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04 Jul 2025, 09:30
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Bunuel
(1) The moving service charged a total of 3.3p dollars for the trip.
Miles travelled = n
p + (n - 5)*0.1p = 3.3p
p + 0.1pn + 0.5p = 3.3p
3.3p-1.5p = 0.1pn
2.8p = pn
n = 28
(2) The moving service charged a total of $132 for the trip.
Assume p = 132
Miles travelled can be upto 5
If p = 31, miles travelled will above 30.
Not sufficient.
Option A
04 Jul 2025, 09:43
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From the first fact alone that the total charge was 3.3 p we know the extra‐mile charge beyond the initial p must have been 2.3 p. Since each extra mile (or part of a mile) costs 0.1 p, that means the mover billed for exactly 23 extra miles. Adding those to the initial 5 miles gives between 28 and 28 2⁄3 miles total so the trip could not have exceeded 30 miles. Thus (1) is enough by itself.
By contrast, knowing only that the bill was $132 leaves p unspecified (aside from being over $30), so different choices of p yield different mileages some under 30, some over. Hence (2) alone is not enough. We don’t need both together once (1) already settles the question.
By contrast, knowing only that the bill was $132 leaves p unspecified (aside from being over $30), so different choices of p yield different mileages some under 30, some over. Hence (2) alone is not enough. We don’t need both together once (1) already settles the question.
Bunuel
MaxFabianKirchner
Joined: 02 Jun 2025
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Schools: ESSEC MiF '26 ESADE HEC Imperial LBS Oxford MFE '26 Sloan (MIT) NYU Stern NUS Bocconi IE'26
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Schools: ESSEC MiF '26 ESADE HEC Imperial LBS Oxford MFE '26 Sloan (MIT) NYU Stern NUS Bocconi IE'26
Posts: 65
04 Jul 2025, 09:55
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The cost structure can be modeled algebraically. Let `x` be the number of additional miles charged beyond the first 5. The phrase "or fraction of a mile" implies `x` must be an integer. The total cost `C` for any trip longer than 5 miles is `C = p + x(0.1p)`. A trip of exactly 30 miles corresponds to `x = 25` additional miles charged. A trip of more than 30 miles corresponds to `x >= 26`. The question "was a particular trip more than 30 miles long?" is therefore equivalent to the question "Is x >= 26?".
Statement (1) states that the total cost was `C = 3.3p`. Substituting this into the cost formula yields `3.3p = p + x(0.1p)`. Since the problem states `p > 30`, `p` is a positive, non-zero value and can be divided from both sides of the equation, resulting in `3.3 = 1 + 0.1x`. Solving this equation gives a single, definitive value: `x = 23`. With this value, the answer to the question "Is x >= 26?" is a definitive "No". Therefore, Statement (1) is sufficient.
Statement (2) states that the total cost was `C = 132`. This gives the equation `132 = p(1 + 0.1x)`. This equation permits multiple solutions for `x` that are consistent with the condition `p > 30`. If `x = 23`, then `p = 40`; this is a valid scenario since `p > 30`, and the answer to the question is "No". If `x = 30`, then `p = 33`; this is also a valid scenario since `p > 30`, and the answer to the question is "Yes". Since the statement does not provide a definitive answer, it is insufficient.
Statement (1) alone is sufficient to answer the question, while Statement (2) alone is not. The correct answer is (A).
Statement (1) states that the total cost was `C = 3.3p`. Substituting this into the cost formula yields `3.3p = p + x(0.1p)`. Since the problem states `p > 30`, `p` is a positive, non-zero value and can be divided from both sides of the equation, resulting in `3.3 = 1 + 0.1x`. Solving this equation gives a single, definitive value: `x = 23`. With this value, the answer to the question "Is x >= 26?" is a definitive "No". Therefore, Statement (1) is sufficient.
Statement (2) states that the total cost was `C = 132`. This gives the equation `132 = p(1 + 0.1x)`. This equation permits multiple solutions for `x` that are consistent with the condition `p > 30`. If `x = 23`, then `p = 40`; this is a valid scenario since `p > 30`, and the answer to the question is "No". If `x = 30`, then `p = 33`; this is also a valid scenario since `p > 30`, and the answer to the question is "Yes". Since the statement does not provide a definitive answer, it is insufficient.
Statement (1) alone is sufficient to answer the question, while Statement (2) alone is not. The correct answer is (A).
