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

 It is currently 17 Oct 2019, 04:00

### 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

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

# Jill bought 6 glasses for her kitchen - white, red, black, grey, yello

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58429
Jill bought 6 glasses for her kitchen - white, red, black, grey, yello  [#permalink]

### Show Tags

29 Jan 2018, 00:16
00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:19) correct 38% (01:52) wrong based on 70 sessions

### HideShow timer Statistics

Jill bought 6 glasses for her kitchen - white, red, black, grey, yellow, and blue - and would like to display 3 of them on the shelf next to each other. If she decides that a red and a blue glass cannot be displayed together at the same time, in how many different ways can Jill arrange the glasses?

A. 24
B. 48
C. 96
D. 120
E. 720

_________________
Intern
Joined: 13 Oct 2017
Posts: 2
GMAT 1: 530 Q43 V20
GPA: 3.99
Re: Jill bought 6 glasses for her kitchen - white, red, black, grey, yello  [#permalink]

### Show Tags

29 Jan 2018, 00:39

First let us take Red in the first position. So we will be left with two places. Now we can’t use red so the remaining number of possibilities will be 4*3=12 ways

In the same way replace red with blue and we get 12 more ways

Now let us eliminate both red and blue and we will be left with 4*3*2 = 24 ways

So total will be 12+12+24 = 48 ways

Sent from my iPhone using GMAT Club Forum
Senior Manager
Joined: 07 Dec 2017
Posts: 316
GMAT 1: 660 Q50 V30
Re: Jill bought 6 glasses for her kitchen - white, red, black, grey, yello  [#permalink]

### Show Tags

29 Jan 2018, 05:08
imo answer would be: 96

No of ways Jill can arrange the glasses = total no of ways for selecting and arranging them - total no of ways when red and blue are together

N.o.w= 6P3 - 4*3*2 = 120-24= 96
Intern
Joined: 16 Sep 2017
Posts: 21
Re: Jill bought 6 glasses for her kitchen - white, red, black, grey, yello  [#permalink]

### Show Tags

29 Jan 2018, 05:39
1
Total no of ways of arranging the glasses =6x5x4= 120ways
Total no of ways in which red and blue glasses can be displayed together =3!x4=24
So total no of ways in which red and blue are not together =120-24=96
So answer should be C

Sent from my Moto G (4) using GMAT Club Forum mobile app
Director
Joined: 28 Jul 2016
Posts: 597
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: Jill bought 6 glasses for her kitchen - white, red, black, grey, yello  [#permalink]

### Show Tags

29 Jan 2018, 10:49
The total ways of arranging the glasses are
1. Arranging 4 from white, black, grey, and yellow = 4P3
2. Selecting any 2 from white, black, grey, and yellow and 1 from red or blue = 2* 4C2*3!
= 4P3 + 2*4C2*3!= 96
Intern
Joined: 22 Jan 2018
Posts: 5
Re: Jill bought 6 glasses for her kitchen - white, red, black, grey, yello  [#permalink]

### Show Tags

30 Jan 2018, 00:28
why is it that "Total no of ways of arranging the glasses =6x5x4= 120ways
Total no of ways in which red and blue glasses can be displayed together =3!x4=24
So total no of ways in which red and blue are not together =120-24=96
So answer should be C "

i totally understand the way of the calculation except for the part where the number of red and blue glasses are subtracted

how do you build the Formular " 3!x4=24"
how do you come up with 3 and 4?
thank you
Intern
Joined: 16 Sep 2017
Posts: 21
Re: Jill bought 6 glasses for her kitchen - white, red, black, grey, yello  [#permalink]

### Show Tags

30 Jan 2018, 05:28
There are 3! Ways in which 3 glasses can be arranged and there are 4 ways in which the 3rd glass can be selected. So 3!x4

Sent from my Moto G (4) using GMAT Club Forum mobile app
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8085
Location: United States (CA)
Re: Jill bought 6 glasses for her kitchen - white, red, black, grey, yello  [#permalink]

### Show Tags

31 Jan 2018, 16:57
Bunuel wrote:
Jill bought 6 glasses for her kitchen - white, red, black, grey, yellow, and blue - and would like to display 3 of them on the shelf next to each other. If she decides that a red and a blue glass cannot be displayed together at the same time, in how many different ways can Jill arrange the glasses?

A. 24
B. 48
C. 96
D. 120
E. 720

We can use the equation:

Number of ways with red and blue glasses not together = total number of arrangements - red and blue glasses together.

Since the order of the glasses is important, we use permutations. Thus, the total number of arrangements is:

6P3 = 6!/(6-3)! = 6!/3! = 6 x 5 x 4 = 120

Since there 4 ways to choose a glass (other than red and blue) along with the red and blue glasses, and once three glasses are picked, there are 3! ways to arrange them, the number of arrangements with red and blue glasses together in a display is:

4 x 3! = 4 x 6 = 24

Thus, the number of ways with red and blue glass not together in a display is:

120 - 24 = 96

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star 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.

Re: Jill bought 6 glasses for her kitchen - white, red, black, grey, yello   [#permalink] 31 Jan 2018, 16:57
Display posts from previous: Sort by

# Jill bought 6 glasses for her kitchen - white, red, black, grey, yello

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

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