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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] New post 18 Mar 2013, 11:43
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87% (05:58) correct 13% (00:32) wrong based on 85 sessions
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, 11:45, edited 1 time in total.
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Re: What is the greatest number of identical bouquets that can [#permalink] New post 18 Mar 2013, 11:54
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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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Re: What is the greatest number of identical bouquets that can [#permalink] New post 18 Mar 2013, 12:04
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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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Re: What is the greatest number of identical bouquets that can [#permalink] New post 06 Jun 2013, 02:00
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Prob Solving - Q112 (official guide - quant) [#permalink] New post 29 Oct 2013, 03:12
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] New post 29 Oct 2013, 05:27
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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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Prob Solving - Q112 (official guide - quant) [#permalink] New post 29 Oct 2013, 05:28
Expert's post
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?


All OG13 questions with solutions are here: the-official-guide-quantitative-question-directory-143450.html

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: Prob Solving - Q112 (official guide - quant)   [#permalink] 29 Oct 2013, 05:28
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