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26 Feb 2012, 15:29
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
85% (02:02) correct
15%
(02:14)
wrong
based on 1274
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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
(A) 65
(B) 100
(C) 115
(D) 130
(E) 135
26 Feb 2012, 15:50
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enigma123
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
Joined: 29 Apr 2013
Last visit: 10 Jan 2016
Posts: 81
Given Kudos: 53
Location: India
Concentration: General Management, Strategy
Schools: PGDM (GM) '15 (A)
GMAT Date: 11-06-2013
WE:Programming (Telecommunications)
04 Oct 2013, 12:03
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enigma123
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 22137 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 21886 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
