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19 May 2026, 19:00
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E
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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.
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M47-161
09 Jun 2026, 01:15
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GMAT Club 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 x/y.
Since the ratio of membership packages sold to guest passes issued was the same at both locations:
N/x = S/y
So:
x/y = N/S
Thus, to determine x/y, we need to determine 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 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 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:
720/90 = 8
That is:
x/N = y/S = 8
However, this still does not determine x/y.
For example, if N = 90 and S = 180, then:
x = 720 and y = 1440
So:
x/y = 1/2
But if N = 180 and S = 270, then:
x = 1440 and y = 2160
So:
x/y = 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 x/y.
Since the ratio of membership packages sold to guest passes issued was the same at both locations:
N/x = S/y
So:
x/y = N/S
Thus, to determine x/y, we need to determine 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 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 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:
720/90 = 8
That is:
x/N = y/S = 8
However, this still does not determine x/y.
For example, if N = 90 and S = 180, then:
x = 720 and y = 1440
So:
x/y = 1/2
But if N = 180 and S = 270, then:
x = 1440 and y = 2160
So:
x/y = 2/3
Not sufficient.
Answer: E.
General Discussion
19 May 2026, 19:27
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I also got (E).
At first I tried setting variables:
North:
guest passes = x
memberships = y
South:
guest passes = x + 720
memberships = y + 90
Since the ratio of memberships to guest passes is the same at both locations:
y/x = (y + 90)/(x + 720)
Cross-multiplying:
xy + 720y = xy + 90x
720y = 90x
x = 8y
But even after getting this relation, we still cannot determine an exact value for the ratio of North guest passes to South guest passes.
Because:
North : South guest passes
= x : (x + 720)
and x itself is not fixed.
Multiple values can satisfy the condition.
So even using both statements together, the ratio cannot be uniquely determined.
Therefore, the answer should be:
(E)
— Rajdeep
At first I tried setting variables:
North:
guest passes = x
memberships = y
South:
guest passes = x + 720
memberships = y + 90
Since the ratio of memberships to guest passes is the same at both locations:
y/x = (y + 90)/(x + 720)
Cross-multiplying:
xy + 720y = xy + 90x
720y = 90x
x = 8y
But even after getting this relation, we still cannot determine an exact value for the ratio of North guest passes to South guest passes.
Because:
North : South guest passes
= x : (x + 720)
and x itself is not fixed.
Multiple values can satisfy the condition.
So even using both statements together, the ratio cannot be uniquely determined.
Therefore, the answer should be:
(E)
— Rajdeep
