May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 27 Dec 2009
Posts: 137

A certain office supply store stocks 2 sizes of selfstick
[#permalink]
Show Tags
17 Apr 2010, 10:05
Question Stats:
70% (02:12) correct 30% (02:19) wrong based on 988 sessions
HideShow timer Statistics
A certain office supply store stocks 2 sizes of selfstick 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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 55228

Re: colors and size of pads
[#permalink]
Show Tags
17 Apr 2010, 10:26
A certain office supply store stocks 2 sizes of selfstick 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 Notepads of the same color = 4 (we have 4 colors). As we have two sizes then total for the same color=4*2=8 Notepads of the different colors = 4C3=4 (we should choose 3 different colors out of 4). As we have two sizes then total for the different color=4*2=8 Total=8+8=16 Answer: C.
_________________




Manager
Joined: 29 Jul 2011
Posts: 85
Location: United States

Re: Permutations and combinations
[#permalink]
Show Tags
09 Jan 2012, 19:29
Kotela, Sorry if I was not clear. I generally keep my answers short. There are two ways this can happen.: 1. Same size same color: There are eight such combinations size 1 1BBB 1GGG 1YYY 1PPP size 2 2BBB 2GGG 2YYY 2PPP total 8 2. Same size different color size 1 4C3 = 4 (BGY, BYP, GYP, BGP) size 2 4C3 = 4 (same as above) Total 8 Notice there there is an OR in the stem, so add 8 + 8 = 16 Hope this helps!
_________________
I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!
DS  If negative answer only, still sufficient. No need to find exact solution. PS  Always look at the answers first CR  Read the question stem first, hunt for conclusion SC  Meaning first, Grammar second RC  Mentally connect paragraphs as you proceed. Short = 2min, Long = 34 min




Manager
Joined: 07 Feb 2010
Posts: 127

Re: colors and size of pads
[#permalink]
Show Tags
22 Dec 2010, 08:08
bunuel can you make me more clear, how it is 4 books of same colour
thank u



Math Expert
Joined: 02 Sep 2009
Posts: 55228

Re: colors and size of pads
[#permalink]
Show Tags
22 Dec 2010, 08:20
anilnandyala wrote: bunuel can you make me more clear, how it is 4 books of same colour
thank u Sure. As the pads are packed in packages that contain only the notepads of same size then let's calculate for one size and then multiply it by 2 to get total. There are 4 colors so there are 4 different packages possible with 3 same color notepads: all 3 Blue, all 3 Green, all 3 Yellow, or all 3 Purple; For 3 different color pads: again as there are 4 colors then 4C3=4 is the # of ways to choose 3 different color pads to make a package: {BGY}, {BGP}, {BYP}, {GYP}; So for one size there are 4+4=8 packages possible thus for 2 sizes there are 8*2=16 packages possible. Answer: C. Hope it's clear.
_________________



Intern
Joined: 01 Jan 2012
Posts: 24
Location: United States
Concentration: Strategy, General Management
GPA: 3.76
WE: Engineering (Consulting)

Re: Permutations and combinations
[#permalink]
Show Tags
08 Jan 2012, 15:33
You have 2 sizes and 4 colors (Call them A,B,C,D) to do this problem you should consider that for each size you can have 2 types of package call them type X and type y
Type X is of all the same color so for size 1 type X is
A B C D
Type Y is of all the different colors for size 1 type Y is all the ways you can have 3 of ABCD
You could say that you are choosing 3 of the 4 colors for each package therefore this is
4C3=4 or you could list them out working as if ABCD are in a circle and you want to list them moving only one letter into and out of your arrangement at a time.
ABC BCD CDA DAB so either way you see 4 ways for Type Y
Since you have 2 sizes and 8 ways to arrange each size you have a total of 16 packages.
Hope this helped



Manager
Joined: 29 Jul 2011
Posts: 85
Location: United States

Re: Permutations and combinations
[#permalink]
Show Tags
08 Jan 2012, 20:24
Too big a question for too small an answer... 2 sizes of B, G, Y and P 1. Same size, same color = 1st size same color (4) and 2nd size same color (4) = 8 2. Same size, diff color = 1st size diff color 4!/3!1! = 4, same for second size = 8 Together = 16
_________________
I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!
DS  If negative answer only, still sufficient. No need to find exact solution. PS  Always look at the answers first CR  Read the question stem first, hunt for conclusion SC  Meaning first, Grammar second RC  Mentally connect paragraphs as you proceed. Short = 2min, Long = 34 min



SVP
Joined: 06 Sep 2013
Posts: 1660
Concentration: Finance

Re: A certain office supply store stocks 2 sizes of selfstick
[#permalink]
Show Tags
30 Dec 2013, 07:26
msand wrote: A certain office supply store stocks 2 sizes of selfstick 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 First scenario 2C1 * 4C3 = 8 Second scenario 2C1*4C1 = 8 Total 16 Hence, answer is C Hope it helps Cheers! J



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14188
Location: United States (CA)

Re: A certain office supply store stocks 2 sizes of selfstick
[#permalink]
Show Tags
12 Feb 2016, 18:35
Hi All, 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: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/



Board of Directors
Joined: 17 Jul 2014
Posts: 2552
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: A certain office supply store stocks 2 sizes of selfstick
[#permalink]
Show Tags
09 Apr 2016, 14:10
msand wrote: A certain office supply store stocks 2 sizes of selfstick 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 we have 2 types of notebooks. we can select either 3 colors or 1 color to select 3 colors: 4C3 = 4 to select 1 color: 4C1 = 4 so for each type of notebook, we have 8 possible arrangements 8x2 = 16 C



Retired Moderator
Joined: 17 Jun 2016
Posts: 503
Location: India
GMAT 1: 720 Q49 V39 GMAT 2: 710 Q50 V37
GPA: 3.65
WE: Engineering (Energy and Utilities)

Re: A certain office supply store stocks 2 sizes of selfstick
[#permalink]
Show Tags
11 May 2017, 21:35
Effectively, selecting 1 out of 4 (colors) is same as 3 out of 4 as 1C4 = 3C4 = 4 And selecting 1 out of 2 sizes = 2 Hence, Packet Type 1 = Packet Type 2 = 4 x 2 = 8 And hence the total type = type1 + type2 = 8 + 8 = 16 Hit Kudos if you like the response !!!
_________________



Director
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 724
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: A certain office supply store stocks 2 sizes of selfstick
[#permalink]
Show Tags
11 May 2017, 23:14
msand wrote: A certain office supply store stocks 2 sizes of selfstick 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 2 sizes of self stick notepads. Also available colors are 4 : Blue, Green, Yellow, Pink. Case 1: The packages can be of 3 notepads of the same size and the same color 1st size : No. of packages possible : 4C1 = 4 2nd size: No. of packages possible = 4C1 = 4 Case 2: The packages can be of 3 notepads of the same size and of 3 different colors 1st size : No. of packages possible : 4C3 = 4 2nd size : No. of packages possible : 4C3 = 4 Total no. of different packages possible if order in which colors are packed is not considered : (4+4)+(4+4) = 16
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler UPSC Aspirants : Get my app UPSC Important News Reader from Play store. MBA Social Network : WebMaggu
Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".



Director
Joined: 17 Dec 2012
Posts: 630
Location: India

Re: A certain office supply store stocks 2 sizes of selfstick
[#permalink]
Show Tags
20 May 2017, 19:56
msand wrote: A certain office supply store stocks 2 sizes of selfstick 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 1. Ordering is not important, so this is a combination problem 2. Is there a constraint? There are two cases each with a constraint 3. In the first case ,Constraint is 3 notebooks of the same color . So there are 2 ways of selecting a size and 4C1 ways of selecting a color. So a total of 2*4= 8 ways 4. In the second case, constraint is 3 notebooks of the same size but 3 different colors. There are 2 ways of selecting a size and 4C3 ways of selecting colors, for a total of 2*4=8 ways 5. Total number of combinations is (3) + (4) = 16
_________________
Srinivasan Vaidyaraman Sravna Test Prep http://www.sravnatestprep.comHolistic and Systematic Approach



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823

Re: A certain office supply store stocks 2 sizes of selfstick
[#permalink]
Show Tags
19 Apr 2018, 18:03
msand wrote: A certain office supply store stocks 2 sizes of selfstick 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
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Manager
Joined: 19 Aug 2016
Posts: 84

Re: A certain office supply store stocks 2 sizes of selfstick
[#permalink]
Show Tags
02 Jun 2018, 17:53
Bunuel wrote: anilnandyala wrote: bunuel can you make me more clear, how it is 4 books of same colour
thank u Sure. As the pads are packed in packages that contain only the notepads of same size then let's calculate for one size and then multiply it by 2 to get total. There are 4 colors so there are 4 different packages possible with 3 same color notepads: all 3 Blue, all 3 Green, all 3 Yellow, or all 3 Purple; For 3 different color pads: again as there are 4 colors then 4C3=4 is the # of ways to choose 3 different color pads to make a package: {BGY}, {BGP}, {BYP}, {GYP}; So for one size there are 4+4=8 packages possible thus for 2 sizes there are 8*2=16 packages possible. Answer: C. Hope it's clear. Hi Bunuel, Sorry but I don't follow this.. When there are 4 colors and 2 sizes there are total of only 8 notepads..how can we have 3 blue. 3 green 3 yellow and 3 purple Pls explain..what am I missing here? Thanks In advance Regards



Math Expert
Joined: 02 Sep 2009
Posts: 55228

Re: A certain office supply store stocks 2 sizes of selfstick
[#permalink]
Show Tags
03 Jun 2018, 04:58
zanaik89 wrote: Bunuel wrote: anilnandyala wrote: bunuel can you make me more clear, how it is 4 books of same colour
thank u Sure. As the pads are packed in packages that contain only the notepads of same size then let's calculate for one size and then multiply it by 2 to get total. There are 4 colors so there are 4 different packages possible with 3 same color notepads: all 3 Blue, all 3 Green, all 3 Yellow, or all 3 Purple; For 3 different color pads: again as there are 4 colors then 4C3=4 is the # of ways to choose 3 different color pads to make a package: {BGY}, {BGP}, {BYP}, {GYP}; So for one size there are 4+4=8 packages possible thus for 2 sizes there are 8*2=16 packages possible. Answer: C. Hope it's clear. Hi Bunuel, Sorry but I don't follow this.. When there are 4 colors and 2 sizes there are total of only 8 notepads..how can we have 3 blue. 3 green 3 yellow and 3 purple Pls explain..what am I missing here? Thanks In advance Regards A certain office supply store stocks 2 sizes of selfstick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. So, we have: Large size notepads: 4 BLUE 4 GREEN 4 YELLOW 4 PINK Small size notepads 4 blue 4 green 4 yellow 4 pink
_________________



Intern
Joined: 09 Aug 2018
Posts: 9

Re: A certain office supply store stocks 2 sizes of selfstick
[#permalink]
Show Tags
26 Aug 2018, 18:46
Hello,
What if there where 5 colours total.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14188
Location: United States (CA)

Re: A certain office supply store stocks 2 sizes of selfstick
[#permalink]
Show Tags
27 Aug 2018, 11:18
Hi andresan, Even if there were 5 colors (instead of 4), the approaches would not change  you can either use the Combination formula or 'brute force' the list of options. Have you attempted either approach (and what answer did you get?)? GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/



Intern
Joined: 21 Nov 2018
Posts: 4

Re: A certain office supply store stocks 2 sizes of selfstick
[#permalink]
Show Tags
21 Dec 2018, 10:17
A certain office supply store stocks 2 sizes of selfstick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. So, we have:
Large size notepads: 4 BLUE 4 GREEN 4 YELLOW 4 PINK
Small size notepads 4 blue 4 green 4 yellow 4 pink[/quote]
Shouldn't this be:
For large size.. 3 Blue 3 Green 3 Yellow 3 Pink
For small size.. 3 Blue 3 Green 3 Yellow 3 Pink




Re: A certain office supply store stocks 2 sizes of selfstick
[#permalink]
21 Dec 2018, 10:17






