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04 Jul 2025, 08:00
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
65% (02:20) correct
35%
(02:53)
wrong
based on 402
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A moving service charges p dollars for the first 5 miles of any trip plus 0.1*p dollars for each additional mile or fraction of a mile. If p > 30, was a particular trip more than 30 miles long?
(1) The moving service charged a total of 3.3p dollars for the trip.
(2) The moving service charged a total of $132 for the trip.
(1) The moving service charged a total of 3.3p dollars for the trip.
(2) The moving service charged a total of $132 for the trip.
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04 Jul 2025, 08:30
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Bunuel
Experts' Global Explanation:
Let total miles be M.
Cost for the first 5 miles = p.
Cost for each of the remaining (M – 5) miles = 0.1p.
Hence, the total cost for M miles = p + 0.1p(M – 5).
We need to find whether M > 30.
Statement (1)
p + 0.1p(M – 5) = 3.3p
Cancelling all “p”, we get: 1 + 0.1(M – 5) = 3.3
0.1(M – 5) = 2.3
M – 5 = 23
M = 28
It is possible to determine with certainty whether M is greater than 30; we can conclude that M is NOT greater than 30. Hence, Statement (1) is sufficient.
Trap alert!
Many students may mistakenly believe that Statement (1) is insufficient, as “M = 28” leads to “No” as answer for “Is M > 30?”. Remember, in Data Sufficiency questions, a Statement is sufficient if it consistently leads to “No” as the answer.
Statement (2)
p + 0.1p(M – 5) = 132
p + 0.1pM – 0.5p = 132
0.5p + 0.1pM = 132
Multiplying both sides by 10, we get: 5p + pM = 1320
M = (1320/p) – 5
Possibility 1: If p = 100, then M < 30.
Possibility 2: If p = 32, then M > 30.
It is NOT possible to determine with certainty whether M is greater than 30. Hence, Statement (2) is insufficient.
A is the correct answer choice.
An interesting discussion:
A student once wrote to us asking whether Statement (1) would be sufficient if the calculated value for M turned out to be exactly 30.
Can you figure out the answer?
The given question asks us whether the value of M is strictly greater than 30. Since the number 30 is NOT greater than 30, we can determine with certainty that M is NOT greater than 30. Hence, Statement (1) would still be sufficient.
General Discussion
04 Jul 2025, 08:26
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Information given:
- A moving service charges p dollars for the first 5 miles
- It charges 0.1*p dollars for each additional mile or fraction of a mile
Question:
- If p>30, was a particular trip more than 30 miles long?
Solution:
- Statement 1: The moving service charged a total of 3.3p dollars for the trip.
- Total cost = p + 0.1*p*(miles over 5) = p + 0.1*p*(d-5)
- Total cost = 3.3p
- So, 3.3p = p + 0.1p * (d-5)
- 2.3p = 0.1p * d-5
- 23 = d - 5
- d = 28
- Therefore, the trip is 28 miles long, which is not more than 30 miles long
- Sufficient
- Statement 2:
- Total cost = 132
- But p is unknown. We know it's over 30, but don't know the exact value
- If p = 40, 132 - 40 = 92, 92/(0.1*40) = 23 miles, total 28 miles (which is less than 30)
- If p = 35, 132 - 35 = 97, 97/(0.1*35) = 27.7 miles, total 32.7 miles (which is more than 30)
- Insufficient
Answer: A, statement 1 alone is sufficient, but statement 2 alone is not sufficient
- A moving service charges p dollars for the first 5 miles
- It charges 0.1*p dollars for each additional mile or fraction of a mile
Question:
- If p>30, was a particular trip more than 30 miles long?
Solution:
- Statement 1: The moving service charged a total of 3.3p dollars for the trip.
- Total cost = p + 0.1*p*(miles over 5) = p + 0.1*p*(d-5)
- Total cost = 3.3p
- So, 3.3p = p + 0.1p * (d-5)
- 2.3p = 0.1p * d-5
- 23 = d - 5
- d = 28
- Therefore, the trip is 28 miles long, which is not more than 30 miles long
- Sufficient
- Statement 2:
- Total cost = 132
- But p is unknown. We know it's over 30, but don't know the exact value
- If p = 40, 132 - 40 = 92, 92/(0.1*40) = 23 miles, total 28 miles (which is less than 30)
- If p = 35, 132 - 35 = 97, 97/(0.1*35) = 27.7 miles, total 32.7 miles (which is more than 30)
- Insufficient
Answer: A, statement 1 alone is sufficient, but statement 2 alone is not sufficient
Bunuel
