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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 [#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, 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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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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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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