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A certain office supply store stocks 2 sizes of

by VJesus12 » Wed Apr 18, 2018 1:41 am

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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 the 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

The OA is C.

I am confused by this question. Can anyone help me? Thanks in advanced.
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by GMATGuruNY » Wed Apr 18, 2018 3:52 am
VJesus12 wrote: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 the 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
Case 1: The notepads are all of the same size and the same color
Number of size options = 2.
Number of color options = 4.
To combine the options above, we multiply:
4*2 = 8.

Case 2: The notepads are all of the same size but of 3 different colors
Number of size options = 2.
From the 4 colors, the number of ways to choose 3 = 4C3 = (4*3*2)/(3*2*1) = 4.
To combine the options above, we multiply:
4*2 = 8.

Total ways = Case 1 + Case 2 = 8+8 = 16.

The correct answer is C.
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by Brent@GMATPrepNow » Wed Apr 18, 2018 4:54 am
VJesus12 wrote: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 the 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

The OA is C.

I am confused by this question. Can anyone help me? Thanks in advanced.
There are two different cases to consider:
1) All 3 pads the same color
2) The 3 pads are 3 different colors

Case 1: All 3 pads the same color
Take the task of packaging pads and break it into stages.

Stage 1: Select a size
There are 2 possible sizes, so we can complete stage 1 in 2 ways.

Stage 2: Select 1 color (to be applied to all 3 pads)
There are 4 possible colors from which to choose, so we can complete stage 2 in 4 ways.

By the Fundamental Counting Principle (FCP) we can complete the two stages in (2)(4) ways (= 8 ways)


Case 2: The 3 pads are 3 different colors
Take the task of packaging pads and break it into stages.

Stage 1: Select a size
There are 2 possible sizes, so we can complete stage 1 in 2 ways.

Stage 2: Select 3 different colors
There are 4 possible colors, and we must choose 3 of them.
Since the order of the selected colors does not matter, we can use combinations.
We can select 3 colors from 4 colors in 4C3 ways (4 ways), so we can complete stage 2 in 4 ways.

By the Fundamental Counting Principle (FCP) we can complete the two stages in (2)(4) ways (= 8 ways)


So, both cases can be completed in a total of 8 + 8 ways =[spoiler] 16 = C[/spoiler]

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by [email protected] » Wed Apr 18, 2018 7:45 pm
Hi VJesus12,

The question is essentially about the Combination Formula and following instructions. However, if you don't realize that, then you can always "brute force" the solution - you just have to draw it all out. We're told that there are 2 sizes of notepads and 4 colors (Blue, Green, Yellow, Prink) of notepads. For organizational purposes, I'm going to refer to the 8 types of pads as:

B = Big blue pad
b = Little blue pad
G = Big green pad
g = Little green pad
Etc.

Now, we just need to figure out how many options fit each description:

1st: 3 notepads of the SAME SIZE and SAME COLOR....

BBB
bbb
GGG
ggg
YYY
yyy
PPP
ppp

8 options

2nd: 3 notepads of the SAME SIZE and 3 DIFFERENT COLORS

BGY
BGP [spoiler]
BYP
GYP
bgy
bgp
byp
gyp

8 options
Total options = 8 + 8 = 16

Final Answer: C

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by Jeff@TargetTestPrep » Thu Apr 19, 2018 5:02 pm
VJesus12 wrote: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 the 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
Let's say the 2 sizes of notepads are small and large. Then, for the small notepads, there are 4 packages of notepads of all the same color (one package for each color) and 4C3 = 4 packages of notepads of three different colors. Thus, for the small notepads, there are a total of 4 + 4 = 8 different packages. Similarly, there are 8 different packages for the large notepads. Thus, there are a total of 8 + 8 = 16 different packages for the 2 sizes of notepads.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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