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23 May 2020, 06:33
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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:
25%
(medium)
Question Stats:
77% (01:44) correct
23%
(02:06)
wrong
based on 1045
sessions
History
Date
Time
Result
Not Attempted Yet
At a certain company, 30 percent of the employees live in City R. If 25 percent of the company’s employees live in apartments in City R, what is the number of the employees who live in apartments in City R ?
(1) Of the employees who live in City R, 6 do not live in apartments.
(2) Of the employees, 84 do not live in City R.
ID: 700143
DS21244
(1) Of the employees who live in City R, 6 do not live in apartments.
(2) Of the employees, 84 do not live in City R.
ID: 700143
DS21244
04 Aug 2020, 13:04
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Bunuel
Given: 30 percent of the employees live in City R. 25 percent of the company’s employees live in apartments in City R
One approach is to use the Double Matrix Method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of employees, and the two characteristics are:
- lives in City R or does not live in City R
- lives in apartment or does not live in apartment
Aside: We can also use Venn diagrams and formulae to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method works every time.
We can set up our diagram as follows:
NOTE: I'm letting x = the total number of employees at the company
30 percent of the employees live in City R
If 30% live in City R, then 70% do NOT live in City R.
So, 0.3x = the NUMBER of employees who live in City R
And 0.7x = the NUMBER of employees who DON'T live in City R
25 percent of the company’s employees live in apartments in City R
So, 0.25x = the NUMBER of employees who live in apartments AND live in City R
NOTE: Since the two boxes in the top row must add to 0.3x, the missing box must be 0.05x
Target question: What is the number of the employees who live in apartments AND live in City R?
In other words, What is the value of 0.25x?
Statement 1: Of the employees who live in City R, 6 do not live in apartments.
The top right box (0.05x) represents the NUMBER of employees who live in the city R but do not live in apartments.
So we can write: 0.05x = 6
Solve: x = 6/0.05 = 120
If x = 120, then 0.25x = 30, which means 30 employees live in apartments AND live in City R
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: Of the employees, 84 do not live in City R.
Since 0.7x = the NUMBER of employees who DON'T live in City R, we can write: 0.7x = 84
Solve: x = 84/0.7 = 120
If x = 120, then 0.25x = 30, which means 30 employees live in apartments AND live in City R
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
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 this video:
EXTRA PRACTICE QUESTION
General Discussion
23 May 2020, 06:38
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Bunuel
Let, Total employees in company = 200x
City R residents = 30% of 200x = 60x
EMployees living in apartments in City R = 25% of 60x = 15x
Question: 15x = ?
Statement 1: Of the employees who live in City R, 6 do not live in apartments.
i.e 60x - 15x = 6
i.e. 45x = 6
i.e. 15x = 2
SUFFICIENT
Statement 2: Of the employees, 84 do not live in City R.
200x - 60x = 84
SUFFICIENT
Answer: Option D
