GMATPrep,set,pls help

[tanviet]

this is from GMATPrep, I do not understand question,pls,help

A certain office supply store stock 2 sized of self-stick notepads, each in 4 colors:blue, green,yellow,pink.The store pack the notepads in packages 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 the colors are packed are not considered, Howmany diferent packages fo the types described above are possible.

a,6
b,8
c,16
d,24
e,32

[papgust]

IMO C

There are 2 cases here:
i. 3 notepads of same size and of same colors
ii. 3 notepads of same size and of different colors

Let's calculate each case independently and then add these 2 cases (Since you have an OR attached to it).
i. 3 notepads of same size --> you have 2 sizes available. So you have 2 ways to select
AND
3 of same colors --> you have 4 colors available. So you have 4 ways to select colors.

Now, multiply 1st and 2nd sub-categories. 2 ways * 4 ways = 8 ways.

ii. 3 notepads of same size --> you have 2 sizes available. So you have 2 ways to select
AND
3 of different colors --> you have 4 colors available. you have to select 3 from 4 colors. So, its 4C3 = 4

Now, multiply 1st and 2nd sub-categories. 2 ways * 4 ways = 8 ways.

Now, add (i) and (ii). 8 + 8 = 16 ways. Can you share the OA?

[thephoenix]

IMO 16

3 stick pads of same size and same color cane be chosen in 2c1*4c1=8 ways

3 stick pads of same size and diff color can be chosen in 2C1 * 4C3=8 ways

[spoiler]tot=16[/spoiler]

[tanviet]

I do not understand. How many notepads are there?

[Testluv]

@duongthang: It doesn't matter how many notepads there are. Instead, we are asked for how many "types" of notepad packages there are.

There are two sizes of notepads. We can call them "large" and "small" if we want. For each size of notepad, the store is selling packages of three notepads. Either the notepads in a package all have to be of the same color or else they all have to be different colors. So, one "type" of notepad is "Large with all blue". Another "type" of notepad is "Small with green, blue and pink". Etc.

The way we'll be able to pull out combinations of colors is unrelated to the size of the notepad, so we can consider just one size of notepad and then multiply our final result by 2.

Considering just one size of notepad (doesn't matter which one):

How many ways are there of getting all three notepads in a package to be the same color? Well, because there's 4 colors, there's 4 ways here. (bbb or ggg etc.)

How many ways of getting all three different colors if order doesn't matter? Well, since all 4 colors are distinct and since order doesn't matter we can just use the combinations formula here: 4C3 = 4.

So, for one size of notepad, there's 4 ways of getting all colors the same + 4 ways of getting all three colors different for a total of 8 ways.

There's 2 sizes of notepad, so we just multiply 8 by 2 for the final answer of 16.

(papgust and thepheonix's approach was also good).

[tanviet]

Thank testluv

normally I can not solve set problem because I do not understand the question. even I know this question is about set I still do not understand question and of course can do nothing.

when a person explain me the question, I understand the solution immediately.

So, Testluv, Do you have any help for my problem?

[Testluv]

Thank testluv

normally I can not solve set problem because I do not understand the question. even I know this question is about set I still do not understand question and of course can do nothing.

when a person explain me the question, I understand the solution immediately.

So, Testluv, Do you have any help for my problem?

Well, while practicing, you need to determine exactly what the question is asking. If you are having trouble doing this, then while reviewing, you should study the way GMAT is asking questions, study the wording, etc, so that you are more comfortable.