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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 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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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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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.

Last edited by mh72 on 09 Aug 2016, 20:40, edited 1 time in total.
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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
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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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
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New post 04 Jan 2017, 03:04
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
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New post 19 Mar 2017, 04:04
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... ?
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Hi mesutthefail,

The wording in the parentheses explains how a bouquet is identical with another bouquet as long as the number and type of flowers are the same.

For example:
A bouquet with 1 red flower and 1 white flower is the SAME as a bouquet with 1 white flower and 1 red flower
So RW and WR are the SAME bouquet

Another example:
RRW, RWR and WRR are all the SAME bouquet

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

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New post 20 Mar 2017, 02:28
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.


maximum number of bouquets will be the number, which will divide 21 as well as 91
therefore the number of bouquets = HCF(21,91) = 7
Option E
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New post 28 Mar 2017, 06:01
(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.)

Can anyone please explain the purpose of mentioning this information?
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New post 28 Mar 2017, 07:37
Shiv2016 wrote:
(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.)

Can anyone please explain the purpose of mentioning this information?


This is explained here: https://gmatclub.com/forum/what-is-the- ... l#p1822895
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Re: What is the greatest number of identical bouquets that can [#permalink]

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New post 28 Mar 2017, 10:10
Bunuel wrote:
Shiv2016 wrote:
(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.)

Can anyone please explain the purpose of mentioning this information?


This is explained here: https://gmatclub.com/forum/what-is-the- ... l#p1822895


Thanks for the reply Bunuel. But does this information play any role in finding the GCD or its just an additional information?
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Re: What is the greatest number of identical bouquets that can [#permalink]

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New post 28 Mar 2017, 23:58
hi Bunuel ,,

(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.)

does it mean a bouquet should contain both white and red flowers??
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Re: What is the greatest number of identical bouquets that can [#permalink]

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New post 29 Mar 2017, 00:09
mohshu wrote:
hi Bunuel ,,

(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.)

does it mean a bouquet should contain both white and red flowers??


You cannot have identical bouquets made out of 21 white and 91 red tulips if each of the bouquets does not contain both white and red tulips.

The answer to the question is that we can make 7 identical bouquets made out of 21 white and 91 red tulips, each containing 3 white and 13 red tulips.
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Re: What is the greatest number of identical bouquets that can   [#permalink] 29 Mar 2017, 00:09
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