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# What is the greatest number of identical bouquets that can

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What is the greatest number of identical bouquets that can [#permalink]  18 Mar 2013, 11:43
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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

Please show me how to solve.
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Mar 2013, 11:45, edited 1 time in total.
RENAMED THE TOPIC.
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Re: What is the greatest number of identical bouquets that can [#permalink]  18 Mar 2013, 11:54
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Expert's post
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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Re: What is the greatest number of identical bouquets that can [#permalink]  18 Mar 2013, 12:04
4
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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
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Re: What is the greatest number of identical bouquets that can [#permalink]  06 Jun 2013, 02:00
Great Explanation wesley +1 kudos
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Prob Solving - Q112 (official guide - quant) [#permalink]  29 Oct 2013, 03:12
I don't understand the solution here.

AND

I think its quite common to post official guide questions. Is there a way to search?
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Re: Prob Solving - Q112 (official guide - quant) [#permalink]  29 Oct 2013, 05:27
Expert's post
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?

Merging similar topics. Please refer to the solutions above.

To search please use search box.
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Kudos [?]: 57548 [0], given: 8818

Re: Prob Solving - Q112 (official guide - quant) [#permalink]  29 Oct 2013, 05:28
Expert's post
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]  04 Jan 2015, 05:42
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Re: What is the greatest number of identical bouquets that can   [#permalink] 04 Jan 2015, 05:42
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