GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Aug 2018, 06:15

Close

GMAT Club Daily Prep

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 GMAT 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.

Close

Request Expert Reply

Confirm Cancel

"Ice-Cold" Ice-cream factory produces only tricolor ice-cream products

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 862
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
"Ice-Cold" Ice-cream factory produces only tricolor ice-cream products  [#permalink]

Show Tags

New post 26 Sep 2015, 11:00
1
4
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (01:33) correct 41% (01:40) wrong based on 106 sessions

HideShow timer Statistics

"Ice-Cold" Ice-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and red. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?

A. 12
B. 14
C. 18
D. 19
E. 20

_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Intern
Intern
avatar
Joined: 29 Mar 2015
Posts: 22
Re: "Ice-Cold" Ice-cream factory produces only tricolor ice-cream products  [#permalink]

Show Tags

New post 26 Sep 2015, 16:00
2
IMO: D - 19

There are 6C3 = 20 ways to create different colored ice cream products. Out of these 20, only 1 (Silver, Blue, Red) will not contain at least one of the colors pink, purple, or orange. 20 - 1 = 19.

The other way would be to calculate the number of ice cream products that contain at least one of the colors pink, purple, or orange (PPO).

#1: Pick one out of PPO and two out of SBP: 3C1 * 3C2 = 3 * 3 = 9
#2: Pick two out of PPO and one out of SBP: 3C2 * 3C1 = 3 * 3 = 9
#3: Pick three out of PPO: 3C3 = 1

9 + 9 + 1 = 19
Manager
Manager
avatar
Joined: 29 Jul 2015
Posts: 159
GMAT ToolKit User
Re: "Ice-Cold" Ice-cream factory produces only tricolor ice-cream products  [#permalink]

Show Tags

New post 26 Sep 2015, 18:09
1
reto wrote:
"Ice-Cold" Ice-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and red. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?

A. 12
B. 14
C. 18
D. 19
E. 20


Number of combinations with pink color:-
Colours available after choosing pink are purple,orange,silver,blue and red. 2 colors are to be chosen.
Number of ways of choosing 2 colours out of 5 is 5C2 = 10

Number of combinations with purple colour:-
Colours available after choosing purple are orange,silver,blue and red.
Number of ways of selecting 2 colours out of 4 is 4C2= 6

Number of combinations with orange colour:-
Colours available after choosing orange are silver,blue and red.
Number of ways of selecting 2 colours out of 3 is 3C2= 3

Total number of combinations are 10+6+3 = 19

Answer:- D
Manager
Manager
User avatar
Joined: 17 Jun 2015
Posts: 236
GMAT 1: 540 Q39 V26
GMAT 2: 680 Q46 V37
GMAT ToolKit User
Re: "Ice-Cold" Ice-cream factory produces only tricolor ice-cream products  [#permalink]

Show Tags

New post 26 Sep 2015, 21:46
There are three cases possible.

Case 1: Only one of the three strip is Orange, pink or purple. Selection of one of these would be 3C1 = 3
The other two empty slots would mean selecting two from the remaining three i.e 3C2=3

Now, we need one of the desired three AND one of two of the other three. That means m ways of doing something and n ways of soing something else together would give me m*n ways. SO ( ways for case 1

Case 2: Reverse of the case above i.e 2 from the desired lot and 1 from the other lot. This gives 3C2 * 3C1 = 9

Case 3: All three are from the desired lot. As, the order is not important, hence only one way of doing so =1

Therefore, total 19 ways of doing so. D.
_________________

Fais de ta vie un rêve et d'un rêve une réalité

Intern
Intern
avatar
Joined: 04 Jun 2008
Posts: 6
Re: "Ice-Cold" Ice-cream factory produces only tricolor ice-cream products  [#permalink]

Show Tags

New post 03 Oct 2015, 20:58
Total Choices are 6C3 = 20
Forbidden Choices aka (no options include pink, purple or orange) = 3C3 = 1

TC-FC = 20-1 = 19

Answer is D
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3182
Location: United States (CA)
Re: "Ice-Cold" Ice-cream factory produces only tricolor ice-cream products  [#permalink]

Show Tags

New post 14 Feb 2018, 10:53
reto wrote:
"Ice-Cold" Ice-cream factory produces only tricolor ice-cream products, where each ice-cream has three stripes of different colors. The factory uses the colors pink, purple, orange, silver, blue and red. How many different ice-cream products have at least one stripe out of the following colors: pink, purple or orange (assume that the order of the stripes in a single ice-cream does not matter)?

A. 12
B. 14
C. 18
D. 19
E. 20


We can use the formula:

Total number of ways to select 3 stripes - number of ways to select stripes without pink, purple or orange = number of ways with at least one of pink, purple or orange

Total number of ways to select 3 stripes:

6C3 = 6!/[3!(6-3)!] = 6!/(3!3!) = (6 x 5 x 4)/(3 x 2 x 1) = 20

The only way to choose 3 stripes, none of which is pink, purple, or orange, is if the 3 stripes are red, blue, and silver. Thus, the total number of ways to select stripes without pink, purple or orange:

3C3 = 1

So the number of ways with at least one of pink, purple or orange is 20 - 1 = 19.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: "Ice-Cold" Ice-cream factory produces only tricolor ice-cream products &nbs [#permalink] 14 Feb 2018, 10:53
Display posts from previous: Sort by

"Ice-Cold" Ice-cream factory produces only tricolor ice-cream products

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.