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29 Mar 2026, 05:11
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
38% (02:42) correct
62%
(02:43)
wrong
based on 26
sessions
History
Date
Time
Result
Not Attempted Yet
A customs officer inspected all the suitcases from a flight. She inspected the first, second, and final thirds of the suitcases at rates of 18, 36, and 72 suitcases per hour, respectively. If it took her 7 hours to inspect all of the suitcases, how long did it take her to inspect the last 90 suitcases?
A. 48 minutes
B. 1 hour
C. 1 hour 15 minutes
D. 1 hour 20 minutes
E. 1 hour 30 minutes
A. 48 minutes
B. 1 hour
C. 1 hour 15 minutes
D. 1 hour 20 minutes
E. 1 hour 30 minutes
29 Mar 2026, 22:32
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Lets go through this step by step.
Step 1: Find the total number of suitcases.
Let the total = S. Each third = S/3.
Time for first third (at 18/hr): (S/3) ÷ 18 = S/54
Time for second third (at 36/hr): (S/3) ÷ 36 = S/108
Time for final third (at 72/hr): (S/3) ÷ 72 = S/216
Total time = 7 hours:
S/54 + S/108 + S/216 = 7
Multiply everything by 216:
4S + 2S + S = 1512
7S = 1512
S = 216
So there are 216 total suitcases, meaning each third = 72 suitcases.
Step 2: Figure out where the last 90 suitcases fall.
Key Insight: The last 90 suitcases span across two sections:
- The final third has 72 suitcases (inspected at 72/hr)
- That leaves 90 - 72 = 18 suitcases from the end of the second third (inspected at 36/hr)
Step 3: Calculate the time.
Time for 18 suitcases at 36/hr = 18/36 = 0.5 hours = 30 minutes
Time for 72 suitcases at 72/hr = 72/72 = 1 hour
Total = 1 hour + 30 minutes = 1 hour 30 minutes.
Answer: E
A common mistake here is assuming the last 90 suitcases all come from the final third and dividing 90 by 72, which gives 1 hour 15 minutes (trap answer C). Always check whether the number of items requested crosses over into a different section with a different rate.
Step 1: Find the total number of suitcases.
Let the total = S. Each third = S/3.
Time for first third (at 18/hr): (S/3) ÷ 18 = S/54
Time for second third (at 36/hr): (S/3) ÷ 36 = S/108
Time for final third (at 72/hr): (S/3) ÷ 72 = S/216
Total time = 7 hours:
S/54 + S/108 + S/216 = 7
Multiply everything by 216:
4S + 2S + S = 1512
7S = 1512
S = 216
So there are 216 total suitcases, meaning each third = 72 suitcases.
Step 2: Figure out where the last 90 suitcases fall.
Key Insight: The last 90 suitcases span across two sections:
- The final third has 72 suitcases (inspected at 72/hr)
- That leaves 90 - 72 = 18 suitcases from the end of the second third (inspected at 36/hr)
Step 3: Calculate the time.
Time for 18 suitcases at 36/hr = 18/36 = 0.5 hours = 30 minutes
Time for 72 suitcases at 72/hr = 72/72 = 1 hour
Total = 1 hour + 30 minutes = 1 hour 30 minutes.
Answer: E
A common mistake here is assuming the last 90 suitcases all come from the final third and dividing 90 by 72, which gives 1 hour 15 minutes (trap answer C). Always check whether the number of items requested crosses over into a different section with a different rate.
