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A fitness studio chain sold membership packages at two locations, North and South. At both locations, the ratio of the number of membership packages sold to the number of guest passes issued was the same. What is the ratio of the number of guest passes issued by the North location to the number of guest passes issued by the South location?
(1) The South location issued 720 more guest passes than the North location.
(2) The South location sold 90 more membership packages than the North location.
(1) The South location issued 720 more guest passes than the North location.
(2) The South location sold 90 more membership packages than the North location.
05 Aug 2026, 23:18
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Official Solution:
A fitness studio chain sold membership packages at two locations, North and South. At both locations, the ratio of the number of membership packages sold to the number of guest passes issued was the same. What is the ratio of the number of guest passes issued by the North location to the number of guest passes issued by the South location?
Let \(N\) be the number of membership packages sold at the North location, and let \(S\) be the number of membership packages sold at the South location.
Let \(x\) be the number of guest passes issued by the North location, and let \(y\) be the number of guest passes issued by the South location.
The question asks for \(\frac{x}{y}\).
Since the ratio of membership packages sold to guest passes issued was the same at both locations:
\(\frac{N}{x} = \frac{S}{y}\)
So:
\(\frac{x}{y} = \frac{N}{S}\)
Thus, to determine \(\frac{x}{y}\), we need to determine \(\frac{N}{S}\).
(1) The South location issued 720 more guest passes than the North location.
This gives:
\(y - x = 720\)
This gives only the difference between \(x\) and \(y\), not the ratio \(\frac{x}{y}\).
Not sufficient.
(2) The South location sold 90 more membership packages than the North location.
This gives:
\(S - N = 90\)
This gives only the difference between \(S\) and \(N\), not the ratio \(\frac{N}{S}\).
Not sufficient.
(1)+(2) From statement (2), the South location sold 90 more membership packages than the North location.
From statement (1), the South location issued 720 more guest passes than the North location.
So the common ratio of guest passes issued to membership packages sold is:
\(\frac{720}{90} = 8\)
That is:
\(\frac{x}{N} = \frac{y}{S} = 8\)
However, this still does not determine \(\frac{x}{y}\).
For example, if \(N = 90\) and \(S = 180\), then:
\(x = 720\) and \(y = 1,440\)
So:
\(\frac{x}{y} = \frac{1}{2}\)
But if \(N = 180\) and \(S = 270\), then:
\(x = 1,440\) and \(y = 2,160\)
So:
\(\frac{x}{y} = \frac{2}{3}\)
Not sufficient.
Answer: E
A fitness studio chain sold membership packages at two locations, North and South. At both locations, the ratio of the number of membership packages sold to the number of guest passes issued was the same. What is the ratio of the number of guest passes issued by the North location to the number of guest passes issued by the South location?
Let \(N\) be the number of membership packages sold at the North location, and let \(S\) be the number of membership packages sold at the South location.
Let \(x\) be the number of guest passes issued by the North location, and let \(y\) be the number of guest passes issued by the South location.
The question asks for \(\frac{x}{y}\).
Since the ratio of membership packages sold to guest passes issued was the same at both locations:
\(\frac{N}{x} = \frac{S}{y}\)
So:
\(\frac{x}{y} = \frac{N}{S}\)
Thus, to determine \(\frac{x}{y}\), we need to determine \(\frac{N}{S}\).
(1) The South location issued 720 more guest passes than the North location.
This gives:
\(y - x = 720\)
This gives only the difference between \(x\) and \(y\), not the ratio \(\frac{x}{y}\).
Not sufficient.
(2) The South location sold 90 more membership packages than the North location.
This gives:
\(S - N = 90\)
This gives only the difference between \(S\) and \(N\), not the ratio \(\frac{N}{S}\).
Not sufficient.
(1)+(2) From statement (2), the South location sold 90 more membership packages than the North location.
From statement (1), the South location issued 720 more guest passes than the North location.
So the common ratio of guest passes issued to membership packages sold is:
\(\frac{720}{90} = 8\)
That is:
\(\frac{x}{N} = \frac{y}{S} = 8\)
However, this still does not determine \(\frac{x}{y}\).
For example, if \(N = 90\) and \(S = 180\), then:
\(x = 720\) and \(y = 1,440\)
So:
\(\frac{x}{y} = \frac{1}{2}\)
But if \(N = 180\) and \(S = 270\), then:
\(x = 1,440\) and \(y = 2,160\)
So:
\(\frac{x}{y} = \frac{2}{3}\)
Not sufficient.
Answer: E
