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What is the greatest number of identical bouquets that can b

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What is the greatest number of identical bouquets that can b [#permalink] New post 24 Feb 2014, 22:55
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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] New post 24 Feb 2014, 22:55
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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).

Answer: E.
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Re: What is the greatest number of identical bouquets that can b [#permalink] New post 25 Feb 2014, 00:47
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Inorder to find the greatest no of identical bouquets we have to find out the Greatest common divisor of 21 and 91

Prime Factors of 21 - 7x3
Prime Factors of 91 - 7x13

The greatest common factor is 7. Hence the maximum no of identical bouquets that can be made is 7. Answer - Option (E)
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Re: What is the greatest number of identical bouquets that can b [#permalink] New post 25 Feb 2014, 03:59
Only 7 is divisible with 21 and 91, So, that should be the answer..

Is this the right way to solve?
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Re: What is the greatest number of identical bouquets that can b [#permalink] New post 25 Feb 2014, 04:09
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Mountain14 wrote:
Only 7 is divisible with 21 and 91, So, that should be the answer..

Is this the right way to solve?


7 is NOT divisible by neither 21 nor by 91. 7 is a factor of both 21 and 91.

P.S. Solutions will be published on weekend.
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Re: What is the greatest number of identical bouquets that can b [#permalink] New post 25 Feb 2014, 04:15
Bunuel wrote:
Mountain14 wrote:
Only 7 is divisible with 21 and 91, So, that should be the answer..

Is this the right way to solve?


7 is NOT divisible by neither 21 nor by 91. 7 is a factor of both 21 and 91.

P.S. Solutions will be published on weekend.


Oops.!.. Ya My bad...

Thanks Bunuel..

Will wait for solutions...
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Re: What is the greatest number of identical bouquets that can b [#permalink] New post 26 Feb 2014, 01:26
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Option E.
21=7*3
91=7*13
If we have 7 bouquets,each will have 3 white tulips and 13 red tulips.So they will be identical.
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Re: What is the greatest number of identical bouquets that can b [#permalink] New post 01 Mar 2014, 03:16
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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).

Answer: E.
_________________

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.


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Re: What is the greatest number of identical bouquets that can b [#permalink] New post 21 Apr 2015, 13:06
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Re: What is the greatest number of identical bouquets that can b [#permalink] New post 21 Apr 2015, 18:44
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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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What is the greatest number of identical bouquets that can b [#permalink] New post 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!
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Re: What is the greatest number of identical bouquets that can b [#permalink] New post 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.

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