Kaplan

[ketkoag]

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 1 hour?
1)Each person in the line has atleast one present to be wrapped by one of the six clerks.
2)If each person in the line had one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in 1 hour.

OA : CI got c as the correct answer but please lemme know is it possible for us to calculate the total no. of presents. Please throw some light on this problem..

[SanjeevK]

IMO [spoiler]C:[/spoiler]
Here is my shot at the problem

A: This tells us that there are 6 clerks. So the minimum number of presents wrapped per hour is 20 and maximum number of presents wrapped per hour is 180. Also the total number of presents is >= 70
This doesn't tell us whether all the presents will be wrapped in one hour

B: Now the initial number of presents be p. So we have p+70=(30x9).
This gives us the number of presents as 200. This by itself is not sufficient since we don't know how many clerks are present.

Combining A and B, we know that 6 clerks can at the maximum wrap 180 presents in an hour. Since the number of presents is 200, it would definitely take more than an hour.

Hope this helps.

[ketkoag]

please elaborate on how the no. of presents is 70 as in question nothing is mentioned about how many presents does a person have..
statement 1 says all have atleast 1 present but there is not definite number..

[SanjeevK]

We have assumed that the initial number of presents be p. Please note that a single person can have one or more than one presents.

2) states that If each person in the line had one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in 1 hour.
Since the number of persons in the line is 70, it means we would have an additional 70 presents to form the equation.

Hope this helps.

[ketkoag]

IMO [spoiler]C:[/spoiler]
Here is my shot at the problem

A: This tells us that there are 6 clerks. So the minimum number of presents wrapped per hour is 20 and maximum number of presents wrapped per hour is 180. Also the total number of presents is >= 70
This doesn't tell us whether all the presents will be wrapped in one hour

B: Now the initial number of presents be p. So we have p+70=(30x9).
This gives us the number of presents as 200. This by itself is not sufficient since we don't know how many clerks are present.

Combining A and B, we know that 6 clerks can at the maximum wrap 180 presents in an hour. Since the number of presents is 200, it would definitely take more than an hour.

Hope this helps.

i think u misunderstood me. i am asking about the bold statement above..
from statement 1 as per ur solution how there are 70 presents?

[carpe_diem]

@ ketkoag


There are 70 people. Each person has "Atleast 1 Present" to be wrapped by clerk.

This means that the total number of Presents should be atleast 70. In equations:
Total number of gifts "P" >=70.

Hope that helps.

[carpe_diem]

IMO [spoiler]C:[/spoiler]
Here is my shot at the problem

A: This tells us that there are 6 clerks. So the minimum number of presents wrapped per hour is 20 and maximum number of presents wrapped per hour is 180. Also the total number of presents is >= 70
This doesn't tell us whether all the presents will be wrapped in one hour

B: Now the initial number of presents be p. So we have p+70=(30x9).
This gives us the number of presents as 200. This by itself is not sufficient since we don't know how many clerks are present.

Combining A and B, we know that 6 clerks can at the maximum wrap 180 presents in an hour. Since the number of presents is 200, it would definitely take more than an hour.

Hope this helps.

I am not sure about the statement B: p+70 = 30 x 9
which gives p = 200.
Here we can use the rate of work as 20 too instead of 30.
In that case p + 70 = 20 X 9; p = 110.
And combining statement A & B we get that clerks can complete the task in 1 hour.

Please suggest.
Thanks.

[Domnu]

The number of presents is between 70 and 110:

Suppose that there are K presents; if K + 70 presents can be wrapped in 1 hour, then we know that K + 70 <= 20 * 9 = 180, so K <= 110. But even if some customers had 0 presents, by having 1 more present, there would be at least 70 presents. So, there are at least 70 and at most 110 presents present (no pun intended).