A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. The store packs the notepads in pacakages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors. If the order in which teh colors are packed is not considered, how many different packages of the types described above are possible?

A) 6
B) 8
C) 16
D) 24
E) 32

Can you please show how you arrived at the answer choice C?

Thank you

Source: GMATPowerPrep(TM) - Practice Test 1

Category 1: consider all the possibilities that will give a same size (2 ways) and same color (4 ways) package. There are 2 packages and 4 colors => 8 different packages.

Category 2: consider all the possibilities for a same size but three different color package. Since you have four colors to choose from, you can use the combination formula to find how many ways to choose 3 from 4 colors. This will give you 4 options, but since you have two sizes, you have total of 8 ways to package the notes in this category.

Finally, you add your two methods of packaging for a total of 16 ways to package the notes. The correct answer is C.

Guest, thanks for the explanation. I like your style!

-dan

Hi,
Are you assuming that there are 3 small size green color notepads,3 big size green color notepads,etc?Question did not explicitly mention about that?If there were more than 3 :cry: small size green color notepads to choose from,The answer would change.

they're asking for the number of qualitatively different packages that can be assembled. this means that packages are only considered "different" if they contain different types of notepads.
in other words, even if i have a warehouse with millions of small green notepads, there's still only one way to make a package of three small green notepads. if i take out one small green notepad and replace it with another small green notepad from my warehouse, that's not a different type of package.
note, for the future, that this is what "different types of packages / sets" means on the gmat (and in the greater english-speaking world as well).

reductio ad absurdum: if a fast-food restaurant only offers 2 types of value meals, does that mean the restaurant can only feed 2 people all day? this is of course ridiculous, but your reasoning above, if extended, would conclude that it is the case.

--

by the way, if you ever think that an official problem statement is phrased incorrectly, then the error will almost certainly lie in your interpretation. therefore, you should look to adapt your interpretations, rather than to criticize or lament the problem statement(s).
this is also the only constructive way to approach a standardized test. after all, they write the test; you don't. they have power over the meaning of wordings on the test; you don't. therefore, since it's their playground, you have to follow their rules.

i was trying to solve this question with the SLOT method.

Intuitively I got to the answer but when I thought abt it later - i got confused. Here's why.

With the slot method, if order does NOT matter, we are supposed to divide by the factorial of the number of things choses.

Let me set it up for easier reference

Let's take the first notepad package
there are 2 ways of choosing the size and 4 ways of choosing the color. the other two notepads must be of the same size and color
thus, we have 2 * 4 * 1 * 1* 1* 1 = 8
However SINCE we have 3 notepads that are EXACTLY the same...and ordering does NOT matter, should we have to divide this by 3! ??

Exam in a few days. Will appreciate prompt feedback.

is it because the other 2 notepads in the package are identical to the first one? So in essence, we dont have three different things but in fact, just one type.
??

read this thread
gmat-prep-combo-question-t10607.html