What is the greatest number of identical bouquets that can b : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 10 Dec 2016, 13:28

### 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 June
Open Detailed Calendar

# What is the greatest number of identical bouquets that can b

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 35950
Followers: 6865

Kudos [?]: 90118 [0], given: 10418

What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

24 Feb 2014, 22:55
Expert's post
10
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

82% (02:13) correct 18% (01:54) wrong based on 441 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

What is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out? (Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal)

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Problem Solving
Question: 112
Category: Arithmetic Properties of numbers
Page: 76
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 35950
Followers: 6865

Kudos [?]: 90118 [2] , given: 10418

Re: What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

24 Feb 2014, 22:55
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
SOLUTION

What is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out? (Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal)

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Since no flowers are to be left out, then the number of bouquets must be a factor of both 21 and 91. For example, we cannot have 2 bouquets since we cannot divide 91 red tulips into 2 bouquets without one tulip left over.

Only answer choice which is a factor of 91 is E (7).

_________________
Manager
Status: Never Give up!!!
Joined: 02 Aug 2012
Posts: 50
Location: India
Concentration: Finance, General Management
Followers: 1

Kudos [?]: 37 [2] , given: 28

Re: What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

25 Feb 2014, 00:47
2
KUDOS
Inorder to find the greatest no of identical bouquets we have to find out the Greatest common divisor of 21 and 91

Prime Factors of 21 - 7x3
Prime Factors of 91 - 7x13

The greatest common factor is 7. Hence the maximum no of identical bouquets that can be made is 7. Answer - Option (E)
Manager
Joined: 14 Jan 2013
Posts: 154
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE: Consulting (Consulting)
Followers: 3

Kudos [?]: 240 [0], given: 30

Re: What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

25 Feb 2014, 03:59
Only 7 is divisible with 21 and 91, So, that should be the answer..

Is this the right way to solve?
_________________

"Where are my Kudos" ............ Good Question = kudos

"Start enjoying all phases" & all Sections

__________________________________________________________________
http://gmatclub.com/forum/collection-of-articles-on-critical-reasoning-159959.html

http://gmatclub.com/forum/percentages-700-800-level-questions-130588.html

http://gmatclub.com/forum/700-to-800-level-quant-question-with-detail-soluition-143321.html

Math Expert
Joined: 02 Sep 2009
Posts: 35950
Followers: 6865

Kudos [?]: 90118 [0], given: 10418

Re: What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

25 Feb 2014, 04:09
Mountain14 wrote:
Only 7 is divisible with 21 and 91, So, that should be the answer..

Is this the right way to solve?

7 is NOT divisible by neither 21 nor by 91. 7 is a factor of both 21 and 91.

P.S. Solutions will be published on weekend.
_________________
Manager
Joined: 14 Jan 2013
Posts: 154
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE: Consulting (Consulting)
Followers: 3

Kudos [?]: 240 [0], given: 30

Re: What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

25 Feb 2014, 04:15
Bunuel wrote:
Mountain14 wrote:
Only 7 is divisible with 21 and 91, So, that should be the answer..

Is this the right way to solve?

7 is NOT divisible by neither 21 nor by 91. 7 is a factor of both 21 and 91.

P.S. Solutions will be published on weekend.

Oops.!.. Ya My bad...

Thanks Bunuel..

Will wait for solutions...
_________________

"Where are my Kudos" ............ Good Question = kudos

"Start enjoying all phases" & all Sections

__________________________________________________________________
http://gmatclub.com/forum/collection-of-articles-on-critical-reasoning-159959.html

http://gmatclub.com/forum/percentages-700-800-level-questions-130588.html

http://gmatclub.com/forum/700-to-800-level-quant-question-with-detail-soluition-143321.html

Senior Manager
Joined: 20 Dec 2013
Posts: 273
Location: India
Followers: 0

Kudos [?]: 79 [3] , given: 29

Re: What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

26 Feb 2014, 01:26
3
KUDOS
Option E.
21=7*3
91=7*13
If we have 7 bouquets,each will have 3 white tulips and 13 red tulips.So they will be identical.
Math Expert
Joined: 02 Sep 2009
Posts: 35950
Followers: 6865

Kudos [?]: 90118 [0], given: 10418

Re: What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

01 Mar 2014, 03:16
SOLUTION

What is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out? (Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal)

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Since no flowers are to be left out, then the number of bouquets must be a factor of both 21 and 91. For example, we cannot have 2 bouquets since we cannot divide 91 red tulips into 2 bouquets without one tulip left over.

Only answer choice which is a factor of 91 is E (7).

_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12907
Followers: 563

Kudos [?]: 158 [0], given: 0

Re: What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

21 Apr 2015, 13:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 8015
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 363

Kudos [?]: 2377 [0], given: 163

Re: What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

21 Apr 2015, 18:44
Hi All,

This question is essentially about prime-factorization, but you can actually avoid some of the work if you're comfortable with basic division.

We're told to make IDENTICAL bouquets using 21 white and 91 red tulips AND we're told that NO flowers are to be left out.

With 21 white tulips, there are only three ways to form identical bouquets:

21 bouquets with 1 white flower each
7 bouquets with 3 white flowers each
3 bouquets with 7 white flowers each

With 91 red tulips, we just have to see which of those options divides into 91...

21 does NOT divide evenly into 91
7 DOES divide evenly (13 times)
3 does NOT divide evenly into 91

We're asked to find the GREATEST number of possible bouquets that can be formed, but since we're making multiple bouquets, there's only one answer that fits.

[Reveal] Spoiler:
E

GMAT assassins aren't born, they're made,
Rich
_________________

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Manager Joined: 07 Apr 2015 Posts: 188 Followers: 2 Kudos [?]: 55 [0], given: 185 What is the greatest number of identical bouquets that can b [#permalink] ### Show Tags 19 May 2015, 00:56 But is it a right approach to calculate GCF of 21 and 91 (which is 7) and therefore in my opinion also the greatest number of identical buquets? Or just by coincidence the same result? Answers appreciated! EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8015 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 363 Kudos [?]: 2377 [0], given: 163 Re: What is the greatest number of identical bouquets that can b [#permalink] ### Show Tags 19 May 2015, 22:54 Hi noTh1ng, Calculating the GCF is one approach to solving this question, although there are others. My approach was based on listing out the possibilities and finding the one that matched all of the information in the prompt; you could also have used the answer choices to your advantage and eliminated the numbers that did not match the info in the prompt. GMAT questions are always carefully designed (even the wrong answers are carefully chosen), so there are almost never any coincidences on Test Day. Sometimes a subtle Number Property or other pattern occurs in a question, and you don't necessarily need to know the rule or pattern to get the correct answer, but the existence of the pattern is never by accident. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 427
Followers: 126

Kudos [?]: 1025 [1] , given: 84

Re: What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

28 May 2015, 03:02
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
noTh1ng wrote:
But is it a right approach to calculate GCF of 21 and 91 (which is 7) and therefore in my opinion also the greatest number of identical buquets? Or just by coincidence the same result? Answers appreciated!

Dear noTh1ng

It is not a coincidence.

To understand this, let's assume that we make n identical bouquets, in each of which:

Number of white flowers = w
Number of red flowers = r

Since we are given that no flower is to be left out, we can write:
wn = 21
And, rn = 91

That is, w = 21/n
And, r = 91/n

Now, w and r, being the number of flowers, have to be integers (because we cannot have 2.5 or 3.3 flowers in a bouquet)

So, n has to be a number that completely divides 21 as well as 91.

But the question asks us to find the greatest possible value of n.

That is, the greatest possible number that completely divides 21 as well as 91.

What is this number known as? Greatest Common Factor

Hope this helped clarify your doubt.

Best Regards

Japinder
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12907
Followers: 563

Kudos [?]: 158 [0], given: 0

Re: What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

23 Jun 2016, 04:02
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 1579
Followers: 34

Kudos [?]: 284 [0], given: 378

What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

25 Nov 2016, 15:18
Hey chetan2u
I am having trouble understanding this Question.
I have seen all the solutions above,but none of them is making sense to me.
You mind solving this one.

Here is what i did
Given => 21 white and 92 red tulips

So to make identical bouquets we can make the arrangement as follows =>
1 each for 21 bouquets in which
2 each for 10 bouquets and and one in the last one.
And we can continue this way to make infinite arrangements.
I understand the use the word "identical" but if w give 2 each => we can make 10 identical bouquets and one bouquets with leftover flowers right ?
What i am missing here?
It feels like a pretty difficult Question to me.

Regards
Stone Cold
_________________

Give me a hell yeah ...!!!!!

Math Forum Moderator
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 2145
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Followers: 83

Kudos [?]: 568 [0], given: 311

Re: What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

26 Nov 2016, 00:20
Bunuel wrote:
What is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out? (Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal)

(A) 3
(B) 4
(C) 5
(D) 6
(E) 7

Greatest no of Identical Bouqets of 21 white tulips and 91 red tulips is HCF of 21& 91 = 7

Now, Check...

Each Boquet must have 3 ( ie, 21/7) White tulips and 13 ( ie, 91/7) red tulips , so all tulips are utilized..

Hence, correct answer will be (E)

stonecold hope this helps...
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4148
Followers: 308

Kudos [?]: 3265 [0], given: 100

Re: What is the greatest number of identical bouquets that can b [#permalink]

### Show Tags

26 Nov 2016, 07:07
stonecold wrote:
Hey chetan2u
I am having trouble understanding this Question.
I have seen all the solutions above,but none of them is making sense to me.
You mind solving this one.

Here is what i did
Given => 21 white and 92 red tulips

So to make identical bouquets we can make the arrangement as follows =>
1 each for 21 bouquets in which
2 each for 10 bouquets and and one in the last one.
And we can continue this way to make infinite arrangements.
I understand the use the word "identical" but if w give 2 each => we can make 10 identical bouquets and one bouquets with leftover flowers right ?
What i am missing here?
It feels like a pretty difficult Question to me.

Regards
Stone Cold

Hi,
What the Q means is that each bouquet is identical so each should have same number of white,w , and same number of red, say r..
Now w has to be a factor of 21 , since if you take 2 the last bouquet will have only 1, thus all will not be identical.
Only w as 1, 3, 7 or 21 will fit in..

Similarly r should be a factor of 91, so 1, 7,13 or 91..
Example each has7,7..., so 91/7=13 bouquets of 7 red, OR each has 13, so 7 bouquets of 7 each...

Now the MAIN point comes out is both white and red have to be divided in same number of bouquets ...
So only identical are 1and 7..
So two ways bouquets can be identical
1) All 21 and 91 together as 1 bouquet
2) We distribute 21 in 7 bouquets and 91 red too in 7 bouquets
So we will have 7 identical bouquets, each bouquet having 21/7=3 white and 91/7=13 red tulips..

So ans 7
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Re: What is the greatest number of identical bouquets that can b   [#permalink] 26 Nov 2016, 07:07
Similar topics Replies Last post
Similar
Topics:
2 What is the greatest number of apples that can be distributed e 2 25 Nov 2016, 09:23
8 There are different 10 circles. What is the number of the greatest pos 3 29 Apr 2016, 19:16
16 What is the greatest number of identical bouquets that can 12 18 Mar 2013, 11:43
1 What is the greatest number of four-digit integers whose 5 15 Sep 2008, 03:15
What is the greatest number of three-digit integers that 7 15 Sep 2008, 03:14
Display posts from previous: Sort by

# What is the greatest number of identical bouquets that can b

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

 Powered by phpBB © phpBB Group and phpBB SEO 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®.