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

 It is currently 16 Jan 2019, 21:17

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# A farmer is planting a row consisting of 4 unique apple trees and 4 un

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52164
A farmer is planting a row consisting of 4 unique apple trees and 4 un  [#permalink]

### Show Tags

08 Apr 2016, 01:42
3
4
00:00

Difficulty:

65% (hard)

Question Stats:

55% (01:46) correct 45% (01:58) wrong based on 173 sessions

### HideShow timer Statistics

A farmer is planting a row consisting of 4 unique apple trees and 4 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?

A. 512
B. 576
C. 1,024
D. 1,152
E. 10,080

_________________
Manager
Joined: 09 Jul 2013
Posts: 109
Re: A farmer is planting a row consisting of 4 unique apple trees and 4 un  [#permalink]

### Show Tags

08 Apr 2016, 06:36
Since no trees of the same type can be adjacent to one another, there must be one apple tree between each pair of orange trees, and one orange tree between each pair of apple trees. In other words, the trees must alternate. This can be done in two ways:
1. AOAOAOAO
2. OAOAOAOA

The two types of trees have 4 unique trees each, so the 4 trees of each type can be arranged in 4! ways.
The orange trees can be arranged in 4! ways, and the apple trees can be arranged in 4! ways.

Total number of arrangements = 4!*4!*2 = 24*24*2 = 1152

_________________

Dave de Koos

Director
Joined: 24 Nov 2015
Posts: 515
Location: United States (LA)
Re: A farmer is planting a row consisting of 4 unique apple trees and 4 un  [#permalink]

### Show Tags

18 Apr 2016, 11:24
1
2 possible arrangements are possible
AOAOAOAO
OAOAOAOA
2 unique type of trees are present consisting of 4 trees each
4 apple trees can be arranged in 4! ways
4 orange trees can be arranged in 4! ways
as 2 arrangements are possible
total arrangements = 2 *4! * 4! = 1152
correct answer option D
Manager
Joined: 20 Mar 2015
Posts: 59
Re: A farmer is planting a row consisting of 4 unique apple trees and 4 un  [#permalink]

### Show Tags

21 Jul 2016, 23:21
Bunuel wrote:
A farmer is planting a row consisting of 4 unique apple trees and 4 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?

A. 512
B. 576
C. 1,024
D. 1,152
E. 10,080

A row consisting of 8 trees is what we need where no two same fruit is placed one after another. Either orange first and then apple or apple first and then orange.

This is our row : $$8*4*3*3*2*2*1*1$$ = 1152
Intern
Joined: 18 Jun 2017
Posts: 9
Re: A farmer is planting a row consisting of 4 unique apple trees and 4 un  [#permalink]

### Show Tags

24 Feb 2018, 06:46
Let the unique Apple trees be A1, A2, A3 and A4
Similary, unique Orange Trees be O1,O2,O3 and O4

Condition: No Apple or orange trees should be adjacent to each other.

Two arrangements are possible:-

Case1:

_A1_A2_A3_A4 (_ represents orange trees)

Apple trees can arrange themselves in 4! way since all are unique and order matters.
Similarly, Orange trees can arrange in 4! ways.

number of arrangements: 4! * 4! = 576

Case2:

A1_A2_A3_A4_

number of arrangements: 4! * 4! = 576

Total number of arrangements : Case 1 + Case 2 = 576 *2 = 1152 (Answer)
Manager
Joined: 08 Sep 2016
Posts: 115
A farmer is planting a row consisting of 4 unique apple trees and 4 un  [#permalink]

### Show Tags

21 Apr 2018, 07:18
There are 2 ways to arrange the trees.
1) AOAOAOAO
2) OAOAOAOA

For the first arrangement, the multiplication sequence will be: 4*4*3*3*2*2*1*1. 4 apples can be placed in the first slot. 4 oranges in the second slot. 3 apples in the 3rd slot. 3 oranges in the 4th slot...etc. This arrangement will equal 576.

The second arrangement will be similar to the first arrangement, but you will consider oranges being placed in the first slot. This arrangement will also equal 576.

576+576 = 1152.

A farmer is planting a row consisting of 4 unique apple trees and 4 un &nbs [#permalink] 21 Apr 2018, 07:18
Display posts from previous: Sort by

# A farmer is planting a row consisting of 4 unique apple trees and 4 un

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

 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®.