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06 Aug 2026, 05:26
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At the beginning of 2023, a fitness club had 800 active members. During 2023, some of the members who had been active at the beginning of the year canceled their memberships and did not rejoin, and every new member who joined during 2023 remained active through the end of the year. If \(x\) percent of the members active at the beginning of 2023 canceled their memberships and did not rejoin, and if the number of active members at the end of 2023 was \(y\) percent greater than the number active at the beginning of 2023, how many new members joined the club during 2023?
(1) \(x - y = 7\)
(2) \(x + y = 35\)
(1) \(x - y = 7\)
(2) \(x + y = 35\)
06 Aug 2026, 05:26
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Official Solution:
At the beginning of 2023, a fitness club had 800 active members. During 2023, some of the members who had been active at the beginning of the year canceled their memberships and did not rejoin, and every new member who joined during 2023 remained active through the end of the year. If \(x\) percent of the members active at the beginning of 2023 canceled their memberships and did not rejoin, and if the number of active members at the end of 2023 was \(y\) percent greater than the number active at the beginning of 2023, how many new members joined the club during 2023?
At the beginning of 2023, the club had 800 active members.
\(x\) percent of those members canceled and did not rejoin, so the number of such members was:
\(800 * \frac{x}{100} = 8x\)
At the end of 2023, the club had \(y\) percent more active members than it had at the beginning of the year, so the net increase was:
\(800 * \frac{y}{100} = 8y\)
The new members had to replace the \(8x\) members who canceled and also account for the net increase of \(8y\) members.
So the number of new members who joined was:
\(8x + 8y = 8(x + y)\)
The question asks for \(8(x + y)\).
(1) \(x - y = 7\)
This gives only the difference between \(x\) and \(y\), not their sum.
For example, \(x = 17\) and \(y = 10\) gives \(x + y = 27\).
But \(x = 21\) and \(y = 14\) gives \(x + y = 35\).
So the number of new members is not fixed.
Not sufficient.
(2) \(x + y = 35\)
So:
\(8(x + y) = 8 * 35 = 280\)
Sufficient.
Answer: B
At the beginning of 2023, a fitness club had 800 active members. During 2023, some of the members who had been active at the beginning of the year canceled their memberships and did not rejoin, and every new member who joined during 2023 remained active through the end of the year. If \(x\) percent of the members active at the beginning of 2023 canceled their memberships and did not rejoin, and if the number of active members at the end of 2023 was \(y\) percent greater than the number active at the beginning of 2023, how many new members joined the club during 2023?
At the beginning of 2023, the club had 800 active members.
\(x\) percent of those members canceled and did not rejoin, so the number of such members was:
\(800 * \frac{x}{100} = 8x\)
At the end of 2023, the club had \(y\) percent more active members than it had at the beginning of the year, so the net increase was:
\(800 * \frac{y}{100} = 8y\)
The new members had to replace the \(8x\) members who canceled and also account for the net increase of \(8y\) members.
So the number of new members who joined was:
\(8x + 8y = 8(x + y)\)
The question asks for \(8(x + y)\).
(1) \(x - y = 7\)
This gives only the difference between \(x\) and \(y\), not their sum.
For example, \(x = 17\) and \(y = 10\) gives \(x + y = 27\).
But \(x = 21\) and \(y = 14\) gives \(x + y = 35\).
So the number of new members is not fixed.
Not sufficient.
(2) \(x + y = 35\)
So:
\(8(x + y) = 8 * 35 = 280\)
Sufficient.
Answer: B
