Data Sufficiency

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 would have one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in one hour

deepesh.gupta wrote: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 would have one more present to be wrapped, nine clerks would be required to guarantee that every present would be wrapped in one hour

Step 1 of the Kaplan Method for DS: Analyze the Stem

Q: Will all the presents be wrapped in within 1 hour? (yes/no)

We know that each clerk wraps between 20 and 30 (inclusive) presents per hour. We know there are 70 people in line.

We don't know how many clerks there are or how many presents each person has, so that's the information we need.

Step 2 of the Kaplan Method for DS: Evaluate the Statements

(1) we know there are at least 70 presents and exactly 6 clerks.

Well, 6 clerks will wrap between 120 and 180 presents in 1 hour, so it's possible that they'll get everything wrapped.

However, it's also possible that everyone in line has 1000 presents, so the wrapping might not be finished.

Maybe yes, maybe no: insufficient, eliminate A and D.

(2) 9 clerks guarantee that 180 presents get wrapped (20 minimum per clerk).

No information about the actual number of clerks, however: insufficient, eliminate B.

Combined:

Now that we have to, let's think about (2) some more.

The guarantee in (2) is based on each of the 70 patrons having 1 more present. So, the actual number of presents must be 180-70 = 110.

We now know that we have 6 clerks for 110 presents, guaranteeing that the work all gets done within an hour. Sufficient, choose C.

Hi Stuart,

For statement 2, I was thinking the opposite i.e 9 clerks guarantees that a maximum of 270 presents to be wrapped in one hour.

Should we take the maximum or the minimum?

But I still get the same answer C. 200 presents to be wrapped by 6 clerks in one hour does not suffice.

To expand on that thought, we're given that (total presents) + 70 are guaranteed to be wrapped by 9 clerks. But what if they all work at the max rate (30 presents per hour)? Then the clerks will wrap 9*30 = 270 presents/hour. 270 - 70 = 200. Therefore, there could be a max of 200 presents that need to be wrapped. 6 clerks cannot wrap 200 presents.

If you buy the argument above, then the answer should be E. Thoughts?

Right. 6 clerks cannot wrap 200 presents in one hour. So the answer to the question stem is always NO, that was what I was thinking. Thus answer is C.

E would be the answer if 6 clerks may or may not wrap the presents in one hour.

Are you thinking answer is E because 6 clerks cannot wrap 200 presents?

dxgamez wrote:Hi Stuart,

For statement 2, I was thinking the opposite i.e 9 clerks guarantees that a maximum of 270 presents to be wrapped in one hour.

Should we take the maximum or the minimum?

But I still get the same answer C. 200 presents to be wrapped by 6 clerks in one hour does not suffice.

9 clerks is the minimum number to guarantee that the presents get wrapped in 1 hour.

Guarantee means that, no matter how much those clerks slack, the presents will get wrapped.

Well, based on the information we have, what's the bare minimum work a clerk can do in 1 hour? Wrap 20 presents.

So, if we have 9 clerks, we have a guaranteed 180 wrapped presents.

Now, if we want to be picky (and we really do on the GMAT), that doesn't mean there are exactly 180 presents - 180 is actually the top of the range.

If we had 8 clerks, that would guarantee 160 wrapped presents. So, we need a 9th clerk to guarantee that anywhere between 161 and 180 presents get wrapped. So, statement (2) actually tells us that there are 161 to 180 presents in total, if each person in line had 1 more.

Once we subtract out the 70, that means that there are actually 91 to 110 presents to be wrapped. Since we have 6 clerks (from statement (1)), we know that they can wrap at least 120 presents in an hour, so the job will definitely get done (a definite "yes" answer to the original question).

Thank Stuart

OA is C

Stuart Kovinsky wrote:

dxgamez wrote:Hi Stuart,

For statement 2, I was thinking the opposite i.e 9 clerks guarantees that a maximum of 270 presents to be wrapped in one hour.

Should we take the maximum or the minimum?

But I still get the same answer C. 200 presents to be wrapped by 6 clerks in one hour does not suffice.

9 clerks is the minimum number to guarantee that the presents get wrapped in 1 hour.

Guarantee means that, no matter how much those clerks slack, the presents will get wrapped.

Well, based on the information we have, what's the bare minimum work a clerk can do in 1 hour? Wrap 20 presents.

So, if we have 9 clerks, we have a guaranteed 180 wrapped presents.

Now, if we want to be picky (and we really do on the GMAT), that doesn't mean there are exactly 180 presents - 180 is actually the top of the range.

If we had 8 clerks, that would guarantee 160 wrapped presents. So, we need a 9th clerk to guarantee that anywhere between 161 and 180 presents get wrapped. So, statement (2) actually tells us that there are 161 to 180 presents in total, if each person in line had 1 more.

Once we subtract out the 70, that means that there are actually 91 to 110 presents to be wrapped. Since we have 6 clerks (from statement (1)), we know that they can wrap at least 120 presents in an hour, so the job will definitely get done (a definite "yes" answer to the original question).