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GMAT695
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According to a report on housing in a certain province, 9/10 Updated on: 27 Sep 2024, 10:15
Originally posted by GMAT695 on 24 Sep 2024, 09:14.
Last edited by GMAT695 on 27 Sep 2024, 10:15, edited 1 time in total.
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X: 24 Y: 18
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35% (medium)

Question Stats:

76% (02:43) correct 24% (02:52) wrong based on 824 sessions

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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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Rishabh_Jain8
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According to a report on housing in a certain province, 9/10 25 Sep 2024, 11:55
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Can someone please post the solution to this question?

Thanks in advance
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According to a report on housing in a certain province, 9/10 27 Sep 2024, 03:55
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Request you to please provide a solution for this question
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According to a report on housing in a certain province, 9/10 27 Sep 2024, 10:12
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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 %.
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According to a report on housing in a certain province, 9/10 27 Sep 2024, 15:44
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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
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According to a report on housing in a certain province, 9/10 25 Nov 2024, 00:59
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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
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According to a report on housing in a certain province, 9/10 07 Dec 2024, 22:18
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GMAT695
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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The easiest way to approach the problem would be with the help of a tree diagram to visualise it



Breakdown of the Tree:
  1. 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%
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According to a report on housing in a certain province, 9/10 12 Dec 2024, 01:39
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can any one explain this ques. through venn diagram?
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According to a report on housing in a certain province, 9/10 01 Jan 2025, 09:34
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harshj7879
can any one explain this ques. through venn diagram?
Hi Harsh,

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


RentOwner
Less than 33/5*30=182/5*60=2442
More than 3123648
30(1/3 of 90)60(2/3 of 90)90

Let me know if any further questions
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