Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GRE score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
A certain office supply store stocks 2 sizes of self-stick notepads, e
[#permalink]
16 Apr 2022, 04:17
Expert Reply
7
Bookmarks
00:00
Question Stats:
53% (02:15) correct
46% (02:40) wrong based on 15 sessions
HideShow
timer Statistics
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?
Re: A certain office supply store stocks 2 sizes of self-stick notepads, e
[#permalink]
16 Apr 2022, 05:57
3
GeminiHeat 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
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 = 16
Answer: C
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
Re: A certain office supply store stocks 2 sizes of self-stick notepads, e
[#permalink]
16 Apr 2022, 06:56
1
Quote:
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?
There are two possible cases:
Case 1: packages that contain 3 notepads of the same size and the same color In one size, there are 4 choices of same colour In other size, there are 4 choices of same colour Total ways of packages that contain 3 notepads of the same size and the same color = 4 + 4 = 8
Case 2: packages that contain 3 notepads of the same size and of 3 different colors In one size, 3 different colors can be packed in 4C3 ways = 4, as the order does not matter In other size, 3 different colors can be packed in 4C3 ways = 4 Total ways of packages that contain 3 notepads of the same size and of 3 different colors = 4 + 4 = 8
Total number of ways 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) = 8 + 8 = 16 ways
Re: A certain office supply store stocks 2 sizes of self-stick notepads, e
[#permalink]
18 Aug 2024, 06:42
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
gmatclubot
Re: A certain office supply store stocks 2 sizes of self-stick notepads, e [#permalink]