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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]

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/what-is-the- ... 67914.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Jun 2017, 04:59, edited 2 times in total.
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Re: What is the greatest number of identical bouquets that can [#permalink]

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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]

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New post 18 Mar 2013, 13:04
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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]

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New post 16 Jun 2017, 04:59
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


OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/what-is-the- ... 67914.html
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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   [#permalink] 16 Jun 2017, 04:59
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