Of the 200 employees in a certain company, 25 percent will

Question

Of the 200 employees in a certain company, 25 percent will be relocated to City X and the remaining 75 percent will be relocated to City Y. However, 40 percent of the employees prefer City Y and 60 percent prefer City X. What is the highest possible number of employees who will be relocated to the city they prefer?

(A) 65
(B) 100
(C) 115
(D) 130
(E) 135

Just can't get this right. Any idea how to solve please?

(A) 65
(B) 100
(C) 115
(D) 130
(E) 135

Bunuel · Accepted Answer

120 prefer X (Group 1);
80 prefer Y (Group 2).

City Y needs 150 people: let  all 80  who prefer Y (entire Group 2) be relocated there, the rest 70 will be those who prefer X from Group 1;
City X needs 50 people: 120-70= 50  from Group 1 will be relocated to X, which they prefer.

So, the highest possible number of employees who will be relocated to the city they prefer is 80+50=130.

Answer: D.

TirthankarP · Answer

The best way to solve questions containing four different items is to draw a matrix box. As per the question: Total employees relocated to X = 25% of 200 = 50 Total employees relocated to Y = 75% of 200 = 150 Total employees who prefer city X = 60% of 200 = 120 Total employees who prefer city Y = 40% of 200 = 80 This can be represented in a matrix box as shown below: Matrix_1.png So we need to maximize the cells marked with green i.e. employees who prefer city X and gets relocated to city X + employees who prefer city Y and gets relocated to city Y. Maximum possible value of Prefer X - Relocate X cell is 50. Then the only possible value for Prefer X - Relocate Y cell is 70 because the total employees who prefer city X is 120. As Prefer X - Relocate X cell is 50, so Prefer Y - Relocate X cell has to be 0 because total employees actually relocated to city X is 50. And if Prefer Y - Relocate X is 0 then Prefer Y - Relocate Y has to be 80 because total employees who preferred city Y is 80. So now the completed matrix box looks like this: Matrix_2.png So total sum of green cells (employees who will be relocated to the city they prefer) = 50 + 80 = 130 Hence the correct answer is D

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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cumulonimbus · Answer

Hi Bunnel,

Will the minimum number of satisfied employees be 30?

Bunuel · Answer

_______________

Yes, absolutely.

avohden · Answer

i know the min/max concept is pretty basic but conceptually can one use overlapping sets/Venn diagram to solve this and other min/max problems? I'm not sure how to arrive at the min value (maybe someone could provide their input) but to solve for the max i think you can set-up two sets of two overlapping sets.

For display purposes i have found a sample overlapping set.
 https://d3scmz9sa6n2x2.cloudfront.net/blog/wp-content/uploads/2012/09/Ques3.jpg 
 https://d3scmz9sa6n2x2.cloudfront.net/blog/wp-content/uploads/2012/09/Ques3.jpg

The first set would represent the max value for City X and the second set would be for City Y. Circle A represents the total amount of people  relocating  to City X and the Circle B represents the total that  prefer  City X. To maximize the number of people that are relocated to their preferred city you would have to have the highest possible value from Circle A in the overlapping set. So for City X, circle A, the overlapping area and circle B would contain the following amounts: 0,50,120.

For City Y the amounts would be 70,80,0. The combined overlapping sets would equal the answer 130.

PareshGmat · Answer

It will come up in this way.... Matrix_1.png

Nunuboy1994 · Answer

The wording is perhaps the only obstacle- the actual math is relatively simple. How? Well, what the question is basically stating is that 25 percent of employees  will  move to city X and 75 percent of employees  will  move to city Y. So the boss is pretty much saying ok 50 of you are going to City X and 150 of going to City Y regardless of who wants what. Who wants what? 80 of the employees want to go to city Y and 120 want to go to City X- but that of course cannot happen because only 50 employees will be moved to city X on the boss' order. So Human Resources basically steps in and says well okay we care about employee happiness and we want to minimize the number of unhappy employees so we need to make sure we get as many employees as possible moved to the city they want to work in. From here have to try to create a distribution of employees that maximizes the placement of employees into City's they want to go to.

As we can see from the diagram- we can put all 80 citizens that want to go to city Y into city Y because city Y requires 150 employees on the boss's order. But wait we still need 70 more employees... so okay how about we move 50 employees that want to work at City X to City X and the 70 employees left that don't want to go to City Y...well too bad because we've just put 80 employees that wanted to go City Y at City and 50 that want to go to City X at X so we've made 130 employees happy- so the other 70 can go suck it up.

Kinshook · Answer

Given: Of the 200 employees in a certain company, 25 percent will be relocated to City X and the remaining 75 percent will be relocated to City Y. However, 40 percent of the employees prefer City Y and 60 percent prefer City X. 
Asked: What is the highest possible number of employees who will be relocated to the city they prefer?

Relocated to City X  Relocated to City Y  Total  
  Prefer City X  x  120-x  120  
  Prefer City Y  50-x  x+30  80  
  Total  50  150  200

Number of employees relocated to city they prefer = x + x + 30 = 2x + 30
x can be max 50

Relocated to City X  Relocated to City Y  Total  
  Prefer City X  50  70  120  
  Prefer City Y  0  80  80  
  Total  50  150  200

Max number of employees relocated to city they prefer = 2x + 30 = 130

IMO D

kayarat600 · Answer

I solved this question but pretending this is a 15% question is ridiculous.

Bunuel · Answer

The difficulty level of a question on the site, after sufficient attempts, is determined automatically based on various parameters collected from users' attempts via timer, such as the percentage of correct answers and the time taken to answer the question. So, this is an easy question based on our statistics. https://gmatclub.com/forum/download/file.php?id=81278 GMAT-Club-Forum-w5yv4d7o.png

Adit_ · Answer

Feel this is a medium level question and not easy. The easiest way to do it is since max of overlaps = the min. of the two. Take min. of X = 25% and min. of Y = 40%

Thus total = 25+40 = 65% of 200 = 130.

Answer:  Option D

___________________________

Is the minimum going to be if All those who prefer Y try to occupy the portion of relocating to X and thus minimum extra is 40-25=15% = 30?
 Bunuel

Of the 200 employees in a certain company, 25 percent will

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	Relocated to City X	Relocated to City Y	Total
Prefer City X	x	120-x	120
Prefer City Y	50-x	x+30	80
Total	50	150	200

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