According to a report on housing in a certain province, 9/10

Question

According to a report on housing in a certain province, 9/10 of housing units (single-family dwellings) are occupied and the rest are vacant. Of the occupied housing units, the report indicates that 2/3 are owner occupied (occupied by one or more of their owners) and the rest are rentals. The report also indicates that 2/5 of owner-occupied housing units and 3/5 of rentals are each occupied by fewer than three people.

Statement: Of all housing units in the province, X percent are owner occupied and occupied by fewer than three people, and Y percent are rentals and occupied by fewer than three people.

Select for X and for Y the options that complete the statement so that it is most accurate based on the information provided. Make only two selections, one in each column.

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Official Answer

X: 24 Y: 18

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Rishabh_Jain8 · Answer

Can someone please post the solution to this question?

Thanks in advance

ameyabarve · Answer

Request you to please provide a solution for this question

GMAT695 · Answer

Take total houses as 150.
Total occupied 9 x 150/ 10 = 135 , vacant = 15.

Owner Occupied , 2 X 135/ 3= 90, rentals 45.

2 X 90/ 5 = 36 are owner occupied and occupied by fewer than three people.

3 X 45/ 5 = 27 are rentals and occupied by people than 3 people.

X% = 36/ 150 = 24%
Y= 27/150 = 18 %.

MartyMurray · Answer

According to a report on housing in a certain province, 9/10 of housing units (single-family dwellings) are occupied and the rest are vacant. Of the occupied housing units, the report indicates that 2/3 are owner occupied (occupied by one or more of their owners) and the rest are rentals. The report also indicates that 2/5 of owner-occupied housing units and 3/5 of rentals are each occupied by fewer than three people.

Statement: Of all housing units in the province,  X  percent are owner occupied and occupied by fewer than three people, and  Y  percent are rentals and occupied by fewer than three people.

Select for  X  and for  Y  the options that complete the statement so that it is most accurate based on the information provided. Make only two selections, one in each column.

The math needed for answering this question is relatively simple. So, mostly, what we need to do to get this question correct is read carefully and execute well.

Pure Math Approach

Calculate X (the percentage that are owner occupied and occupied by fewer than three people)

9/10 occupied × 2/3 owner occupied = 6/10

6/10 × 2/5 occupied by fewer than three people = 12/50 = 24%

For X, select   24  .

Calculate Y (the percentage that are rentals and occupied by fewer than three people)

9/10 occupied × 1/3 rentals = 3/10

3/10 × 3/5 occupied by fewer than three people = 9/50 = 18%

For Y, select   18  .
 
  Smart Numbers Approach

Start with 100 for the province total.

Calculate X (the percentage that are owner occupied and occupied by fewer than three people)

100 × 9/10 occupied = 90

90 × 2/3 owner occupied = 60

60 × 2/5 occupied by fewer than three people = 24 = 24% of the total

For X, select   24  .

Calculate Y (the percentage that are rentals and occupied by fewer than three people)

100 × 9/10 occupied = 90

90 × 1/3 rentals = 30

30 × 3/5 occupied by fewer than three people = 18 = 18% of the total

For Y, select   18  .

Correct answer:    24  ,   18

hemanthPA · Answer

Say 100 housing units present in the province

Given info
100*9/10 = 90 – occupied, 10 - vacant

90*2/3 = 60 owner occupied, 30 rentals

60*2/5 = 24 owner occupied with fewer than three people

30*3/5 = 18 rentals occupied with fewer than three people

(24/100*100) = X = 24
(18/100*100) = Y = 18

VikramMarkiv · Answer

The easiest way to approach the problem would be with the help of a tree diagram to visualise it https://gmatclub.com/forum/download/file.php?id=83262 Breakdown of the Tree: Total Units (N) : Occupied Units : 9/10N Vacant Units : 1/10 2. Occupied Units: Owner-Occupied: 2/3 are owner-occupied, and the rest are rentals. 0.6N ----> (2/3 x 9/10N = 3/5N or 6/10N 0r 0.6N) Owner-Occupied with < 3 people : 2/5 of owner-occupied units are occupied by fewer than three people. 2/5 x 0.6N = 0.24N Owner-Occupied with ≥ 3 people : 1/5 x 0.6N = 0.36N Rental Units : 1 /3 are rental 0.3N (1/3 x 9/10N = 3/10N or 0.3N) Rental with < 3 people : 3/5 of rental units are occupied by fewer than three people.3/5 x 0.3N = 0.18N Rental with ≥ 3 people : 2/5 x 0.3N = 0.12N Percentages: X% (Owner-Occupied and Occupied by Fewer Than 3 People of all housing) : X= 0.24N × 100 = 24% Y% (Rental and Occupied by Fewer Than 3 People of all housing) : Y= 0.18N ×100 = 18% GMAT-Club-Forum-d31l9dtr.png GMAT-Club-Forum-ohex9zfv.png

harshj7879 · Answer

can any one explain this ques. through venn diagram?

Shikhar0711 · Answer

Hi Harsh,

I Hope this helps
Have taken total as 90,(mentioned 9/10 houses are occupied)

Rent 
 Owner

Less than 3 
  3/5*30=18  
  2/5*60=24  
 42 
 
  More than 3 
 12 
 36 
 48

30(1/3 of 90) 
 60(2/3 of 90) 
 90

Let me know if any further questions

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=86768 --- Harsha GMAT-Club-Forum-t4vqpjhu.png

According to a report on housing in a certain province, 9/10

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	Rent	Owner
Less than 3	3/5*30=18	2/5*60=24	42
More than 3	12	36	48
	30(1/3 of 90)	60(2/3 of 90)	90

GMAT Two-part Analysis (TPA) Questions

According to a report on housing in a certain province, 9/10

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My Rewards