Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 03 Apr 2017
Posts: 36

A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
Updated on: 05 May 2018, 00:12
Question Stats:
64% (02:27) correct 36% (02:25) wrong based on 107 sessions
HideShow timer Statistics
A portfolio of 11 stocks will be assembled from 7 technology stocks, 6 energy stocks and 2 restaurant stocks. How many portfolios are possible if the majority must be technology stocks A. 231 B. 462 C. 693 D. 924 E. 1155
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by mitrakaushi on 04 May 2018, 19:07.
Last edited by Bunuel on 05 May 2018, 00:12, edited 1 time in total.
Renamed the topic.



Intern
Joined: 03 Apr 2017
Posts: 36

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
04 May 2018, 19:12
Why can't we employ the simple strategy as follows:
Min tech stocks needed: 6
Number of ways they can be selected: 7C6 = 7
Stocks left (Including the left out tech stock) : 9
To complete the number 11, we need to find 5 more stocks: 9C5 = 126
So Total Number: 126 * 9 = 1134.
My calculation is wrong, but I can't figure out the flaw in the logic. Can someone help me with this?



Intern
Joined: 22 Feb 2018
Posts: 2

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
04 May 2018, 20:31
Here is my way:
Majority must be tech stock so chose 6 or 7 from 7 tech stocks 7C6 and 7C7
then chose the rest from the other 8 stocks
So we get 7c6 x 8c5 + 7c7 x 8c4 = 7x56 + 70 =462
Cheers!



Senior Manager
Joined: 21 Jan 2015
Posts: 347
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28 GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
04 May 2018, 23:16
WY919 wrote: Here is my way:
Majority must be tech stock so chose 6 or 7 from 7 tech stocks 7C6 and 7C7
then chose the rest from the other 8 stocks
So we get 7c6 x 8c5 + 7c7 x 8c4 = 7x56 + 70 =462
Cheers! My Confusion/doubt.... What if we take 5 Tech Stock, 4 out of 6 and 2 out of 2. it still gives us majority of Tech stock. So what does majority actually means here?? is it means greater then all other stock combined or greater than any other individual type of tock in the set??
_________________
 The Mind is Everything, What we Think we Become. Kudos will encourage many others, like me. Please Give Kudos !! Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 49206

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
05 May 2018, 00:33
mitrakaushi wrote: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6 energy stocks and 2 restaurant stocks. How many portfolios are possible if the majority must be technology stocks
A. 231 B. 462 C. 693 D. 924 E. 1155 In a portfolio of 11 stocks the majority to be technology stocks, the number of technology stocks must be more than or equal to 6. Since there are only 7 technology stocks available then there should be 6 or 7 technology stocks in the portfolio of 11 stocks. Case 1: 6 technology stocks.6 technology stocks, any 5 stocks from 6 + 2 = 8 stocks 7C6*8C5 = 7*56 = 392. Case 2: 7 technology stocks.7 technology stocks, any 4 stocks from 6 + 2 = 8 stocks. 7C7*8C4 = 1*70 = 70. Total = 392 + 70 = 462. Answer: B.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 31 May 2017
Posts: 325

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
05 May 2018, 09:34
Total stocks: 7 Technology stocks 6 Energy Stocks 2 Restaurant Stocks Total Stocks needed in portfolio = 11 stocks Constraint: Majority of stocks in portfolio should be technology stocks. So technology shares should be 6 or 7. 1. If the technology stock is 6  then other stocks should be 5 7C6 * 8C5 = 7 * 56 = 392 2. If the technology stock is 7  then other stocks should be 4 7C7 * 8C4 = 1 * 70 = 70 Total = 70 + 392 = 462 Ans: B
_________________
Please give kudos if it helps
Resources Ultimate GMAT Quantitative Megathread  ALL YOU NEED FOR QUANT ! ! !  SC Blogs by Magoosh  How to improve your verbal score  Things i wish i could've done earlier  Ultimate Q51 Guide



Intern
Joined: 14 Aug 2017
Posts: 3

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
05 May 2018, 13:13
WY919 wrote: Here is my way:
Majority must be tech stock so chose 6 or 7 from 7 tech stocks 7C6 and 7C7
then chose the rest from the other 8 stocks
So we get 7c6 x 8c5 + 7c7 x 8c4 = 7x56 + 70 =462
Cheers! ++++++++++++++++++++++++++++++++++++++++ I can choose 5 + 4 + 2 = 11 as well. In this case the tech stocks are still in the majority



Intern
Joined: 04 Mar 2018
Posts: 15

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
05 May 2018, 13:46
i think there should be 3 cases. The two cases as mentioned in previous replies while third one mentioned below.
Case 3: 5 Technology stocks, 4 Energy Stocks, 2 Restaurant stocks. Still technology stocks are in majority. so, 7C5 * 6C4 * 2C2 = 315
Total = 70 +392+315 = 777 (which is not in the option though)
Can anyone tell what is mistake in this particular case.



Senior Manager
Joined: 31 May 2017
Posts: 325

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
05 May 2018, 13:53
nightvisionThe third case you mentioned (5 Technology stocks, 4 Energy Stocks, 2 Restaurant stocks) is not included because in this case the technology shares might be higher than the individual Energy and Restaurant stocks , but not the majority in the portfolio as whole (5 out of 11) The portfolio should consists of 11 shares out of which 5 technology shares (as in case 3) might not be major part of portfolio. Technology shares should be 6 or 7 [In this 7 is maximum available] to have tech shares as majority.
_________________
Please give kudos if it helps
Resources Ultimate GMAT Quantitative Megathread  ALL YOU NEED FOR QUANT ! ! !  SC Blogs by Magoosh  How to improve your verbal score  Things i wish i could've done earlier  Ultimate Q51 Guide



Intern
Joined: 03 Apr 2017
Posts: 36

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
06 May 2018, 10:14
Bunuel wrote: mitrakaushi wrote: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6 energy stocks and 2 restaurant stocks. How many portfolios are possible if the majority must be technology stocks
A. 231 B. 462 C. 693 D. 924 E. 1155 In a portfolio of 11 stocks the majority to be technology stocks, the number of technology stocks must be more than or equal to 6. Since there are only 7 technology stocks available then there should be 6 or 7 technology stocks in the portfolio of 11 stocks. Case 1: 6 technology stocks.6 technology stocks, any 5 stocks from 6 + 2 = 8 stocks 7C6*8C5 = 7*56 = 392. Case 2: 7 technology stocks.7 technology stocks, any 4 stocks from 6 + 2 = 8 stocks. 7C7*8C4 = 1*70 = 70. Total = 392 + 70 = 462. Answer: B. BunuelWhy can't we employ the simple strategy as follows: Min tech stocks needed: 6 Number of ways they can be selected: 7C6 = 7 Stocks left (Including the left out tech stock) : 9 To complete the number 11, we need to find 5 more stocks: 9C5 = 126 So Total Number: 126 * 9 = 1134. My calculation is wrong, but I can't figure out the flaw in the logic. Can someone help me with this?



Manager
Joined: 29 Sep 2017
Posts: 113
Location: United States
Concentration: Strategy, Leadership
GPA: 3.3
WE: Consulting (Consulting)

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
06 May 2018, 13:26
I did the way I listed below, but it's a long solution and prone to errors. Use the solution bunnel posted above. It's much quicker. My method: Technology stocks must be majority per question stem. This can be true when there are either 6 technology stocks or 7 (why? because it must be greater than 11/2 = 5.5 and there are only 7 tech stocks available). Tech stocks = 6:nCr(7,6) * nCr(6,5) + nCr(7,6) * nCr(6,4) * nCr(2,1) + nCr(7,6) * nCr(6,3) * nCr(2,2)This sums to 392 Tech stocks = 7: nCr(7,7) * nCr(6,4) + nCr(7,7) * nCr(6,3) * nCr(2,1) + nCr(7,7) * nCr(6,2) * nCr(2,2)
This sums to 70 392 + 70 = 462.
_________________
If this helped, please give kudos!



Director
Joined: 02 Oct 2017
Posts: 618

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
06 May 2018, 13:53
mitrakaushi
As per me first of all as per your approach total should be =7*126=882
Next flaw in your approach I would say u have already selected tech stocks 6 out of 7 then you included the left over among other and start selecting from them Whereas principle of selection says if one thing is selected then it should not be included in remaining items that's why u r getting wrong result
Make 2 cases as bunuel mentioned above then you will surely get correct answer
Posted from my mobile device



Manager
Joined: 22 Jan 2014
Posts: 177
WE: Project Management (Computer Hardware)

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
07 May 2018, 03:13
Bunuel wrote: mitrakaushi wrote: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6 energy stocks and 2 restaurant stocks. How many portfolios are possible if the majority must be technology stocks
A. 231 B. 462 C. 693 D. 924 E. 1155 In a portfolio of 11 stocks the majority to be technology stocks, the number of technology stocks must be more than or equal to 6. Since there are only 7 technology stocks available then there should be 6 or 7 technology stocks in the portfolio of 11 stocks. Case 1: 6 technology stocks.6 technology stocks, any 5 stocks from 6 + 2 = 8 stocks 7C6*8C5 = 7*56 = 392. Case 2: 7 technology stocks.7 technology stocks, any 4 stocks from 6 + 2 = 8 stocks. 7C7*8C4 = 1*70 = 70. Total = 392 + 70 = 462. Answer: B. why can't we take the case where 5 are tech stocks, 4 are energy stocks, and 2 are restaurant stocks.
_________________
Illegitimi non carborundum.



Director
Joined: 02 Oct 2017
Posts: 618

A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
07 May 2018, 12:25
thefibonacci wrote: Bunuel wrote: mitrakaushi wrote: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6 energy stocks and 2 restaurant stocks. How many portfolios are possible if the majority must be technology stocks
A. 231 B. 462 C. 693 D. 924 E. 1155 In a portfolio of 11 stocks the majority to be technology stocks, the number of technology stocks must be more than or equal to 6. Since there are only 7 technology stocks available then there should be 6 or 7 technology stocks in the portfolio of 11 stocks. Case 1: 6 technology stocks.6 technology stocks, any 5 stocks from 6 + 2 = 8 stocks 7C6*8C5 = 7*56 = 392. Case 2: 7 technology stocks.7 technology stocks, any 4 stocks from 6 + 2 = 8 stocks. 7C7*8C4 = 1*70 = 70. Total = 392 + 70 = 462. Answer: B. why can't we take the case where 5 are tech stocks, 4 are energy stocks, and 2 are restaurant stocks. Because question talks about being majority of technology stocks. In your case other than tech becomes 6 which is majority as compared to 5 of tech. So that case is not relevant here. Give kudos if it helps Posted from my mobile device



Senior Manager
Joined: 12 Feb 2015
Posts: 427

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
13 Jun 2018, 08:32
Since the majority of the stocks should be tech companies then this could be achieved by (7C7 * 8C4) + (7C6*8C5) = 462 ways.
_________________
"Please hit +1 Kudos if you like this post"
_________________ Manish
"Only I can change my life. No one can do it for me"



Manager
Joined: 11 Apr 2018
Posts: 120
Location: India
GPA: 4
WE: Information Technology (Computer Software)

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
13 Jun 2018, 23:52
11 stocks to be chosen from 7 technology stocks, 6 energy stocks and 2 restaurant stocks. Condition: the majority must be technology stocks.
For technology stocks to be in majority of 11 stocks, the split should be ( 6, 5 ) or ( 7, 4 ). Case 1: ( 6, 5 ) Choosing 6 technology stocks can be done in 7C6 ways. Remaining 5 stocks should be chosen from 6 + 2 stocks. This can be done in 8C5 ways. Total = 7C6 X 8C5.
Case 2: ( 7, 4 ) Choosing 7 technology stocks can be done in 7C7 ways. Remaining 4 stocks should be chosen from 6 + 2 stocks. This can be done in 8C4 ways. Total = 7C7 X 8C4.
Total = 7C6 X 8C5 + 7C7 X 8C4 = 462. Option B



Senior Manager
Joined: 14 Dec 2017
Posts: 471

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
14 Jun 2018, 14:12
mitrakaushi wrote: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6 energy stocks and 2 restaurant stocks. How many portfolios are possible if the majority must be technology stocks
A. 231 B. 462 C. 693 D. 924 E. 1155 If the majority of the stock has to be from technology, then either atleast 6 technology stocks or 7 technology stocks should be chosen. (i) 6 tech stocks can be selected in \(7C6\) ways & the balance 5 stocks can be selected in \(8C5\) ways hence # of ways if 6 tech stocks are selected = \(7C6 * 8C5\) = 392 (ii) 7 tech stocks can be selected in \(7C7\) ways & the balance 4 stocks can be selected in \(8C4\) ways hence # of ways if 7 tech stocks are selected = \(7C7 * 8C4\) = 70 Total # of ways = 392 + 70 = 462 Answer B. Thanks, GyM
_________________
New to GMAT Club  https://gmatclub.com/forum/newtogmatclubneedhelp271131.html#p2098335



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835

Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6
[#permalink]
Show Tags
17 Jun 2018, 19:41
mitrakaushi wrote: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6 energy stocks and 2 restaurant stocks. How many portfolios are possible if the majority must be technology stocks
A. 231 B. 462 C. 693 D. 924 E. 1155 If technology stocks are to have majority, either 7 or 6 of the stocks in the portfolio must be technology stocks. When there are 7 technology stocks in the portfolio, we have 8 stocks left for 4 spots, which can be chosen in 8C4 = (8 x 7 x 6 x 5)/4! = = (8 x 7 x 6 x 5)/(4 x 3 x 2) = 70 ways. When there are 6 technology stocks in the portfolio, we have 5 stocks left for 5 spots, which can be chosen in 8C5 = (8 x 7 x 6 x 5 x 4)/5! = = (8 x 7 x 6 x 5 x 4)/(5 x 4 x 3 x 2) = 56 ways. Furthermore, 6 technology stocks can be chosen from a total of 7 technology stocks in 7C6 = 7 ways. Thus, in total, there are 7 x 56 = 392 ways to have 6 technology stocks in the portfolio. So are a total of 70 + 392 = 462 portfolios where the technology stocks have majority. Answer: B
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: A portfolio of 11 stocks will be assembled from 7 technology stocks, 6 &nbs
[#permalink]
17 Jun 2018, 19:41






