On a business trip, 30 percent of 60 sales representatives

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Fri Jun 29, 2018 12:04 pm

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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

The OA is A.

Please, can anyone explain this PS question? I can't get the correct answer, I got 42 but this isn't the correct answer <i class="em em-disappointed"></i>. I need help. Thanks.

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Source: Beat The GMAT — Problem Solving | Fri Jun 29, 2018 12:04 pm

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sat Jun 30, 2018 1:37 pm

Hi swerve,

We're told that 30% of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70% will be given accommodations at Hotel ABC. However, 55% of the sales representatives prefer to stay at Hotel XYZ and 45% prefer to stay at Hotel ABC. We're asked for the highest possible number of sales representatives that were NOT given accommodations at the hotel they prefer. 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: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Jul 23, 2018 5:40 pm

swerve 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

We see that 0.3 x 60 = 18 sales representatives will be given accommodations at Hotel XYZ, and the remaining 60 - 18 = 42 will be given accommodations at Hotel ABC. However, we see that 0.55 x 60 = 33 sales representatives prefer to stay at Hotel XYZ and the remaining 60 - 33 = 27 prefer to stay at Hotel ABC.

Since we want to determine the highest possible number of sales representatives not given accommodations at the hotel they prefer, we can assume 33 of the 42 representatives who are given accommodations at Hotel ABC prefer to stay at Hotel XYZ. So only 9 representatives are given the accommodations at the hotel they prefer.

For the 18 sales representatives will be given accommodations at Hotel XYZ, we can assume that none of them are given the accommodations at the hotel they prefer.

So the highest possible number of sales representatives not given accommodations at the hotel they prefer is 60 - 9 = 51.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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Karishma BL: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Wed Nov 10, 2010 11:43 am; Location: Pune, India

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by Karishma BL » Mon Jul 23, 2018 11:12 pm

swerve 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

The OA is A.

Please, can anyone explain this PS question? I can't get the correct answer, I got 42 but this isn't the correct answer <i class="em em-disappointed"></i>. I need help. Thanks.

Let's assume that the number of reps is 100 and find the max percentage as required. That way, we can find the actual number at the end and save ourselves a ton of calculations.
All below figures are in percentages:
30 will be accommodated in XYZ. Say all of them are out of 45 who want ABC. The leftover 15 who want ABC will need to be given ABC.
The 55 who want XYZ then will all be given ABC.

Hence only 15% get what they want and 85% do not get what they want in this case.
85% of 60 = (17/20)*60 = 51

Answer (A)

Karishma
Private Tutor for GMAT
Contact: [email protected]

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