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What is the greatest number of identical bouquets that can b

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

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New post 26 Nov 2016, 08:07
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
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Re: What is the greatest number of identical bouquets that can [#permalink]

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

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New post 19 Mar 2017, 11:04
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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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Re: What is the greatest number of identical bouquets that can [#permalink]

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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 b [#permalink]

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New post 23 Aug 2017, 15:12
The conditional in this problem (i.e.) "if no flowers are to be left out" is the key to solving; you should interpret this conditional statement as "I need to find the Greatest common divisor among Red and White Tulips.

1. Red Tulips = 91 ; White Tulips = 21
2. To find the Greatest Common Divisor, the quickest method is prime factorization.
3. So, with prime factorization, red tulips = 91 = 7 x 13. White tulips = 21 = 3 x 7.
4. The divisor common in both (7 x 13) and (3 x 7) is 7.

Therefore, the answer to this problem is (E) 7

This problem is on both the 2013 and 2017 GMAT OG.

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Re: What is the greatest number of identical bouquets that can b   [#permalink] 23 Aug 2017, 15:12

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