistics [#permalink] New post 20 Feb 2010, 02:46
GMAT10 wrote:
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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Re: Statistics [#permalink] New post 21 Aug 2012, 11:15
Bunuel wrote:
GMAT10 wrote:
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 ?
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Re: Statistics [#permalink] New post 22 Aug 2012, 00:38
Expert's post
badribaba1984 wrote:
Bunuel wrote:
GMAT10 wrote:
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.

The same way for the second statement.

Hope it's clear.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Last year, the five employees of company X took an average [#permalink] New post 28 May 2014, 08:19
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Re: Last year, the five employees of company X took an average   [#permalink] 28 May 2014, 08:19
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