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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

Problem Solving Question: 112 Category:Arithmetic Properties of numbers Page: 76 Difficulty: 600

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Re: What is the greatest number of identical bouquets that can b [#permalink]
24 Feb 2014, 22:55

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Expert's post

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SOLUTION

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

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).

Re: What is the greatest number of identical bouquets that can b [#permalink]
01 Mar 2014, 03:16

Expert's post

SOLUTION

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

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).

Re: What is the greatest number of identical bouquets that can b [#permalink]
21 Apr 2015, 13:06

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Re: What is the greatest number of identical bouquets that can b [#permalink]
21 Apr 2015, 18:44

Expert's post

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.

What is the greatest number of identical bouquets that can b [#permalink]
19 May 2015, 00:56

But is it a right approach to calculate GCF of 21 and 91 (which is 7) and therefore in my opinion also the greatest number of identical buquets? Or just by coincidence the same result? Answers appreciated!

Re: What is the greatest number of identical bouquets that can b [#permalink]
19 May 2015, 22:54

Expert's post

Hi noTh1ng,

Calculating the GCF is one approach to solving this question, although there are others. My approach was based on listing out the possibilities and finding the one that matched all of the information in the prompt; you could also have used the answer choices to your advantage and eliminated the numbers that did not match the info in the prompt.

GMAT questions are always carefully designed (even the wrong answers are carefully chosen), so there are almost never any coincidences on Test Day. Sometimes a subtle Number Property or other pattern occurs in a question, and you don't necessarily need to know the rule or pattern to get the correct answer, but the existence of the pattern is never by accident.

Re: What is the greatest number of identical bouquets that can b [#permalink]
28 May 2015, 03:02

Expert's post

noTh1ng wrote:

But is it a right approach to calculate GCF of 21 and 91 (which is 7) and therefore in my opinion also the greatest number of identical buquets? Or just by coincidence the same result? Answers appreciated!

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