On a business trip, 30 percent of 60 sales representatives will be giv : GMAT Problem Solving (PS)
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# On a business trip, 30 percent of 60 sales representatives will be giv

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Manager
Joined: 04 Apr 2010
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On a business trip, 30 percent of 60 sales representatives will be giv [#permalink]

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20 Mar 2011, 15:48
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88% (02:11) correct 13% (00:00) wrong based on 8 sessions

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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) 51
B) 52
C) 53
D) 54
E) 55
[Reveal] Spoiler: OA

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Re: On a business trip, 30 percent of 60 sales representatives will be giv [#permalink]

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20 Mar 2011, 16:14
30% of 60 will be accommodated at XYZ = 18
70% of 60 will be accommodated at ABC = 42

55% of 60 prefer XYZ = 33
45% of 60 prefer ABC = 27

we were asked to find number of maximum possible people who were accommodated at hotels they dont prefer,

So for 18 XYZ accommodations , we can choose 18 ABC preferring people (so xyz is filled up) Here 18 were given to people who dont prefer XYZ
for 42 ABC accommodations, we can choose 33 ABC preferring people and rest to ABC. Here 33 were given to people who dont prefer ABC.

So total people who were accommodated at hotel they dont prefer = 18+33 = 51

bhandariavi wrote:
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) 51
B) 52
C) 53
D) 54
E ) 55

I got 42 but the answer is ....
Manager
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Re: On a business trip, 30 percent of 60 sales representatives will be giv [#permalink]

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20 Mar 2011, 16:52
I calculated it using percentage figures alone 85% * 65 / 100 = 51
Thanks for the idea.
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Re: On a business trip, 30 percent of 60 sales representatives will be giv [#permalink]

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20 Mar 2011, 17:51
30/100 * 60 = 18 will be at XYZ

and the 42 will be at ABC

So Max # of representatives NOT given accommodations at the hotel they prefer = Total # of Rep - MIN # of representatives given accommodations at the hotel they prefer

So, all the 55% of rep who want to stay at XYZ can be moved to hotel ABC

and out of the 45% who want to stay in ABC, only 15% will be there and the remaining ones (45-15 = 30%) in hotel XYZ.

So total 85% are not give hotels of their preferences

=> 85/100 * 60 = 5100/100 = 51

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Re: On a business trip, 30 percent of 60 sales representatives will be giv   [#permalink] 20 Mar 2011, 17:51
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