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# PS: sets with sales representatives

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Senior Manager
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PS: sets with sales representatives [#permalink]

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02 Aug 2009, 20:27
00:00

Difficulty:

(N/A)

Question Stats:

100% (06:04) correct 0% (00:00) wrong based on 3 sessions

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I do not know how to solve this problem so I need help.

On a business trip, 30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 55 percent of the sales representatives prefer to stay at Hotel XYZ and 45 percent prefer to stay at Hotel ABC. What is the highest possible number of sales representatives NOT given accommodations at the hotel they prefer?

A) 11
B) 18
C) 36
D) 45
E) 51
Senior Manager
Joined: 08 Jan 2009
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Re: PS: sets with sales representatives [#permalink]

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02 Aug 2009, 20:53
xyz = 60 * .3 = 18
ABC = 42

xyz = .55 * 60 = 33
ABC = .45 * 60 = 27

xyz only 18 accomadations is possible.
the answer is = 33 - 18 = 15.

I am not able to find it among the choices.
Senior Manager
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Re: PS: sets with sales representatives [#permalink]

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02 Aug 2009, 20:57
I can't figure this out: I'm getting 15 as my answer, which is not one of the choices.

25% of the 60 people is the max number who might not get their first preference, which comes to 15.
Manager
Joined: 19 Jun 2009
Posts: 141
Location: India
Concentration: Strategy, General Management
GMAT 1: 650 Q51 V27
GMAT 2: 710 Q48 V39
GPA: 3.2
WE: Engineering (Computer Hardware)
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Kudos [?]: 18 [0], given: 21

Re: PS: sets with sales representatives [#permalink]

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02 Aug 2009, 22:31
Allocation :
XYZ = 18.
ABC = 42.

Preference :
XYZ = 33.
ABC = 27.

Now, we have to maximise the number of people who have got not-preferred accommodation. So consider worst condition.

All 33 who prefer in XYZ are given accommodation in ABC(42). So, all 18 allocation of XYZ are not preferred type.

And, out of 27 who prefer ABC, 18 are given accommodation in XYZ(18).

So total = 18+18 = 36.
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Senior Manager
Affiliations: ACA, CPA
Joined: 26 Apr 2009
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Schools: BC
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Re: PS: sets with sales representatives [#permalink]

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03 Aug 2009, 05:07
This is the way i solved it.

Taking it up from the previous poster

Allocation given :
XYZ = 18.
ABC = 42.
Preference wanted :
XYZ = 33.
ABC = 27.
So we force all the people who wanted XYZ into taking ABC ---> 42
Left space in ABC --- 42-33 = 9
Disappointed XYZ people ---- 33 (all)

Then we force all the people in ABC into taking XYZ ----> 18 (capped out)
Left space in XYZ --- NIL
Disappointed ABC people --- 18
So now we can give the rest 9 to what they want.

So total disappointed people = 33+18 = 51
Ans E

what is OA
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Manager
Joined: 19 Jun 2009
Posts: 141
Location: India
Concentration: Strategy, General Management
GMAT 1: 650 Q51 V27
GMAT 2: 710 Q48 V39
GPA: 3.2
WE: Engineering (Computer Hardware)
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Kudos [?]: 18 [0], given: 21

Re: PS: sets with sales representatives [#permalink]

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03 Aug 2009, 05:17
alpeshvc wrote:
Allocation :
XYZ = 18.
ABC = 42.

Preference :
XYZ = 33.
ABC = 27.

Now, we have to maximise the number of people who have got not-preferred accommodation. So consider worst condition.

All 33 who prefer in XYZ are given accommodation in ABC(42). So, all 18 allocation of XYZ are not preferred type.

And, out of 27 who prefer ABC, 18 are given accommodation in XYZ(18).

So total = 18+18 = 36.

Err.... I have done a mistake. In first case when we put 33 who prefer in XYZ in (42). I considered 18 unsatisfied. It should be 33.

33+18 = 51. Snipertrader is right.
_________________

I am ready to fall, but not before I fly.

Senior Manager
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Posts: 276
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Re: PS: sets with sales representatives [#permalink]

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04 Aug 2009, 10:27
The OA is E, but i do not understand the second step: Where does the 9 come from??
Senior Manager
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Re: PS: sets with sales representatives [#permalink]

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04 Aug 2009, 12:57
Not getting their perference...

70% can stay in ABC while 45 % wants to stay here 30% gets to stay in XYZ while 55% wants to stay

so whats the least amount of people that can get satisfied? move all 55% who wants to stay in XYZ to ABC, while 30% in XYZ are all who wanted to go to ABCs, so we have 15% left that gets their preference to go to ABC, in the end, 85% of 60 people (51 people) doesn't get their preference.
Manager
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Re: PS: sets with sales representatives [#permalink]

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07 Aug 2009, 03:18
ANS is 51

Quote:
one suggestion plz solve this question in percentages only dont convert 30% of 60 or 45% of 60....it will not add any value rather eat lot of time for no reason.......

consider a case when all 30% of ppl staying in hotel XYZ are unhappy....
this gives us 30% from 45% are staying in XYZ..leaving 15% happy ppl in ABC but that also means 70%-15% = 55% are unhappy in hotal ABC

This means 30% of XYZ + 55% of ABc are unhappy ppl = 85% of 60 = 51
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Re: PS: sets with sales representatives [#permalink]

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08 Aug 2009, 00:59
netcaesar wrote:
I do not know how to solve this problem so I need help.

On a business trip, 30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 55 percent of the sales representatives prefer to stay at Hotel XYZ and 45 percent prefer to stay at Hotel ABC. What is the highest possible number of sales representatives NOT given accommodations at the hotel they prefer?

A) 11
B) 18
C) 36
D) 45
E) 51

xyz = 18, abc = 42

preference: xyz = 33, abc = 27 ( start by allocating the vice versa - abc preference into the xyz hotel)

42 places in abc hotel fill them with xyz preferecne 33 ( unsatisfied customers), we would be left with extra 9 places in abc hotel that we would fill from the abc preference of 27 and we would have 18 to move to the xyz hotel( another patch of unsatisfied customers)

total unsatisfied customers = 18+33 = 51
Manager
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Re: PS: sets with sales representatives [#permalink]

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09 Aug 2009, 01:18
55% liked to stay at XYZ and remaining 45% at ABC.
1)Worst case condition when all 55% liked to stay at xyz are force to stay in ABC and the capacity left out in ABC is (70-55)%=15%
2)Now out of 45% liked to stay in ABC max only 15% can stay, so the remainig 30% has to stay in XYZ
totally 55%+30% sales representatives NOT given accommodations at the hotel they prefer, which is 85% of 60 = 51

/Prabu
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26 May 2010, 16:31

On a business trip, 30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 55 percent of the sales representatives prefer to stay at Hotel XYZ and 45 percent prefer to stay at Hotel ABC. What is the highest possible number of sales representatives NOT given accommodations at the hotel they prefer?

A)11

B)18

C)36

D)51

E)23
Intern
Joined: 05 May 2010
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26 May 2010, 17:07
This type of question is more an IQ test than maths. It's very easy to mis-read the question when under time constraints. But if you are careful, it is actually a very easy Q.

Anyway, here's the solution and discussion regarding the same question posted elsewhere in the forum:

ps-sets-with-sales-representatives-81848.html
Intern
Joined: 18 May 2010
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Schools: Marshall (In with $$), Babson (In with$$), Simon (In with \$ - Declined), Kellogg (Ding), Ross (Ding), Fuqua (Ding), Darden (Ding), Tepper (Ding)
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26 May 2010, 17:09
Manager
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27 May 2010, 02:10
I guess there is a similar ques in OG12 also. You can check that one for explanation and procedure to approach these question types.
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27 May 2010, 03:25
Re: 750 Level question   [#permalink] 27 May 2010, 03:25
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