12 Days of Christmas GMAT Competition - Day 8: The parking fee at

Question

12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

The parking fee at a certain lot is $1.00 for the first 2 hours, plus $0.25 for each additional hour or fraction of an hour beyond the first 2 hours. Did the car remain parked for more than 12 hours at the parking lot?

(1) The total parking fee would have been $3.75 if the car had stayed 30 minutes longer.
(2) The total parking fee would have been $3.25 if the car had stayed 90 minutes less.

Bunuel · Accepted Answer

GMAT Club's Official Explanation: The parking fee at a certain lot is $1.00 for the first 2 hours, plus $0.25 for each additional hour or fraction of an hour beyond the first 2 hours. Did the car remain parked for more than 12 hours at the parking lot? For any time exceeding 2 hours, the fee is calculated as 1 + (⌈x⌉ - 2) * 0.25, where ⌈x⌉ denotes the least integer greater than or equal to x. The phrase "for each additional hour or fraction of an hour" means that if a car is parked for, say, 2.1 hours, it is rounded up and assumed to have been parked for 3 hours. Thus: • If 10 < x ≤ 11, the fee would be 1 + (11 - 2) * 0.25 = $3.25. • If 11 < x ≤ 12, the fee would be 1 + (12 - 2) * 0.25 = $3.50. • If 12 < x ≤ 13, the fee would be 1 + (13 - 2) * 0.25 = $3.75. Assuming the car was parked for t hours, the question asks whether t > 12. (1) The total parking fee would have been $3.75 if the car had stayed 30 minutes longer. This implies: 12 < t + 0.5 ≤ 13 11.5 < t ≤ 12.5 Not sufficient. (2) The total parking fee would have been $3.25 if the car had stayed 90 minutes less. This implies: 10 < t - 1.5 ≤ 11 11.5 < t ≤ 12.5 Not sufficient. (1) + (2) Both statements provide the exact same information: 11.5 < t ≤ 12.5. Thus, even when combined, we still cannot determine if t > 12. Not sufficient. Answer: E

Kinshook · Answer

The parking fee at a certain lot is $1.00 for the first 2 hours, plus $0.25 for each additional hour or fraction of an hour beyond the first 2 hours. Did the car remain parked for more than 12 hours at the parking lot?

Parking fee for 11 hours = $1 + 9*$.25 = $3.25
Parking fee for 12 hours = $1 + 10*$.25 = $3.5
Parking fee for 13 hours = $1 + 11*$.25 = $3.75

(1) The total parking fee would have been $3.75 if the car had stayed 30 minutes longer.
Case 1: Car was parked for 11 hours 50 minutes (less than 12 hours parking)
11 hours 50 minutes + 30 minutes = 12 hours 20 minutes
Parking fee if the car had stayed 30 minutes longer = $3.75
Case 2: Car was parking for 12 hours 10 minutes (more than 12 hours parking)
12 hours 10 minutes + 30 minutes = 12 hours 40 minutes
Parking fee if the car had stayed 30 minutes longer = $3.75
In both cases above, parking fee would have been $3.75 if the car had stayed 30 minutes longer.
NOT SUFFICIENT

(2) The total parking fee would have been $3.25 if the car had stayed 90 minutes less.
Case 1: Car was parked for 11 hours 50 minutes (less than 12 hours parking)
11 hours 50 minutes - 90 minutes = 10 hours 20 minutes
Parking fee if the car had stayed 90 minutes less = $3.25
Case 2: Car was parking for 12 hours 10 minutes (more than 12 hours parking)
12 hours 10 minutes - 90 minutes = 10 hours 40 minutes
Parking fee if the car had stayed 90 minutes less = $3.25
In both cases above, parking fee would have been $3.25 if the car had stayed 90 minutes less.
NOT SUFFICIENT

(1) + (2) 
(1) The total parking fee would have been $3.75 if the car had stayed 30 minutes longer.
(2) The total parking fee would have been $3.25 if the car had stayed 90 minutes less.

Case 1: Car was parked for 11 hours 50 minutes (less than 12 hours parking)
11 hours 50 minutes + 30 minutes = 12 hours 20 minutes
Parking fee if the car had stayed 30 minutes longer = $3.75
11 hours 50 minutes - 90 minutes = 10 hours 20 minutes
Parking fee if the car had stayed 90 minutes less = $3.25

Case 2: Car was parking for 12 hours 10 minutes (more than 12 hours parking)
12 hours 10 minutes + 30 minutes = 12 hours 40 minutes
Parking fee if the car had stayed 30 minutes longer = $3.75
12 hours 10 minutes - 90 minutes = 10 hours 40 minutes
Parking fee if the car had stayed 90 minutes less = $3.25

In both cases above, parking fee would have been $3.75 if the car had stayed 30 minutes longer.
In both cases above, parking fee would have been $3.25 if the car had stayed 90 minutes less.
NOT SUFFICIENT

IMO E

GraCoder · Answer

Lets enumerate the prices at given timestamps:

Additional time:
8:01 - 9-> 3.25
9:01 - 10 -> 3.5
10:01 - 11 -> 3.75
11:01 - 12 -> 4
12:01 - 13 -> 4.25

Now case 1:
if price was 3.75 it could be any time from 12:01 - 13:00 subtracting 30 min => 11:31 - 12:30 => not enough to determine

Now case 2:
if price was 3.25 it could be 10:01 - 11 adding 90 min => 11:31 - 12:30 => not enough to determine

Hence answer is E.

missionmba2025 · Answer

Between 10 hours and 11 hours, the parking fee is $3.25

Between 11 hours and 12 hours, the parking fee is $3.5

Between 12 hours and 13 hours, the parking fee is $3.75

1)

Let's assume the car was parked for 11 hours 55 mins, adding 30 mins will push the timing to a bracket where the car is between 12 hours and 13 hours, the parking fee would be $3.75. In this case, the car was not parked for more than 12 hours at the parking lot.

Let's assume the car was parked for 12 hours 05 mins, adding 30 mins will push the timing to a bracket where the car is between 12 hours and 13 hours, the parking fee would be $3.75. In this case, the car was parked for more than 12 hours at the parking lot.

As we have two answers, we can eliminate A, and D as statement 1 alone is not sufficient.

2)

Let's assume the car was parked for 11 hours 55 mins, subtracting 90 mins will push the timing to a bracket where the car is between 10 hours and 11 hours, the parking fee would be $3.25. In this case, the car was not parked for more than 12 hours at the parking lot.

Let's assume the car was parked for 12 hours 05 mins, subtracting 90 mins will push the timing to a bracket where the car is between 10 hours and 11 hours, the parking fee would be $3.25. In this case, the car was parked for more than 12 hours at the parking lot.

As we have two answers, we can eliminate B.

(1) + (2)

The statements combined are not sufficient as well, as the same case holds true for both the statements and we cannot eliminate anything.

Option E

As we have two answers, we can eliminate A, and D as statement 1 alone is not sufficient.

RahulPMT · Answer

Please check the handwritten soluton in the image attached

andreagonzalez2k · Answer

t=real time in hours T=time in hours rounded to the nearest upper integer fee=1+0.25(T-2) t>12? (1) if real time is t+0.5, fee=3.75 3.75=1+0.25(T-2) -> T=13 if T=13, it means that real time (t+0.5) is between 12 (not inclusive) and 13 (inclusive) 12 T=11 if T=11, it means that real time (t-1.5) is between 10 (not inclusive) and 11 (inclusive) 10

HarshaBujji · Answer

Parking Fee Structure:
 
 The first 2 hours cost $1.00. 
 Each additional hour or fraction of an hour costs $0.25.  
The parking fee for a total duration of x hours can be expressed as:
Fee=1.00+0.25*⌈x−2⌉,where ⌈x−2⌉ is the ceiling of the time beyond 2 hours.

We need to determine whether the car remained parked for  more than 12 hours

Statement (1): 
The total parking fee would have been $3.75 if the car had stayed 30 minutes longer.
Analyze:
Let the actual time parked be xxx. If the car stayed 30 minutes longer, the time parked would be x+0.5

The parking fee for x+0.5 hours is $3.75:

3.75 = 1 + 0.25*  => 2.75 = 0.25* .

So   = 11. Which means 10<x-1.5<11.

So 11.5<x<12.5. 11.6 is possible and 12 is also possible we cannot definitely say anything. Hence Stmt 1 is insuffiecnet.

Statement (2): 
The total parking fee would have been $3.25 if the car had stayed 90 minutes less.
 If the car stayed x−1.5 hours, the fee would have been $3.25:

3.25 = 1 + 0.25*

8<x-3.5<9 So x is (11.5,12.5) same as above. So x can be 12 or 11.8. Insufficient. 
 
Combining also won't help. Hence IMO E

OmerKor · Answer

Hi everyone

1$ = 2Hours 0.25$ = 1 hour or fraction of an hour : time parked > 12 in converting to money: 12.X->13 = 3.75$ 11.X->12 = 3.5$ 10.X->11 = 3.25$ Thus, We are asked if the car parked > 12, in money we need to know if its: Time>=3.75$ = Sufficient (more than 12) Time<3.75$ = Sufficient Both = Insufficient (1) Time parked +30 mins = 3.75$ Case 1: Time parked 11:50 + 30 mins = 12:20 = 3.75$ Less than 12 Hours Case 2: Time parked 12:10 + 30 mins = 12:40 = 3.75$ More than 12 Hours Insufficient. (2) Time parked - 90 mins = 3.25$ Case 1: Time parked 11:50 - 90 mins = 10:20 = 3.25$ Less than 12 Hours Case 2: Time parked 12:10 - 90 mins = 10:40 = 3.25$ More than 12 Hours Insufficient. (1)+(2) As we can see the same Cases is presenting in each of the statements, so we can conclude that either together we got Insufficient. Answer is E

Lizaza · Answer

Let's deal with extra conditions from the onset, trying to discern whether 10 extra hours are completed or not:

(1)  3.75 - 1 = 2.75  
 Then, we would pay 2.75 for the extra hours after 2. In 2.75, there're 0.25* 11 hours  embedded 
 Therefore, there're only 2 options for the time the person stayed, for example: 
 
   9:47    + 30 = 10:17  
   10:03    + 30 = 10:33

Hence, the person could've stayed within 10 or 11 extra hours;  insufficient .

(2)  3.25-1=2.25  
 Then, we would pay 2.25 for the extra hours after 2. In 2.25, there're 0.25* 9   hours  embedded  
 Therefore, there're only 2 options for the time the person stayed, for example: 
 
  8:44 + 90 =    10:14   
  8:08 + 90 =    9:38    
 
Hence, the person could've stayed within 10 or 11 extra hours;  insufficient .

(1) + (2) 
 Even with two conditions together, we get either 10 or 11 hours, although not full ones but the ones priced for parking. Therefore, between these two options, we still cannot answer the question whether we passed into 11-hour territory. Insufficient together.

Therefore,    the answer is E.

MinhChau789 · Answer

Let the total parking hours be a. Let total parking hours, including any fraction of an hour to be rounded up to the nearest whole number, be  . So a would be within the range of (  - 1) < a <=

Total fee = 1 + 0.25 x (  - 2)

(1) The total parking fee would have been $3.75 if the car had stayed 30 minutes longer.
1 + 0.25 x (  - 2) = 3.75
  - 2 = 11
  = 13
so 12 < a + 0.5 <= 13
11.5 < a <= 12.5
We don't know if the car remain parked for more than 12 hours at the parking lot or not

(2) The total parking fee would have been $3.25 if the car had stayed 90 minutes less. 
1 + 0.25 x (  - 2) = 3.25
  - 2 = 9
  = 11
so 10 < a - 1.5 <= 11
11.5 < a <= 12.5
We don't know if the car remain parked for more than 12 hours at the parking lot or not

both (1) & (2) are similar, so we don't know the right answer. Final answer: E

Navya442001 · Answer

Given:
The parking fee structure is as follows:
 
 $1.00 for the first 2 hours. 
 $0.25 for each additional hour or fraction of an hour beyond the first 2 hours.  
The total fee is calculated as:
Fee=1.00+0.25×⌈t−2⌉ 
where ⌈t−2⌉ is the smallest integer greater than or equal to t−2
 
Statement (1):
 The total parking fee would have been $3.75 if the car had stayed 30 minutes longer. 
The total fee for t+0.5 hours is given as $3.75:
3.75=1.00+0.25×⌈t−2+0.5⌉
2.75=0.25×⌈t−2+0.5⌉
Divide through by 0.25:
⌈t−2+0.5⌉=11
Thus:
t−2+0.5=11 or t−2+0.5<11
If t−2+0.5=11, then:
t=12.5
If t−2+0.5<11, then:
t<12.5
From this statement alone, t could be  just below 12.5  (e.g., 12.49), meaning the car might not have stayed more than 12 hours.  Statement (1) is not sufficient. 
 
Statement (2):
 The total parking fee would have been $3.25 if the car had stayed 90 minutes less. 
The total fee for t−1.5 hours is given as $3.25:
3.25=1.00+0.25×⌈t−2−1.5⌉
2.25=0.25×⌈t−3.5⌉
Divide through by 0.25:
⌈t−3.5⌉=9
Thus:
t−3.5=9 or t−3.5<9
If t−3.5=9, then:
t=12.5.
If t−3.5<9, then:
t<12.5
From this statement alone, t could also be  just below 12.5  (e.g., 12.49), meaning the car might not have stayed more than 12 hours.  Statement (2) is not sufficient. 
 
Combining Statements (1) and (2):
From Statement (1), t could be up to 12.5 but also just below 12.5. From Statement (2), t could again be up to 12.5 but also just below 12.5.
Even when combining the statements, we cannot determine whether ttt exceeded 12 hours. For example:
 
 t=12.5 satisfies both conditions (car stayed more than 12 hours). 
 t=12.49 also satisfies both conditions (car stayed less than or equal to 12 hours).  
 Combining the statements does not resolve the ambiguity. 
 
Final Answer:
 E.  Neither statement alone nor together is sufficient.

IssacChan · Answer

Let's calculate how much will be charged for 12 hours at the parking lot
$1+$0.25*(12-2) = $3.5

As fraction of hour is charge for $0.25 additional hour, so possible range for $3.5 would be 11.01- 12 hours

(1) Calculate the hours for $3.75
(3.75-1)/0.25+2 = 13
Possible range will be 12.01 - 13 hours

Applying 30 minutes lesser, the range will become 11.31 - 12.5 hours
If 11.31 it will be less than 12 hours
If 12.5 it will be more than 12 hours (Insufficient)

(2) Calculate the hours for $3.25
(3.25-1)/0.25+2 = 11
Possible range will be 10.01 to 11 hours

Applying 90 minutes more, the range will become 11:31 to 12.5 hours
If 11.31 it will be less than 12 hours
If 12.5 it will be more than 12 hours (Insufficient)

(1) + (2) After applying both cases, the range are 11:30 to 12.5 hours
It is possible that the hours could be less than 12, equal to 12 or more than 12 (Insufficient)

Therefore the answer is E

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