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11 Mar 2026, 22:52
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
39% (03:28) correct
61%
(03:38)
wrong
based on 33
sessions
History
Date
Time
Result
Not Attempted Yet
One-fourth of the houses in San Isidoro are currently wheelchair accessible (WA). City regulations require that by 2040 at least one-half of the houses be WA. By then, one-third of the houses that are not WA will have been demolished, but no other houses will be demolished. By 2040, enough new houses will have been built to increase the total number of houses in San Isidoro by 50 percent. Three-fifths of these new houses will be WA. To meet the regulation, what fraction of the houses that are currently not WA and that will not be demolished must be converted to WA?
A. 1/10
B. 1/8
C. 1/6
D. 1/5
E. 2/5
A. 1/10
B. 1/8
C. 1/6
D. 1/5
E. 2/5
12 Mar 2026, 03:04
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This is a multi-step Fractions and Ratios question — the kind that looks complex but becomes very clean once you pick a smart starting number. The key concept is Smart Number / Picking Values with fractions.
The common trap: students try to track percentages and fractions algebraically, lose track of which group is which, and end up with the wrong denominator. Picking 60 as your starting total makes everything work out to whole numbers.
Step 1 — Assign a starting number: Let the current total = 60 houses.
• Currently WA: (1/4) × 60 = 15
• Currently not WA: 45
Step 2 — Work out what happens by 2040:
• Total houses increases by 50%: new total = 60 × 1.5 = 90
• One-third of non-WA houses are demolished: (1/3) × 45 = 15 demolished
• Remaining old non-WA (not demolished): 45 − 15 = 30
• Old WA houses remain: 15 (no WA houses are demolished)
• Old houses remaining: 15 + 30 = 45
• New houses built: 90 − 45 = 45 new houses
• New houses that are WA: (3/5) × 45 = 27
Step 3 — Calculate total WA houses in 2040 before conversions:
WA so far = 15 (old WA) + 27 (new WA) = 42
Step 4 — Find the required WA count and the shortfall:
Required: at least (1/2) × 90 = 45 WA houses
Shortfall = 45 − 42 = 3 houses need to be converted
Step 5 — Find the fraction of eligible houses that must be converted:
Eligible houses = old non-WA houses that were NOT demolished = 30
Fraction = 3/30 = 1/10
The answer is A.
Common trap: Some students use the total new houses (45) as the denominator instead of the eligible old non-WA survivors (30). The question specifically asks about "houses that are currently not WA AND will not be demolished" — those are only the 30 old surviving non-WA houses.
Takeaway: On multi-condition fraction problems, always list out each subgroup separately before doing any arithmetic — rushing to combine groups is where most errors happen.
The common trap: students try to track percentages and fractions algebraically, lose track of which group is which, and end up with the wrong denominator. Picking 60 as your starting total makes everything work out to whole numbers.
Step 1 — Assign a starting number: Let the current total = 60 houses.
• Currently WA: (1/4) × 60 = 15
• Currently not WA: 45
Step 2 — Work out what happens by 2040:
• Total houses increases by 50%: new total = 60 × 1.5 = 90
• One-third of non-WA houses are demolished: (1/3) × 45 = 15 demolished
• Remaining old non-WA (not demolished): 45 − 15 = 30
• Old WA houses remain: 15 (no WA houses are demolished)
• Old houses remaining: 15 + 30 = 45
• New houses built: 90 − 45 = 45 new houses
• New houses that are WA: (3/5) × 45 = 27
Step 3 — Calculate total WA houses in 2040 before conversions:
WA so far = 15 (old WA) + 27 (new WA) = 42
Step 4 — Find the required WA count and the shortfall:
Required: at least (1/2) × 90 = 45 WA houses
Shortfall = 45 − 42 = 3 houses need to be converted
Step 5 — Find the fraction of eligible houses that must be converted:
Eligible houses = old non-WA houses that were NOT demolished = 30
Fraction = 3/30 = 1/10
The answer is A.
Common trap: Some students use the total new houses (45) as the denominator instead of the eligible old non-WA survivors (30). The question specifically asks about "houses that are currently not WA AND will not be demolished" — those are only the 30 old surviving non-WA houses.
Takeaway: On multi-condition fraction problems, always list out each subgroup separately before doing any arithmetic — rushing to combine groups is where most errors happen.
12 Mar 2026, 07:14
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kevincan
Let the number of houses currently be 100.
(1/4)th of the houses are WA = (1/4)*100 = 25
Houses which are NOT WA = 75.
Houses which are NOT WA but demolished = (1/3)*75 = 25.
Houses which are NOT WA but NOT demolished = 50.
By 2040, the population increased by 50%.
The population is 150 by 2040.
At least (1/2) of the population is WA = (1/2)*150 = 75.
OLD population = 25 (WA) + 50(~ WA NOT demolished) = totally 75.
So, new population must include 75.
(3/5) of the new houses will be WA = (3/5)*75 = 45
Total WA (2040) = 25 + 45 = 70
To meet the regulation, what fraction of the houses that are currently not WA and that will not be demolished must be converted to WA?
We need an extra 5 to meet the criteria : at least (1/2) of population must be WA. = (1/2)*150 = 75.
To meet the requirements, we need 5 extra.
That 5 needs to be selected from 50(~ WA NOT demolished).
(5/50) = 1/10
Option A
