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E
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Difficulty:
85%
(hard)
Question Stats:
60% (02:27) correct
40%
(02:48)
wrong
based on 88
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Not Attempted Yet
One year ago, \(\frac{2}{5}\) of the adults residing in Keaston had a bicycle. Since then, \(\frac14\) of the adults residing in Keaston who did not have a bicycle have acquired one, and the 20 adults who have moved to Keaston in the last year have bicycles and still reside there. Adults residing in Keaston who own bicycles now outnumber those who do not by 62. Assuming that no people residing in Keaston one year ago have died, moved away or become adults, how many adults now reside in Keaston?
(A) 140
(B) 160
(C) 400
(D) 420
(E) 440
(A) 140
(B) 160
(C) 400
(D) 420
(E) 440
06 May 2026, 01:57
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Take the LCM of 5 and 4.
LCM = 20
So assume total residents last year = 20x
Then:
Residents with bicycles
= (2/5)(20x)
= 8x
Residents without bicycles
= 12x
---
Now:
1/4 of the people without bicycles acquired one.
So new bicycle owners added:
= (1/4)(12x)
= 3x
Therefore current bicycle owners:
= 8x + 3x + 20
= 11x + 20
(the extra 20 people who moved in already own bicycles)
---
Current residents without bicycles:
= 12x - 3x
= 9x
Now according to the question:
people with bicycles outnumber people without bicycles by 62.
So:
(11x + 20) - 9x = 62
2x + 20 = 62
2x = 42
x = 21
---
Current total residents:
= 20x + 20
= 20(21) + 20
= 440
Answer = E
---
The fastest step here is taking the LCM of 5 and 4 first.
That makes the fractions disappear immediately.
— Rajdeep
LCM = 20
So assume total residents last year = 20x
Then:
Residents with bicycles
= (2/5)(20x)
= 8x
Residents without bicycles
= 12x
---
Now:
1/4 of the people without bicycles acquired one.
So new bicycle owners added:
= (1/4)(12x)
= 3x
Therefore current bicycle owners:
= 8x + 3x + 20
= 11x + 20
(the extra 20 people who moved in already own bicycles)
---
Current residents without bicycles:
= 12x - 3x
= 9x
Now according to the question:
people with bicycles outnumber people without bicycles by 62.
So:
(11x + 20) - 9x = 62
2x + 20 = 62
2x = 42
x = 21
---
Current total residents:
= 20x + 20
= 20(21) + 20
= 440
Answer = E
---
The fastest step here is taking the LCM of 5 and 4 first.
That makes the fractions disappear immediately.
— Rajdeep
18 Aug 2026, 04:08
Kudos
Bookmarks
edited the heading only
