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Difficulty:
65%
(hard)
Question Stats:
48% (01:45) correct
52%
(01:54)
wrong
based on 62
sessions
History
Date
Time
Result
Not Attempted Yet
In 2020, 1/4 of all convenience stores in Brockville closed. Since 2021, 21 new convenience stores have opened, and no others have closed. The total number of convenience stores in Brockville is now 10% greater than at the end of 2020.
How many convenience stores were there in Brockville at the beginning of 2020?
A. 60
B. 140
C. 210
D. 280
E. 350
How many convenience stores were there in Brockville at the beginning of 2020?
A. 60
B. 140
C. 210
D. 280
E. 350
18 Mar 2026, 23:23
Kudos
Bookmarks
Nice problem. The trick is keeping track of what moment in time you're calculating for.
Let x = number of convenience stores at the beginning of 2020.
1. In 2020, 1/4 closed. So after the closures, the number remaining = x - x/4 = (3/4)x.
2. Since 2021, 21 new stores opened, no others closed. Current count = (3/4)x + 21.
3. The current count is 10% greater than "immediately after the closures" (which was (3/4)x).
So: (3/4)x + 21 = 1.1 * (3/4)x
Solve for x:
(3/4)x + 21 = (3.3/4)x
21 = (3.3/4)x - (3/4)x
21 = (0.3/4)x
21 = 0.075x
x = 21 / 0.075 = 280
Quick check: if x = 280, after closures = 210. Add 21 new stores = 231. Is 231 exactly 10% more than 210? 210 * 1.1 = 231. Yes.
Answer: D (280).
The trap is option C (210), which is the number right after closures, not the original count. Easy to grab if you lose track of which snapshot the question is asking about.
Let x = number of convenience stores at the beginning of 2020.
1. In 2020, 1/4 closed. So after the closures, the number remaining = x - x/4 = (3/4)x.
2. Since 2021, 21 new stores opened, no others closed. Current count = (3/4)x + 21.
3. The current count is 10% greater than "immediately after the closures" (which was (3/4)x).
So: (3/4)x + 21 = 1.1 * (3/4)x
Solve for x:
(3/4)x + 21 = (3.3/4)x
21 = (3.3/4)x - (3/4)x
21 = (0.3/4)x
21 = 0.075x
x = 21 / 0.075 = 280
Quick check: if x = 280, after closures = 210. Add 21 new stores = 231. Is 231 exactly 10% more than 210? 210 * 1.1 = 231. Yes.
Answer: D (280).
The trap is option C (210), which is the number right after closures, not the original count. Easy to grab if you lose track of which snapshot the question is asking about.
