At a certain department store present-wrapping counter, each

Question

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.

Bunuel · Accepted Answer

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.

Answer: C.

Hope it's clear.

coolfrequency · Answer

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.

I'd say Answer is C.

portland · Answer

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?

Bunuel · Answer

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

portland · Answer

Ah! Damn important words hidden in plain sight.

Thanks Bunuel

BrentGMATPrepNow · Answer

Given : At a certain department store present-wrapping counter, each clerk will wrap no fewer than twenty and no more than thirty presents per hour.

Target question :    If seventy people are standing in line, will all of their presents be wrapped after one hour?

Statement 1 : Each person in line has at least one present to be wrapped by one of the six clerks at the counter.   
Since we aren't told the MAXIMUM number of presents each person has, there's no way to answer the target question. 
To see what I mean, consider these two conflicting scenarios: 
 Case a : Each person in line has 1 present. So, there are 70 presents to be wrapped by 6 clerks. Since each clerk can wrap AT LEAST 20 presents (for a total of 120 presents), the answer to the target question is  YES, all of the presents will be wrapped after 1 hour 
 Case b : Each person in line has 1 trillion presents. Here, the answer to the target question is  NO, all of the presents will NOT be wrapped after 1 hour 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 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. 
Here, we aren't given any information about the actual number of clerks. 
Consider these two conflicting scenarios: 
 Case a : There are 9 clerks available. If 9 clerks can wrap all of the presents in the hypothetical situation in which everyone has 1 EXTRA present, then 9 clerks will definitely be enough to wrap the presents. In other words, the answer to the target question is  YES, all of the presents will be wrapped after 1 hour 
 Case b : There is are ZERO clerks available (all on lunch break). Here, the answer to the target question is  NO, all of the presents will NOT be wrapped after 1 hour 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Let T = the TOTAL number of presents to be wrapped 
IF each of the 70 people in line had one more present, then there WOULD be T + 70 presents to be wrapped
Since each of the 9 clerks can wrap AT LEAST 20 presents per hour, they can wrap AT LEAST 180 presents. 
So, we can write:  T + 70 < 180 
Subtract 70 from both sides to get:  T < 110 
So, statement 2 is telling us (indirectly) that there are fewer than 110 presents to be wrapped

Statement 1 tells there are 6 clerks. 
Since each clerk can wrap AT LEAST 20 presents in one hour, they can can wrap AT LEAST 120 presents in total. 
Since statement 2 tells us that there are FEWER THAN 110 presents, the answer to the target question is  YES, all of the presents will be wrapped after 1 hour 
Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

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At a certain department store present-wrapping counter, each

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