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19 May 2026, 19:00
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E
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Difficulty:
35%
(medium)
Question Stats:
71% (02:14) correct
29%
(02:16)
wrong
based on 55
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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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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
20 May 2026, 05:49
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Answer: (E)
This is a Data Sufficiency ratio problem, and the key insight is that the question asks for a specific ratio (N/S), not just whether the two locations are related.
Let r = the common ratio of memberships to guest passes at both locations.
Let N = guest passes issued by North, S = guest passes issued by South.
Then memberships at North = rN, memberships at South = rS.
S1 alone: S - N = 720. We just know the difference. N/S could be 100:820, or 200:920, or infinitely many other values. Insufficient.
S2 alone: rS - rN = 90, meaning r(S - N) = 90. We know the product of r and (S - N), but neither value individually. For example, r = 1/8 with S - N = 720 works, but so does r = 1/10 with S - N = 900. Without knowing S - N, we can't find N/S. Insufficient.
Together: From S2, r * (S - N) = 90. From S1, S - N = 720. So r = 90/720 = 1/8. Good, we know the ratio. But does knowing r help us find N/S? No — r is the membership-to-guest-pass ratio, not the North-to-South ratio. We still only know S - N = 720, which is one equation with two unknowns N and S.
N = 100, S = 820 → N/S = 100/820
N = 200, S = 920 → N/S = 200/920
Both satisfy all conditions with r = 1/8. So N/S is not determined.
The trap is thinking that knowing r uniquely determines the ratio of the locations. It doesn't. We'd need an absolute value (like the total guest passes, or individual numbers) to pin down N/S.
This is a Data Sufficiency ratio problem, and the key insight is that the question asks for a specific ratio (N/S), not just whether the two locations are related.
Let r = the common ratio of memberships to guest passes at both locations.
Let N = guest passes issued by North, S = guest passes issued by South.
Then memberships at North = rN, memberships at South = rS.
S1 alone: S - N = 720. We just know the difference. N/S could be 100:820, or 200:920, or infinitely many other values. Insufficient.
S2 alone: rS - rN = 90, meaning r(S - N) = 90. We know the product of r and (S - N), but neither value individually. For example, r = 1/8 with S - N = 720 works, but so does r = 1/10 with S - N = 900. Without knowing S - N, we can't find N/S. Insufficient.
Together: From S2, r * (S - N) = 90. From S1, S - N = 720. So r = 90/720 = 1/8. Good, we know the ratio. But does knowing r help us find N/S? No — r is the membership-to-guest-pass ratio, not the North-to-South ratio. We still only know S - N = 720, which is one equation with two unknowns N and S.
N = 100, S = 820 → N/S = 100/820
N = 200, S = 920 → N/S = 200/920
Both satisfy all conditions with r = 1/8. So N/S is not determined.
The trap is thinking that knowing r uniquely determines the ratio of the locations. It doesn't. We'd need an absolute value (like the total guest passes, or individual numbers) to pin down N/S.
