Last visit was: 19 Jul 2024, 17:06 It is currently 19 Jul 2024, 17:06
Toolkit
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.
Request Expert Reply

# What is the greatest number of identical bouquets that can be made out

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642363 [56]
Given Kudos: 86332
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642363 [11]
Given Kudos: 86332
Intern
Joined: 03 Aug 2012
Status:Never Give up!!!
Posts: 42
Own Kudos [?]: 103 [6]
Given Kudos: 28
Location: India
Concentration: Finance, General Management
General Discussion
Manager
Joined: 14 Jan 2013
Posts: 114
Own Kudos [?]: 1552 [0]
Given Kudos: 30
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE:Consulting (Consulting)
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
Only 7 is divisible with 21 and 91, So, that should be the answer..

Is this the right way to solve?
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642363 [1]
Given Kudos: 86332
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
1
Kudos
Expert Reply
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 either 21 or 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: 114
Own Kudos [?]: 1552 [0]
Given Kudos: 30
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE:Consulting (Consulting)
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
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...
Manager
Joined: 20 Dec 2013
Posts: 183
Own Kudos [?]: 291 [3]
Given Kudos: 35
Location: India
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
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.
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11787 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
Expert Reply
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.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
Manager
Joined: 07 Apr 2015
Posts: 127
Own Kudos [?]: 192 [0]
Given Kudos: 185
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
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!
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11787 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
Expert Reply
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
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3711
Own Kudos [?]: 17337 [4]
Given Kudos: 165
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
4
Kudos
Expert Reply
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
Intern
Joined: 09 Feb 2016
Posts: 5
Own Kudos [?]: [0]
Given Kudos: 1
Schools:
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
"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.)"

What's to stop you from creating 21 bouquets, each containing 1 white tulip and 1 red tulip, and 1 bouquet containing 70 red tulips? In that scenario, you have 21 identical bouquets.

Originally posted by mh72 on 09 Feb 2016, 09:56.
Last edited by mh72 on 09 Aug 2016, 20:40, edited 1 time in total.
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11787 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
Expert Reply
mh72 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.)"

What's to stop you from creating 21 bouquets, each containing 1 white tulip and 1 red tulip, and 1 bouquet containing 70 red tulips? In that scenario, you have 21 identical bouquets. Basically, my question is this: Is the question stem necessarily read to require that each bouquet made be identical?

Hi mh72,

In your 'scenario', you've left out 70 red tulips from the 21 bouquets that you made - but the prompt says that NO flowers are to be left out. Thus, your solution does not match the specific restrictions that the prompt gave you to work with.

GMAT assassins aren't born, they're made,
Rich
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11787 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
Expert Reply
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.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
Senior Manager
Joined: 15 Oct 2015
Posts: 367
Own Kudos [?]: 1587 [0]
Given Kudos: 342
Concentration: Finance, Strategy
GPA: 3.93
WE:Account Management (Education)
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
GMAThirst 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

Please show me how to solve.

This is a case of a question u don't understand but ended up getting it right.
only 7 is a factor of 21 and 91
Alum
Joined: 12 Aug 2015
Posts: 2271
Own Kudos [?]: 3197 [1]
Given Kudos: 893
GRE 1: Q169 V154
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
1
Kudos
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
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6049
Own Kudos [?]: 4766 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
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...
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11476
Own Kudos [?]: 34445 [0]
Given Kudos: 322
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
Expert Reply
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
Manager
Joined: 04 Jun 2015
Posts: 62
Own Kudos [?]: 698 [0]
Given Kudos: 2
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
Here's my take.

Divide 91 red tulips by 21 white ones.
We get quotient of 4 and a remainder of 6 (these 6 are the white tulips) and 4 is the no. of identical bouquets. Now put the 6 white ones in each of the 2 bouquets (one white in first and one in second and so on). Thus we get 4+3 = 7
Intern
Joined: 12 Dec 2016
Posts: 10
Own Kudos [?]: 1 [0]
Given Kudos: 4
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
The part in paranthesis really got me confused here, and i could not understand anything written there. I get the part outside the paranthesis, but then... ?
Re: What is the greatest number of identical bouquets that can be made out [#permalink]
1   2
Moderator:
Math Expert
94421 posts