Bouquets are to be made using white tulips and red tulips, and the rat : Problem Solving (PS)

Bunuel

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16 Jun 2017, 04:54

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Bunuel

AbdurRakib

Bouquets are to be made using white tulips and red tulips, and the ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet. If there are 15 white tulips and 85 red tulips available for the bouquets, what is the greatest number of bouquets that can be made using all the tulips available?

A. 3
B. 5
C. 8
D. 10
E. 13

Since we should use all the tulips available, then the number of bouquets must be a factor of both 15 and 85. For example, we cannot have 2 bouquets since we cannot divide 15 white tulips into 2 bouquets without one tulip left over.

The greatest common factor of 15 and 85 is 5.

Answer: B.

Similar question to practice: https://gmatclub.com/forum/what-is-the- ... 67914.html

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02 Jul 2017, 06:40

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AbdurRakib

Bouquets are to be made using white tulips and red tulips, and the ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet. If there are 15 white tulips and 85 red tulips available for the bouquets, what is the greatest number of bouquets that can be made using all the tulips available?

A. 3
B. 5
C. 8
D. 10
E. 13

Let's use some prime factorization...

We have 15 white tulips and 85 red tulips
15 = (3)(5)
85 = (5)(17)

So, for the white tulips, we can create 5 groups of 3 flowers
So, for the red tulips, we can create 5 groups of 17 flowers

This means we can create 5 BOUQUETS in which each bouquet has 3 red tulips and 17 white tulips
In other words, the ratio of red tulips to white tulips is the same for each bouquet (3 : 17).

Answer:

Show Spoiler

B

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Solution:

Step 1: 15 white tulips and 85 red tulips are available for bouquets. The bouquets must be made from these tulips using the same ratio of white tulips and red tulips from the 15 white tulips and 85 red tulips provided.

Step 2: Since all the tulips available must be used without any left over, then the number of bouquets possible must be a factor of the available tulips. Hence, the highest possible common factor of 15 white tulips and 85 red tulips is obtained as follows:

15 = 3 x 5
85 = 5 x 17

5 is common to both 15 and 85. Therefore, the greatest number of bouquets that can be made is 5 and the answer is

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B

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Video Solution from Quant Reasoning:

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23 Nov 2020, 12:40

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CONCEPT:HCF of Numbers (Highest common factor)

Let us say the number of bouquets to be made =x.
x has to be a whole number. This implies x has to be a factor of both 15 and 85.
x also has to the greatest such number.

Hence, we are looking for the HCF(5,85)that is 5.
Thus, number of bouquets or "x" =5. (B)

Hope this helps. Keep studying.

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I understand prime factoring but I don't understand why 15 bouquets can't be made with 1 white rose in each and 5 red.

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26 Jan 2021, 17:19

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raekay18

I understand prime factoring but I don't understand why 15 bouquets can't be made with 1 white rose in each and 5 red.

15 bouquets with 5 red roses in each bouquet would require 75 red roses.
The question tells us that we have a 85 red roses and that we must use all of them

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AbdurRakib

Bouquets are to be made using white tulips and red tulips, and the ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet. If there are 15 white tulips and 85 red tulips available for the bouquets, what is the greatest number of bouquets that can be made using all the tulips available?

A. 3
B. 5
C. 8
D. 10
E. 13

Answer: Option B

Video solution by GMATinsight

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Quote:

The question clearly states that each bouquet must have the same ratio of white to red tulips, but it doesn't say that each bouquet must have the same number of white tulips in it. Therefore, why does the author say that each bouquet must have the same number of white tulips in it? I'm guessing the key lies in the fact that all of the tulips have to be used.
My question: How does the fact that all tulips have to be used lead to the corollary that each bouquet has to have the same number of white tulips?
The only stipulation in the question is that each bouquet has to have the same RATIO OF WHITE TO RED TULIPS.

I have the same question as the one previously mentioned. The question only says the "ratio of white to red tulips" should be the same in each bouquet, but never says the number of tulips must be the same in each bouquet. Taking one example bouquet A has 2 white and 10 red tulips, so the ratio is 1:5; bouquet B has 4 white and 20 tulips, so the ratio is also 1:5. Why all solutions in the thread default to the same number of white/red tulips in each bouquet？

Need help, thanks in advance.

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16 Jun 2022, 00:35

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Bunuel

Bouquets are to be made using white tulips and red tulips, and the ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet

the ration should be 1 :1 how can assume as 3:17?

Bunuel

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16 Jun 2022, 01:39

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romasharma1998

Bunuel

Bouquets are to be made using white tulips and red tulips, and the ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet

the ration should be 1 :1 how can assume as 3:17?

"..the ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet"

The above means that the RATIO of white to red tulips in EACH bouquet must be the same, say x:y in the first, second, ...

Hope it's clear.

Bunuel

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16 Jun 2022, 01:56

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AcceleratorCC

Quote:

The question clearly states that each bouquet must have the same ratio of white to red tulips, but it doesn't say that each bouquet must have the same number of white tulips in it. Therefore, why does the author say that each bouquet must have the same number of white tulips in it? I'm guessing the key lies in the fact that all of the tulips have to be used.
My question: How does the fact that all tulips have to be used lead to the corollary that each bouquet has to have the same number of white tulips?
The only stipulation in the question is that each bouquet has to have the same RATIO OF WHITE TO RED TULIPS.

I have the same question as the one previously mentioned. The question only says the "ratio of white to red tulips" should be the same in each bouquet, but never says the number of tulips must be the same in each bouquet. Taking one example bouquet A has 2 white and 10 red tulips, so the ratio is 1:5; bouquet B has 4 white and 20 tulips, so the ratio is also 1:5. Why all solutions in the thread default to the same number of white/red tulips in each bouquet？

Need help, thanks in advance.

If you increase the number of tulips in one (or more) of the bouquets and keep the ratio (3:17), so if you put say 6 white and 34 red tulips in a bouquet, then by doing so (by increasing the number of flowers in a bouquet) you are decreasing the number of bouquets that can be made with 15 white tulips and 85 red tulips. But notice that we need "... the [i]greatest number of bouquets that can be made using all the tulips available"[/i] so we should put the lowest possible number of flowers in each bouquet to increase the number of bouquets.

Hope it's clear.

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Why can't it be 15 bouquets? 1 white tulip + 7 red tulips.

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19 Jan 2023, 23:51

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jackwarner

Why can't it be 15 bouquets? 1 white tulip + 7 red tulips.

Hi jackwarner
Thanks for your query.

Please observe that we have a total of 15 white tulips and 85 red tulips to make bouquets from.

Considering these total numbers, let’s see if it’s even possible to make 15 bouquets, each with 1 white tulip and 7 red tulips:

Total white tulips needed in 15 bouquets = 1 × 15 = 15
Total red tulips needed in 15 bouquets = 7 × 15 = 105
- But that is not possible! We only had 85 red tulips in total.

Remember that we cannot use more than what is available to us. Strictly follow all information given in a question! 😊

If you still have any confusion about the full solution, please feel free to ask!

Hope this helps!

Best,
Aditi Gupta
Quant expert, e-GMAT

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Updated on: 26 Jun 2024, 13:01

Originally posted by Kawal1986 on 26 Jun 2024, 12:19.
Last edited by Kawal1986 on 26 Jun 2024, 13:01, edited 1 time in total.

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What if the no of red tulips were 75?

In that case,
We could have 1W and 5R in 12 jars
And 3W and 15R in 1 har

Total jars = 13

And the ratio W:R is the same in all the jars.

In all the jars, the ratio of W:R is 1:5.

However, the number of tulips is not equal in all the jars. Yet, all the conditions mentioned in the question are met.

So in the first place, in the original question with 85 R tulips, how can we start by assuming that the no of tulips would be equal in all the jars?

Posted from my mobile device

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26 Jun 2024, 12:55

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Kawal1986

What if the no of red tulips were 75?

In that case,
We could have 1W and 5R in 12 jars
And 3W and 15R in 1 har

Total jars = 13

And the ratio W:R is the same in all the jars.

In this case, the number of tulips is not equal in all the jars. However, all the conditions mentioned in the question are met.

So in the first place, in the original question with 85 R tulips, how can we start by assuming that the no of tulips would be equal in all the jars?

Posted from my mobile device

"..the ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet"

The above means that the RATIO of white to red tulips in EACH bouquet must be the same, say x:y in the first, second, ...

Hope it's clear.

Kawal1986

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26 Jun 2024, 13:03

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Bunuel

Kawal1986

What if the no of red tulips were 75?

In that case,
We could have 1W and 5R in 12 jars
And 3W and 15R in 1 har

Total jars = 13

And the ratio W:R is the same in all the jars.

In this case, the number of tulips is not equal in all the jars. However, all the conditions mentioned in the question are met.

So in the first place, in the original question with 85 R tulips, how can we start by assuming that the no of tulips would be equal in all the jars?

Posted from my mobile device

"..the ratio of the number of white tulips to the number of red tulips is to be the same in each bouquet"

The above means that the RATIO of white to red tulips in EACH bouquet must be the same, say x:y in the first, second, ...

Hope it's clear.

In the example that I have taken, the ratio of W:R is the same in all the jars. 1:5.

Bouquets are to be made using white tulips and red tulips, and the rat

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