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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]

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New post 18 Mar 2013, 12:43
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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, 12:45, edited 1 time in total.
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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).

Answer: E.
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New post 18 Mar 2013, 13:04
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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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New post 06 Jun 2013, 03:00
Great Explanation wesley +1 kudos
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Prob Solving - Q112 (official guide - quant) [#permalink]

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New post 29 Oct 2013, 04:12
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]

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New post 29 Oct 2013, 06:27
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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.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules 1, 2, 3, 6, and 7. Thank you.

To search please use search box.
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Re: What is the greatest number of identical bouquets that can [#permalink]

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

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New post 09 Feb 2016, 09:56
"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?
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Re: What is the greatest number of identical bouquets that can [#permalink]

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New post 12 Feb 2016, 18:27
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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.

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

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New post 12 Feb 2016, 18:31
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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:
[Reveal] Spoiler:
E


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

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New post 15 Feb 2016, 03:02
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
Re: What is the greatest number of identical bouquets that can   [#permalink] 15 Feb 2016, 03:02
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