Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 11 Feb 2016, 01:46

### 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

Author Message
TAGS:
Math Expert
Joined: 02 Sep 2009
Posts: 31297
Followers: 5357

Kudos [?]: 62382 [0], given: 9455

What is the greatest number of identical bouquets that can b [#permalink]  24 Feb 2014, 22:55
Expert's post
5
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

81% (02:13) correct 19% (01:47) wrong based on 310 sessions
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:
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

_________________
 Kaplan GMAT Prep Discount Codes Knewton GMAT Discount Codes GMAT Pill GMAT Discount Codes
Math Expert
Joined: 02 Sep 2009
Posts: 31297
Followers: 5357

Kudos [?]: 62382 [1] , given: 9455

Re: What is the greatest number of identical bouquets that can b [#permalink]  24 Feb 2014, 22:55
1
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).

_________________
Intern
Status: Never Give up!!!
Joined: 02 Aug 2012
Posts: 49
Location: India
Concentration: Finance, General Management
Followers: 0

Kudos [?]: 33 [1] , given: 28

Re: What is the greatest number of identical bouquets that can b [#permalink]  25 Feb 2014, 00:47
1
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: 152
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE: Consulting (Consulting)
Followers: 2

Kudos [?]: 159 [0], given: 29

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

percentages-700-800-level-questions-130588.html

700-to-800-level-quant-question-with-detail-soluition-143321.html

Math Expert
Joined: 02 Sep 2009
Posts: 31297
Followers: 5357

Kudos [?]: 62382 [0], given: 9455

Re: What is the greatest number of identical bouquets that can b [#permalink]  25 Feb 2014, 04:09
Expert's post
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: 152
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE: Consulting (Consulting)
Followers: 2

Kudos [?]: 159 [0], given: 29

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

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

percentages-700-800-level-questions-130588.html

700-to-800-level-quant-question-with-detail-soluition-143321.html

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

Kudos [?]: 70 [2] , given: 29

Re: What is the greatest number of identical bouquets that can b [#permalink]  26 Feb 2014, 01:26
2
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: 31297
Followers: 5357

Kudos [?]: 62382 [0], given: 9455

Re: What is the greatest number of identical bouquets that can b [#permalink]  01 Mar 2014, 03:16
Expert's post
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: 8214
Followers: 417

Kudos [?]: 111 [0], given: 0

Re: What is the greatest number of identical bouquets that can b [#permalink]  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: 5599
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 225

Kudos [?]: 1592 [0], given: 153

Re: What is the greatest number of identical bouquets that can b [#permalink]  21 Apr 2015, 18:44
Expert's post
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/ Manager Joined: 07 Apr 2015 Posts: 187 Followers: 2 Kudos [?]: 42 [0], given: 185 What is the greatest number of identical bouquets that can b [#permalink] 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: 5599 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 225 Kudos [?]: 1592 [0], given: 153 Re: What is the greatest number of identical bouquets that can b [#permalink] 19 May 2015, 22:54 Expert's post 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/

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 338
Followers: 82

Kudos [?]: 634 [0], given: 83

Re: What is the greatest number of identical bouquets that can b [#permalink]  28 May 2015, 03:02
Expert's post
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
_________________
Re: What is the greatest number of identical bouquets that can b   [#permalink] 28 May 2015, 03:02
Similar topics Replies Last post
Similar
Topics:
3 What is the greatest power that 5 can be raised to so that the resulti 4 24 Sep 2015, 22:06
4 A car ferry can hold up to 50 tons of cargo. What is the greatest 5 10 May 2015, 01:25
11 What is the greatest number of identical bouquets that can 9 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