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

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Of the 200 employees in a certain company, 25 percent will [#permalink]

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26 Feb 2012, 15:29
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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?
[Reveal] Spoiler: OA

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Re: Relocation [#permalink]

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26 Feb 2012, 15:50
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enigma123 wrote:
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?

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.
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Re: Of the 200 employees in a certain company, 25 percent will [#permalink]

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14 Jun 2013, 05:28
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Re: Relocation [#permalink]

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24 Jun 2013, 23:42
Bunuel wrote:
enigma123 wrote:
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?

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.

Hi Bunnel,

Will the minimum number of satisfied employees be 30?
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Re: Relocation [#permalink]

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25 Jun 2013, 02:38
cumulonimbus wrote:
Bunuel wrote:
enigma123 wrote:
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?

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.

Hi Bunnel,

Will the minimum number of satisfied employees be 30?

_______________

Yes, absolutely.
_________________
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Re: Of the 200 employees in a certain company, 25 percent will [#permalink]

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04 Oct 2013, 01:34
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.

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.
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Re: Of the 200 employees in a certain company, 25 percent will [#permalink]

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04 Oct 2013, 12:03
enigma123 wrote:
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

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:
Attachment:

Matrix_1.png [ 2.51 KiB | Viewed 3332 times ]

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:
Attachment:

Matrix_2.png [ 2.85 KiB | Viewed 3334 times ]

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
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Re: Of the 200 employees in a certain company, 25 percent will [#permalink]

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Hi Bunnel,

Will the minimum number of satisfied employees be 30?

It will come up in this way....
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Re: Of the 200 employees in a certain company, 25 percent will   [#permalink] 11 Mar 2017, 03:50
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# Of the 200 employees in a certain company, 25 percent will

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Of the 200 employees in a certain company, 25 percent will [#permalink]

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26 Feb 2012, 15:29
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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?
[Reveal] Spoiler: OA

_________________

Best Regards,
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MGMAT 1 --> 530
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GMAT ==> 730

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Kudos [?]: 106115 [1] , given: 11607

Re: Relocation [#permalink]

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26 Feb 2012, 15:50
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enigma123 wrote:
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?

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.
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Re: Of the 200 employees in a certain company, 25 percent will [#permalink]

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14 Jun 2013, 05:28
Expert's post
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Re: Relocation [#permalink]

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24 Jun 2013, 23:42
Bunuel wrote:
enigma123 wrote:
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?

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.

Hi Bunnel,

Will the minimum number of satisfied employees be 30?
Math Expert
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Posts: 38871
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Re: Relocation [#permalink]

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25 Jun 2013, 02:38
cumulonimbus wrote:
Bunuel wrote:
enigma123 wrote:
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?

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.

Hi Bunnel,

Will the minimum number of satisfied employees be 30?

_______________

Yes, absolutely.
_________________
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Re: Of the 200 employees in a certain company, 25 percent will [#permalink]

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04 Oct 2013, 01:34
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.

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.
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Re: Of the 200 employees in a certain company, 25 percent will [#permalink]

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04 Oct 2013, 12:03
enigma123 wrote:
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

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:
Attachment:

Matrix_1.png [ 2.51 KiB | Viewed 3332 times ]

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:
Attachment:

Matrix_2.png [ 2.85 KiB | Viewed 3334 times ]

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
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Hi Bunnel,

Will the minimum number of satisfied employees be 30?

It will come up in this way....
Attachment:

Matrix_1.png [ 3.61 KiB | Viewed 2397 times ]

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Re: Of the 200 employees in a certain company, 25 percent will   [#permalink] 11 Mar 2017, 03:50
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6 If 75 percent of the employees of a certain company take a winter 7 22 Sep 2016, 12:48
3 In a company of 300 employees, 120 are females. A total of 200 employ 5 18 Nov 2016, 11:49
7 Among the employees of a certain company, 52 percent of the 10 11 Oct 2014, 13:16
5 There are 200 female managers in a certain company. Find the 8 01 Jul 2016, 20:04
1 Today a manufacturing company sold 200 units of a certain 4 05 Dec 2015, 03:14
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# Of the 200 employees in a certain company, 25 percent will

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user
The content of the passage suggests that the author would be most likely to agree with which of the following statements?

I. Those who are interested in the development of the novel as a literary genre should concentrate on the eighteenth and nineteenth centuries.

II. The study of precursors of a literary genre is more important to the study of the genre itself than is the study of the genre's conventions.

III. The novel is a genre whose development can be seen in the context of other literary genres of the same period.

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III

I think the answer is (C) III only. The passage suggests that the development of the novel can be understood in the context of other literary genres of the same period, but it does not suggest that those interested in the development of the novel should concentrate on the eighteenth and nineteenth centuries, nor does it suggest that the study of precursors is more important than the study of the genre's conventions. Can you confirm this?