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Hotels

by j_shreyans » Mon May 11, 2015 9:14 am
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


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by [email protected] » Mon May 11, 2015 9:33 am
Hi j_shreyans,

While this prompt is "thick" with data, the math involved isn't too bad (you just have to stay organized and label your work).

The first sentence gives us data about the number of reps (out of 60) who will stay at each hotel:

Hotel XYZ = (.30)(60) = 18 reps
Hotel ABC = the rest = 42 reps

Next, we're told about the PREFERENCES of the reps

Hotel XYZ = (.55)(60) = 33 reps PREFER to stay at this hotel
Hotel ABC = (.45)(60) = 27 reps PREFER to stay at this hotel

From this, we can clearly see that some of the reps (at least 15) who want to stay at XYZ will NOT get what they want because there are not enough spots.

We're asked for the MAXIMUM number of reps who would NOT be assigned to the hotel that they prefer....

Here, we're limited by the number of reps who COULD stay at each hotel.

There are only 18 'reservations' at Hotel XYZ, so we can shift 18 reps from ABC to XYZ (making 18 reps who DON'T get what they want).
Next, we can put the remaining 42 people in ABC (making 33 reps who DON'T get what they want and 9 who DO).

Total reps who DON'T get what they want = 18+33 = 51

Final Answer: E

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by DavidG@VeritasPrep » Mon May 11, 2015 10:37 am
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
Matrix! First, let's set up our matrix. (I'm putting everything in terms of percent to start. We'll convert to the actual number of people at the end.) 30% are staying at XYZ. 70% are staying at ABC. 55% prefer XYZ. 45% prefer ABC. The initial matrix will look like this:


Image


Now, let's try to maximize the suffering of these poor people. The 30% who are staying in XYZ? Let's say all of them would have preferred ABC. Now we'll have the following:


Image


Next, simply fill in the rest of the table to get:

Image

Notice that only 15% of the people are staying where they want to stay; .15* 60 = 9. If 9 are staying where they want, 60-9 =51 are unhappy.

(Or we can reason like this: 30% are in XYZ, but prefer ABC. 55% are in ABC but prefer XYZ. So 30 + 55 or 85% are unhappy. .85*60 = 51.)
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by Brent@GMATPrepNow » Mon May 11, 2015 11:49 am
It's worth noting that David's Double Matrix approach can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of sales representatives, and the two characteristics are:
- staying at Hotel ABC or staying at Hotel XYZ
- preferring to stay at Hotel ABC or preferring to stay at Hotel XYZ

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
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by j_shreyans » Mon May 11, 2015 10:23 pm
Hi Rich ,

Thanks for the reply, but i don't get below .

Here, we're limited by the number of reps who COULD stay at each hotel.

There are only 18 'reservations' at Hotel XYZ, so we can shift 18 reps from ABC to XYZ (making 18 reps who DON'T get what they want).
Next, we can put the remaining 42 people in ABC (making 33 reps who DON'T get what they want and 9 who DO).

Total reps who DON'T get what they want = 18+33 = 51

According to the question Hotel XYZ prefer is 33 reps and given only 18 reps, so 15 reps don't get XYZ hotel right . NOw what next?

Please suggest

Thanks
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by [email protected] » Tue May 12, 2015 9:16 am
Hi j_shreyans,

To MAXIMIZE the number of reps who don't get what they want, we have to move AS MANY as we can to the Hotel that they DON'T want to be in.

To start from your "last line" from your post.....

Take ALL 33 reps who WANT to be in XYZ and put them in ABC.
Next, take 18 people who WANT to be in ABC and put them in XYZ.

Now you have 33+18 people who are in hotels that they DON'T want to be in.

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by gmatbeater1989 » Tue Oct 20, 2015 2:50 pm
j_shreyans 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) 11
B) 18
C) 36
D) 45
E) 51


OAE
It seems like we have enough information to use the formula:
Total = group 1 + group 2 - both + neither

But I don't know what it means to be in the "both" group or the "neither" group.
Anyone?
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by [email protected] » Tue Oct 20, 2015 6:57 pm
Hi gmatbeater1989,

Take a look at David's approach (above) if you want to see how to use that approach on this prompt.

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