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26 Apr 2026, 13:03
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On January 1, 2026, Atlas Fitness had 48,000 more active members than Beacon Fitness. During 2026, the number of active members at each gym increased by \(p\) percent. After the increase, how many more active members did Atlas Fitness have than Beacon Fitness did?
(1) On January 1, 2026, Beacon Fitness’s number of active members was \(\frac{5}{11}\) of Atlas Fitness’s number of active members.
(2) \(p = 15\)
(1) On January 1, 2026, Beacon Fitness’s number of active members was \(\frac{5}{11}\) of Atlas Fitness’s number of active members.
(2) \(p = 15\)
26 Apr 2026, 13:04
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Official Solution:
On January 1, 2026, Atlas Fitness had 48,000 more active members than Beacon Fitness. During 2026, the number of active members at each gym increased by \(p\) percent. After the increase, how many more active members did Atlas Fitness have than Beacon Fitness did?
Let Atlas and Beacon start with \(A\) and \(B\) active members.
Given:
\(A - B = 48,000\)
After the \(p\) percent increase at both gyms:
Atlas becomes \(A * (1 + \frac{p}{100})\)
Beacon becomes \(B * (1 + \frac{p}{100})\)
So the new difference is:
\(A * (1 + \frac{p}{100}) - B * (1 + \frac{p}{100}) = (A - B) * (1 + \frac{p}{100}) = 48,000 * (1 + \frac{p}{100})\)
So, to answer the question, we only need \(p\).
(1) On January 1, 2026, Beacon Fitness’s number of active members was \(\frac{5}{11}\) of Atlas Fitness’s number of active members.
This only gives a relationship between \(A\) and \(B\), but \(p\) is still unknown, so the new difference is unknown. Not sufficient.
(2) \(p = 15\)
This gives the missing value of \(p\), so the new difference is \(48,000 * (1 + \frac{15}{100})\). Sufficient.
Answer: B
On January 1, 2026, Atlas Fitness had 48,000 more active members than Beacon Fitness. During 2026, the number of active members at each gym increased by \(p\) percent. After the increase, how many more active members did Atlas Fitness have than Beacon Fitness did?
Let Atlas and Beacon start with \(A\) and \(B\) active members.
Given:
\(A - B = 48,000\)
After the \(p\) percent increase at both gyms:
Atlas becomes \(A * (1 + \frac{p}{100})\)
Beacon becomes \(B * (1 + \frac{p}{100})\)
So the new difference is:
\(A * (1 + \frac{p}{100}) - B * (1 + \frac{p}{100}) = (A - B) * (1 + \frac{p}{100}) = 48,000 * (1 + \frac{p}{100})\)
So, to answer the question, we only need \(p\).
(1) On January 1, 2026, Beacon Fitness’s number of active members was \(\frac{5}{11}\) of Atlas Fitness’s number of active members.
This only gives a relationship between \(A\) and \(B\), but \(p\) is still unknown, so the new difference is unknown. Not sufficient.
(2) \(p = 15\)
This gives the missing value of \(p\), so the new difference is \(48,000 * (1 + \frac{15}{100})\). Sufficient.
Answer: B
