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# What is the greatest number of identical bouquets that can

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Intern
Joined: 14 Jul 2012
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Concentration: Marketing, Entrepreneurship
WE: Sales (Other)
What is the greatest number of identical bouquets that can [#permalink]

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18 Mar 2013, 12:43
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Question Stats:

83% (01:46) correct 17% (01:11) wrong based on 397 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/what-is-the- ... 67914.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Jun 2017, 04:59, edited 2 times in total.
RENAMED THE TOPIC.

Kudos [?]: 28 [3], given: 4

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

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18 Mar 2013, 12:54
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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.

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).

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

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18 Mar 2013, 13:04
7
KUDOS
Look for the factors of 21 and 91:

white = 21 = 3 x 7
red = 91 = 13 x 7

The common factor is 7, thus the greatest number of identical bouquets is 7.

Let me explain graphically:

_______Identical Bouquets (7 bouquets)______________
$$\;\;\;\;\;\;$$White $$\;\;\;\;$$ Red
$$\;\;\;\;$$3 tulips$$\;\;\;\;$$ 13 tulips = 3 white and 13 red tulips
$$\;\;\;\;$$3 tulips$$\;\;\;\;$$ 13 tulips = 3 white and 13 red tulips
$$\;\;\;\;$$3 tulips$$\;\;\;\;$$ 13 tulips = 3 white and 13 red tulips
$$\;\;\;\;$$3 tulips$$\;\;\;\;$$ 13 tulips = 3 white and 13 red tulips
$$\;\;\;\;$$3 tulips$$\;\;\;\;$$ 13 tulips = 3 white and 13 red tulips
$$\;\;\;\;$$3 tulips$$\;\;\;\;$$ 13 tulips = 3 white and 13 red tulips
$$\;\;\;\;$$3 tulips$$\;\;\;\;$$ 13 tulips = 3 white and 13 red tulips

Kudos [?]: 152 [7], given: 6

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

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29 Oct 2013, 06:28
zeallous wrote:
I don't understand the solution here.

AND

I think its quite common to post official guide questions. Is there a way to search?

All OG13 questions with solutions are here: the-official-guide-quantitative-question-directory-143450.html

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

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04 Jan 2015, 06:42
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Re: What is the greatest number of identical bouquets that can [#permalink]

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07 Jan 2016, 17:20
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).

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

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16 Jun 2017, 04:59
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/what-is-the- ... 67914.html
_________________

Kudos [?]: 129537 [0], given: 12201

Re: What is the greatest number of identical bouquets that can   [#permalink] 16 Jun 2017, 04:59
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