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

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08 Feb 2006, 01:16

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A

B

C

D

E

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95% (hard)

Question Stats:

42% (02:00) correct
58% (02:17) wrong based on 298 sessions

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At a certain department store present-wrapping counter, each clerk will wrap no fewer than twenty and no more than thirty presents per hour. If seventy 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 clerks at the counter. (2) If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in one hour.

agree with C)
from stem we know that one clerk can wrap 30 gifts at most per hour. Seventy people on the line,
From A we know that there are six clerks and minimum 70 presents which is insufficient
From B) we can calculate the number of gifts in the people on the line 9x30=270-70=200 approx. but we do not know how many clerks are currently working
combining both it is clear that 270-70=200 presents hold the people in the line, currently there are 6 clerks working who can pack 30 gifts at most, so the clerks will not be able to complete the job in one hour

I actually find this question confusing. Please correct me if I'm wrong.

Combining (1) and (2) we know that:
if (2) assumes that a clerk can wrap 20 gifts per hour, then we have 9*20=180, but since the customers have 1 more, subtract 70 ->110
if (2) assumes that a clerk can wrap 30 gifts per hour, than we have 9*30=270, ->200

If there are six clerks and they work at 20 g/h, in the case of 110 they would be able to wrap all the gifts, otherwise they wouldn't.

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_________________

Please allow me to introduce myself: I'm a man of wealth and taste

Hi,
=======================================
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 seventy people are standing in line, will all of their presents be wrapped after one hour?
=======================================
So the slowest clerk can wrap 20 gifts
As a worst case the number of gifts wrapped in an hour is
20 * number of clerks.

=======================================
(1) Each person in line has at least one present to be wrapped by one of the six clerks at the counter.
=======================================
This does not give the number of gifts, hence is insufficient.

=======================================
(2)If each person in line had one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in one hour.
=======================================
This means that if there are 70 more gifts, nine clerks are needed.
If you can guarantee that 9 slow clerks can wrap all gifts in an hour, you can pretty much say any combination of clerks, slow or fast can do it within an hour.

Total number of gifts + 70 <= 9clerks * 20 Gifts wrapped by each
Total number of gifts <= 180 - 70
<= 110

However (2) does not give the number of clerks at the counter, hence is insufficient.

Using (1) and (2) together -
Number of clerks = 6
Number of gifts <= 110

Assume all 6 clerks are slow; They can wrap 120 gifts in an hour.
Since we have 110 or less, this can be done.

This means that if there are 70 more gifts, nine clerks are needed. If you can guarantee that 9 slow clerks can wrap all gifts in an hour, you can pretty much say any combination of clerks, slow or fast can do it within an hour.

Total number of gifts + 70 <= 9clerks * 20 Gifts wrapped by each Total number of gifts <= 180 - 70 <= 110

However (2) does not give the number of clerks at the counter, hence is insufficient.

Using (1) and (2) together - Number of clerks = 6 Number of gifts <= 110

Assume all 6 clerks are slow; They can wrap 120 gifts in an hour. Since we have 110 or less, this can be done.

I'd say Answer is C.

I am lost on this one. Kaplan has a very similar solution noted too. However, instead of slowest case scenario, if I take the highest numbers: Total number of gifts + 70 <= 9clerks * 30 Gifts wrapped by each Total number of gifts <= 270 - 70 <= 200

Using (1) and (2) together - Number of clerks = 6 Number of gifts <= 200 Maximum gifts that can be wrapped 6 clerks: 6*30 = 180.

Which contradicts the slow case and so the answer to the main question will be E.

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

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20 Oct 2013, 10:21

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

Say each clerk can wrap x presents per hour. We are given that \(20\leq{x}\leq{30}\).

(1) Each person in line has at least one present to be wrapped by one of the six clerks at the counter. From that we can get that the number of presents to be wrapped is at least 70 and that there are 6 clerks at the counter. Now, the number of presents 6 clerks can wrap in an hour is \(120\leq{x}\leq{180}\). Still not sufficient to answer the question: if the # of presents is 70, then the answer would be YES but if the # of presents is greater than 180, then the answer would be NO. Not sufficient.

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

Say 70 people in line have total of n presents. We are told that n+70 presents can be wrapped by 9 clerks. 9 clerks can for sure wrap 9*20=180 presents. Thus we are given that \(n+70\leq{180}\) --> \(n\leq{110}\). So, there are at most 110 presents to be wrapped.

To guarantee wrapping 110 presents minimum 6 clerks are needed (6 slowest clerks can wrap 120 presents). We don't know how many clerks are there at the counter. Not sufficient.

(1)+(2) From (1) we know that there are 6 clerks, thus they can for sure wrap minimum 120 presents, since the # of presents is less than or equal 110, then these 6 can wrap all the presents. Sufficient.

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

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20 Oct 2013, 11:27

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Thanks Bunuel What I don't understand is, why did you choose the minimum speed as opposed to maximum in your calculation for n You used: n+70 <= 180 Why not: n+ 70 <=270

The statement says 9 clerks can wrap n+70 presents at a speed of between 20...30 presents per hour. Why choose 20 and not 30? Is it because of the use of the word "guarantee" in statement 2?

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

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20 Oct 2013, 11:31

Expert's post

portland wrote:

Thanks Bunuel What I don't understand is, why did you choose the minimum speed as opposed to maximum in your calculation for n You used: n+70 <= 180 Why not: n+ 70 <=270

The statement says 9 clerks can wrap n+70 presents at a speed of between 20...30 presents per hour. Why choose 20 and not 30? Is it because of the use of the word "guarantee" in statement 2?

Absolutely. We need to guarantee that every gift will be wrapped, thus we must consider that the clerks work at the slowest possible rate. _________________

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

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