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09 Sep 2020, 04:46
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
70% (03:03) correct
30%
(02:36)
wrong
based on 150
sessions
History
Date
Time
Result
Not Attempted Yet
A call center responds to telephone inquiries between the hours of 9 am and 12 pm. Including the idle time, on average, it takes 1.5 minutes to answer an inquiry between 9 and 10 in the morning, 4.5 minutes between 10 and 11, and 5 minutes between 11 and 12. What is the fraction of total inquiries answered between 9 and 12 that the call center, on average, responds to between 9 and 10 in the morning?
A. 30/98
B. 3/22
C. 30/49
D. 3/9
E. 9/10
A. 30/98
B. 3/22
C. 30/49
D. 3/9
E. 9/10
bM22
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09 Sep 2020, 09:32
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Average time taken to answer an inquiry :
1. between 9 and 10 in the morning = 1.5 mins. => \(\frac{1}{1.5}* 60 \) queries answered in 1 hr on an avg. = 40 queries
2. between 10 and 11 = 4.5 mins. => \(\frac{1}{4.5}* 60 \) queries answered in 1 hr on an avg. = 40/3 queries
3. between 11 and 12 = 5 mins. => \(\frac{1}{5}* 60 \) queries answered in 1 hr on an avg. = 12 queries
Total inquiries responded in the 3 hours = 40 + 40/3 +12 = 52 + 40/3 = 196/3 inquiries
Asked what fraction of the total inquiries are answered between 9 and 10. = \(\frac{40}{(196/3)\)}
=120/196
=30/49.
Answer is C.
1. between 9 and 10 in the morning = 1.5 mins. => \(\frac{1}{1.5}* 60 \) queries answered in 1 hr on an avg. = 40 queries
2. between 10 and 11 = 4.5 mins. => \(\frac{1}{4.5}* 60 \) queries answered in 1 hr on an avg. = 40/3 queries
3. between 11 and 12 = 5 mins. => \(\frac{1}{5}* 60 \) queries answered in 1 hr on an avg. = 12 queries
Total inquiries responded in the 3 hours = 40 + 40/3 +12 = 52 + 40/3 = 196/3 inquiries
Asked what fraction of the total inquiries are answered between 9 and 10. = \(\frac{40}{(196/3)\)}
=120/196
=30/49.
Answer is C.
09 Sep 2020, 09:55
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Between 9am and 10am, the center answers queries 3 times faster than between 10am and 11am. So it will answer 3 times as many queries in that early period. The 10am-11am and 11am-12pm periods are very similar. If we assume they're identical, the ratio of queries answered in the three periods would be 3 to 1 to 1, and 3/5 of queries would be answered in the 10am-11am period. Since the 11am-12pm period is even slower than our estimate, the exact answer will be slightly bigger than 3/5, and from the choices, only 30/49 is even remotely plausible.
