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 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 is not considered, how many different packages of the types described above are possible?
A. 6
B. 8
C. 16
D. 24
E. 32
gprep ps
This topic has expert replies
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
There are 2 size options: small and large.abhasjha 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 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 is not considered, how many different packages of the types described above are possible?
A. 6
B. 8
C. 16
D. 24
E. 32
There are 4 color options: blue, green, yellow, and pink.
Case 1: 3 notepads of the same size and of the same color
Number of ways to choose 1 size from 2 choices = 2C1 = 2.
Number of ways to choose 1 color from 4 choices = 4C1 = 4.
To combine these options, we multiply:
2*4 = 8.
Case 2: 3 notepads of the same size and of 3 different colors
Number of ways to choose 1 size from 2 choices = 2C1 = 2.
Number of ways to choose 3 colors from 4 choices = 4C3 = (4*3*2)/(3*2*1) = 4.
To combine these options, we multiply:
2*4 = 8.
Total ways to form a package = 8+8 = 16.
The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
There are two different cases to consider:A certain office supply store stocks 2 sizes of stick notepads,each in 4 colours : blue,green,yellow or pink.The store packs the note pads in packages that contain either 3 notepads of the same size and the same colour or 3 notepads of the same size and different colours.If the order in which the colours are packed doesnt matter,how many different packages of the types described above are possible?
a)6
b)8
c)16
d)24
e)32
Thanks
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]
--------------------------
Note: the FCP can be used to solve the majority of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775
Then you can try solving the following questions:
EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html
- https://www.beatthegmat.com/mouse-pellets-t274303.html
MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html
DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/ps-counting-t273659.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/please-solve ... 71499.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/laniera-s-co ... 15764.html
Cheers,
Brent
- GMATinsight
- Legendary Member
- Posts: 1100
- Joined: Sat May 10, 2014 11:34 pm
- Location: New Delhi, India
- Thanked: 205 times
- Followed by:24 members
Answer: Option Cabhasjha 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 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 is not considered, how many different packages of the types described above are possible?
A. 6
B. 8
C. 16
D. 24
E. 32
image hosting adult
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
HI abhasjha,
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
BYP
GYP
bgy
bgp
byp
gyp
8 options
Total options = 8 + 8 = 16
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
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
BYP
GYP
bgy
bgp
byp
gyp
8 options
Total options = 8 + 8 = 16
Final Answer: C
GMAT assassins aren't born, they're made,
Rich