T03 wrote:

A logistics company sends at least 2 packages every day. Does the total number of packages sent on any 5 given days exceed 19?

1) 12 packages are sent on one of the 5 days.

2) A different number of packages is sent each day.

Dear

T03,

I'm happy to help.

In a five-day period, at least 2 packages are sent every day. Does the total exceed 19?

Our strategy will be to find the minimum that the company could send in the five days, with each condition. If the minimum is 19 or more, then we would answer "yes" to the prompt. If the minimum possible is less than 19, then we don't know, and don't have sufficient information.

Statement #1:

12 packages are sent on one of the 5 days. Let's assume that the minimum of two is sent on the other four days--that's 2*4 = 8 more, for a total of 12 + 8 = 20. That's the minimum, so it's definitely over 19 in the five-day period. This statement allows us to give a definitive answer to the prompt question, so this statement is

sufficient.

Now, we have to ignore statement #1, and consider statement #2 in isolation.

Statement #2:

A different number of packages is sent each day. The five smallest distinct positive integers possible here are {2, 3, 4, 5, 6}, and that sum is 20. Again, that's the minimum, so it's definitely over 19 in the five-day period. Again, this statement allows us to give a definitive answer to the prompt question, so this statement is

sufficient.

A cool question. OA =

(D) Does all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)