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At the end of the day, February 14th, a florist had 120 [#permalink]

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27 Dec 2005, 13:46

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00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

62% (04:59) correct
38% (02:44) wrong based on 702 sessions

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At the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 20 of which were white and 15 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red?

(A) 20%
(B) 25%
(C) 50%
(D) 75%
(E) 80%

this is from the Manhattan GMAT email I get which attempts to solicit my business. I am posting because I believe I have solved it, but cannot find the answer on their website. Please post your answer and method!

number of short stemmed roses=1/3*120=40 Number of short stemmed red roses=40 - (15 + 20)

given: [ no. of short stemmed red roses/ no. of red roses ] = [no. of short stemmed pink roses/ no. of pink roses]

let : no. of long stemmed red roses= y

=> 5 / ( 5+y) = 15 / (15 + (80-y)) => y=20

so % of long stem red roses= 20 / (20+5)= 80%

I think you found the wrong percentage here.
You need to find the percentage of long stemmed red roses out of ALL long stemmed roses. (you found the percent of long stemmed Red roses out of all RED roses).

I get B - 25%

I should also add that I found using a table and filling in the blanks made this question super easy (or so it appears).

At the end of the day, February 14th, a florist had 120 [#permalink]

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01 Sep 2006, 00:44

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At the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 20 of which were white and 15 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red?

(A) 20% (B) 25% (C) 50% (D) 75% (E) 80%

Last edited by GMATT73 on 01 Sep 2006, 07:29, edited 2 times in total.

Interesting Q, keep posting these GMATT
IMO it should be like this
short-stemmed-40
of these 20 white,15-pink, 5 red

Long-stemmed-80

From second part-15/p=5/r or r=3p, and p+r=80 then r=20, p=60
The required percentage is 15/80*100 or 18,75%
I must be wrong....it is not among the ans

This may not be the best way to do it, but here's how I did it:
Given: 5/x = 15/y, where 5, x and 15, y are the numbers of short stemmed and total number of red and pink roses respectively.
But,
x+y=100, since there are no long stemmed whites.
Solving,
5/x=15/(100-x)
100-x = 3x
x=25
Verifying
5/25=15/75 -------> CORRECT.
So, percentage of long stemmed roses left = (20/25)*100 =80%

At the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 20 of which were white and 15 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red?

(A) 20% (B) 25% (C) 50% (D) 75% (E) 80%

If there are 120 roses, we see that 20 are white (20 white-short but none white-long), so 100 are either red or pink

Let r and 100-r be the number of red and pink roses respectively. 5 of the red roses and 15 of the pink roses are short, so the number of long reds and long pinks are r-5 and 85-r respectively.

The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed

So, (85-r)/(100-r)=(r-5)/r =>r=25.

Thus there are a total of 20+60=80 long roses, 20 of which are red

if there are 120 roses, we see that 20 are white (20 white-short but none white-long), so 100 are either red or pink

Let r and 100-r be the number of red and pink roses respectively. 5 of the red roses and 15 of the pink roses are short, so the number of long reds and long pinks are r-5 and 85-r respectively.

The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed

So, (85-r)/(100-r)=(r-5)/r =>r=25.

Thus there are a total of 20+60=80 long roses, 20 of which are red

20/80= 25% B --------------------------------------------------------------------------- @Kevincan: If i am not mistaken this solution is still controversial: (85-r)/(100-r)=(r-5)/r =>r=25.>>>>>This indicates that the ratio of long stemmed pink roses is equal to long stemmed red roses which is not so. Further, we need to find out the %age of long stemmed roses only and not the %age of roses. Pls resolve the paradox.
_________________

At the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 20 of which were white and 15 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red?

(A) 20% (B) 25% (C) 50% (D) 75% (E) 80%

Attachments

Red_White_Pink_Roses_Set.PNG [ 22.75 KiB | Viewed 13443 times ]

Re: At the end of the day, February 14th, a florist had 120 [#permalink]

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07 Sep 2012, 06:24

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Don't you guys feel that there is some problem with the language of the problem. Percentage of pink roses that were short stemmed means 15/120, in fact that's what I have learnt from SC. I agree with the solution that fluke gave and this had been my approach when I was struck by the language of the question. Please correct me if I am wrong.
_________________

Don't you guys feel that there is some problem with the language of the problem. Percentage of pink roses that were short stemmed means 15/120, in fact that's what I have learnt from SC. I agree with the solution that fluke gave and this had been my approach when I was struck by the language of the question. Please correct me if I am wrong.

"The percentage of pink roses that were short-stemmed ..." so the percentage is {short-stemmed pink}/{total pink}.

Re: At the end of the day, February 14th, a florist had 120 [#permalink]

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07 Sep 2012, 07:29

Can't this be -> percentage of pink roses that are short stemmed. And if it goes this way then why can't the solution be 15/120. Bunuel doesn't this question sound ambiguous to you?
_________________

Re: At the end of the day, February 14th, a florist had 120 [#permalink]

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25 Oct 2013, 15:27

haotian87 wrote:

I keep averaging 3 min on solving this problem, please advise if there is any shortcuts on solving this.

This is a pretty calculation intensive problem. 3 min is below the average for the people who solved this correctly as per the timer results above; so you are doing better than the average.

Re: At the end of the day, February 14th, a florist had 120 [#permalink]

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04 Nov 2013, 10:52

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avohden wrote:

haotian87 wrote:

I keep averaging 3 min on solving this problem, please advise if there is any shortcuts on solving this.

This is a pretty calculation intensive problem. 3 min is below the average for the people who solved this correctly as per the timer results above; so you are doing better than the average.

I went at it like this:

5 were red and short, 15 were pink and short and 40 roses were short so 80 roses were long. if we take 5:15 we will get 1:3, so because we know that there are no long white, we can take the 80 long, and split them into 4 parts. red will be one part (20) and pink will be 3 part (60)

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