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What is the greatest number of identical bouquets that can b [#permalink]
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24 Feb 2014, 23:55
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The Official Guide For GMAT® Quantitative Review, 2ND EditionWhat 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 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
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Re: What is the greatest number of identical bouquets that can b [#permalink]
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24 Feb 2014, 23:55



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Re: What is the greatest number of identical bouquets that can b [#permalink]
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25 Feb 2014, 01:47
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]
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25 Feb 2014, 04:59
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]
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25 Feb 2014, 05:15
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]
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26 Feb 2014, 02:26
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]
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21 Apr 2015, 19:44
Hi All, This question is essentially about primefactorization, 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: GMAT assassins aren't born, they're made, Rich
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What is the greatest number of identical bouquets that can b [#permalink]
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19 May 2015, 01:56
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]
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19 May 2015, 23:54
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. GMAT assassins aren't born, they're made, Rich
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Re: What is the greatest number of identical bouquets that can b [#permalink]
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28 May 2015, 04:02
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! Dear noTh1ngIt is not a coincidence. To understand this, let's assume that we make n identical bouquets, in each of which: Number of white flowers = w Number of red flowers = r Since we are given that no flower is to be left out, we can write: wn = 21 And, rn = 91 That is, w = 21/n And, r = 91/n Now, w and r, being the number of flowers, have to be integers (because we cannot have 2.5 or 3.3 flowers in a bouquet) So, n has to be a number that completely divides 21 as well as 91. But the question asks us to find the greatest possible value of n. That is, the greatest possible number that completely divides 21 as well as 91. What is this number known as? Greatest Common Factor Hope this helped clarify your doubt. Best Regards Japinder
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What is the greatest number of identical bouquets that can be ma [#permalink]
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Updated on: 09 Aug 2016, 20:40
"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.)"
What's to stop you from creating 21 bouquets, each containing 1 white tulip and 1 red tulip, and 1 bouquet containing 70 red tulips? In that scenario, you have 21 identical bouquets.
Originally posted by mh72 on 09 Feb 2016, 09:56.
Last edited by mh72 on 09 Aug 2016, 20:40, edited 1 time in total.



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Re: What is the greatest number of identical bouquets that can [#permalink]
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12 Feb 2016, 18:27
mh72 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.)"
What's to stop you from creating 21 bouquets, each containing 1 white tulip and 1 red tulip, and 1 bouquet containing 70 red tulips? In that scenario, you have 21 identical bouquets. Basically, my question is this: Is the question stem necessarily read to require that each bouquet made be identical? Hi mh72, In your 'scenario', you've left out 70 red tulips from the 21 bouquets that you made  but the prompt says that NO flowers are to be left out. Thus, your solution does not match the specific restrictions that the prompt gave you to work with. GMAT assassins aren't born, they're made, Rich
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Re: What is the greatest number of identical bouquets that can [#permalink]
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12 Feb 2016, 18:31
Hi All, This question is essentially about primefactorization, 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: GMAT assassins aren't born, they're made, Rich
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Re: What is the greatest number of identical bouquets that can [#permalink]
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15 Feb 2016, 03:02
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. This is a case of a question u don't understand but ended up getting it right. only 7 is a factor of 21 and 91



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What is the greatest number of identical bouquets that can b [#permalink]
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25 Nov 2016, 16:18
Hey chetan2uI am having trouble understanding this Question. I have seen all the solutions above,but none of them is making sense to me. You mind solving this one. Here is what i did Given => 21 white and 92 red tulips So to make identical bouquets we can make the arrangement as follows => 1 each for 21 bouquets in which 2 each for 10 bouquets and and one in the last one. And we can continue this way to make infinite arrangements. I understand the use the word "identical" but if w give 2 each => we can make 10 identical bouquets and one bouquets with leftover flowers right ? What i am missing here? It feels like a pretty difficult Question to me. Regards Stone Cold
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Re: What is the greatest number of identical bouquets that can b [#permalink]
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26 Nov 2016, 01:20
Bunuel 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 Greatest no of Identical Bouqets of 21 white tulips and 91 red tulips is HCF of 21& 91 = 7 Now, Check... Each Boquet must have 3 ( ie, 21/7) White tulips and 13 ( ie, 91/7) red tulips , so all tulips are utilized.. Hence, correct answer will be (E)stonecold hope this helps...
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Re: What is the greatest number of identical bouquets that can b [#permalink]
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26 Nov 2016, 08:07
stonecold wrote: Hey chetan2uI am having trouble understanding this Question. I have seen all the solutions above,but none of them is making sense to me. You mind solving this one. Here is what i did Given => 21 white and 92 red tulips So to make identical bouquets we can make the arrangement as follows => 1 each for 21 bouquets in which 2 each for 10 bouquets and and one in the last one. And we can continue this way to make infinite arrangements. I understand the use the word "identical" but if w give 2 each => we can make 10 identical bouquets and one bouquets with leftover flowers right ? What i am missing here? It feels like a pretty difficult Question to me. Regards Stone Cold Hi, What the Q means is that each bouquet is identical so each should have same number of white,w , and same number of red, say r.. Now w has to be a factor of 21 , since if you take 2 the last bouquet will have only 1, thus all will not be identical. Only w as 1, 3, 7 or 21 will fit in.. Similarly r should be a factor of 91, so 1, 7,13 or 91.. Example each has7,7..., so 91/7=13 bouquets of 7 red, OR each has 13, so 7 bouquets of 7 each... Now the MAIN point comes out is both white and red have to be divided in same number of bouquets ... So only identical are 1and 7.. So two ways bouquets can be identical 1) All 21 and 91 together as 1 bouquet 2) We distribute 21 in 7 bouquets and 91 red too in 7 bouquets So we will have 7 identical bouquets, each bouquet having 21/7=3 white and 91/7=13 red tulips.. So ans 7
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Re: What is the greatest number of identical bouquets that can [#permalink]
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04 Jan 2017, 03:04
Here's my take. Divide 91 red tulips by 21 white ones. We get quotient of 4 and a remainder of 6 (these 6 are the white tulips) and 4 is the no. of identical bouquets. Now put the 6 white ones in each of the 2 bouquets (one white in first and one in second and so on). Thus we get 4+3 = 7
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Re: What is the greatest number of identical bouquets that can [#permalink]
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19 Mar 2017, 04:04
The part in paranthesis really got me confused here, and i could not understand anything written there. I get the part outside the paranthesis, but then... ?




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