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# At a certain department store present-wrapping counter, each

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At a certain department store present-wrapping counter, each [#permalink]

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06 Oct 2003, 20:04
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

At a certain department store present-wrapping counter, each clerk will wrap no fewer than 20 and no more than 30 presents per hour. If 70 people are standing in line, will all of their presents be wrapped after one hour?

1. Each person in line has at least one present to be wrapped by one of the six clearks at the counter.

2. If each person in line had one more present to be wrapped, 9 clerks would be required to guarantee that every present would be wrapped in one hour.

CEO
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08 Oct 2003, 16:52
tsg wrote:
At a certain department store present-wrapping counter, each clerk will wrap no fewer than 20 and no more than 30 presents per hour. If 70 people are standing in line, will all of their presents be wrapped after one hour?

1. Each person in line has at least one present to be wrapped by one of the six clearks at the counter.

2. If each person in line had one more present to be wrapped, 9 clerks would be required to guarantee that every present would be wrapped in one hour.

We have to consider the "minimum" number of presents that will be wrapped in an hour..

A ...says the minimum # of presents are 70...thats no good ...we need the total # of presents

B... If 9 clerks are required to "guarantee" ... then the total number of presents are 9 * 20 = 180 ( minimum rate of wrapping is 20 per hour)

But this is the case where each person in line has ONE MORE present in hand...so the actual # of presents is 180 - 70 =110

But we dont know the existing # of clerks..so insufficient

Combine...we now know existing # of clerks is 6 ..and they can wrap a minimum of 120 presents in an hour...so yes, all the presents will be wrapped in an hour.

thanks
praetorian
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08 Jan 2004, 07:50
If 9 people wrap at the rate of max number of presents 30 per hr then total presents = 270
If 6 peole wrap at the same rate then it would be 180
so 270-180 = 90
SInce 70 people are there they should have on an average 3-4 presents
because 270/70 = 3.8
Because of second condition which says "if they have 1 more present" leads us to believe that average is between 2 and 3
If average is 2 then all presents can be wrapped. if the avarage is 2.8 or 3 then they cannot wrap all the presents.

I think the answer should be E.
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08 Jan 2004, 07:53
Sorry we shoudl take minimum number of presents per hour.
I guess C is correct.

If the rate is 20 then total number of presents wrapped by 9 = 180
Since there are 70 people then average present per person = 180/70 = 2.6
9 people are needed if each has one more present. So they have an average of 1.6 presents per person.
so 1.6*70 = 112 < 120
SO 6 people can wrap all the presents in one hour
08 Jan 2004, 07:53
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