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At the end of the day, February 14th, a florist had 120

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At the end of the day, February 14th, a florist had 120 [#permalink] New post 31 Aug 2006, 23:44
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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%
[Reveal] Spoiler: OA

Last edited by GMATT73 on 01 Sep 2006, 06:29, edited 2 times in total.
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 [#permalink] New post 01 Sep 2006, 00:45
E for me.

R W P
L 5x 0 15x
S 5 20 15

20x=80
x=4
5x=20
% = 20/25 = 80
Hence E
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 [#permalink] New post 01 Sep 2006, 00:53
Interesting Q, keep posting these GMATT :-D
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
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 [#permalink] New post 01 Sep 2006, 04:22
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%

Ans (E)
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Re: PS Roses @Kevin: Please help! [#permalink] New post 01 Sep 2006, 06:15
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GMATT73 wrote:
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

20/80= 25% B
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 [#permalink] New post 01 Sep 2006, 06:51
anandsebastin wrote:
So, percentage of long stemmed roses left = (20/25)*100 =80%
Ans (E)


percentage of long stemmed roses left = (20/80)*100 =25% ,
Ans (B)
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Re: PS Roses Solved [#permalink] New post 26 Mar 2011, 05:52
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.
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Re: PS Roses Solved [#permalink] New post 26 Mar 2011, 09:39
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GMATT73 wrote:
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%

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Re: PS Roses Solved [#permalink] New post 26 Mar 2011, 10:57
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I think here the important thing s to first understand that from the Question we get - No of red and short stemmed roses = 5.

second - we know that there no white and long stemmed roses.

Third - 120-40 = 80 are long stemmed and red & pink.

Last - 80 has to be split into two parts that, 5 of one part and 15 of the other are the same in terms of percentage of their respective parts.

So, 5+15 = 20, since the total is 80 , We can solve by 80/20=4.

Hence 5*4 = 20(red roses)
15*4 =60(pink roses)

Now 20/80 * 100 = 25 %

Ans B
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Re: PS Roses Solved [#permalink] New post 27 Mar 2011, 01:28
R + W + P = 120

S + L = 120

1/3 * 120 = 40

Short-Stemmed White = 20

Short-Stemmed Pink = 15

=> Short-Stemmed Red = 5

15/P = 5/R

=> R = P/3

So Total Long Stemmed = 80

And Long Stemmed Red + Long Stemmed Pink = 80

So Long Stemmed Red/Long Stemmed = ?

Total White = 20 (As no Long stemmed white)

=> R + 3R + 20 = 120

=> 4R = 100 and R = 25

Long Stemmed R = 25 - 5 = 20


So Long Stemmed Red/R = 20/80 = 25%

Answer - B
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Re: At the end of the day, February 14th, a florist had 120 [#permalink] New post 07 Sep 2012, 05:24
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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.
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Re: At the end of the day, February 14th, a florist had 120 [#permalink] New post 07 Sep 2012, 06:00
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siddharthasingh wrote:
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}.

Hope it's clear.
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Re: At the end of the day, February 14th, a florist had 120 [#permalink] New post 07 Sep 2012, 06:29
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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?
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Re: At the end of the day, February 14th, a florist had 120 [#permalink] New post 12 Oct 2013, 17:57
I keep averaging 3 min on solving this problem, please advise if there is any shortcuts on solving this.
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Re: At the end of the day, February 14th, a florist had 120 [#permalink] New post 25 Oct 2013, 14:27
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.
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Re: At the end of the day, February 14th, a florist had 120 [#permalink] New post 04 Nov 2013, 09:52
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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Re: At the end of the day, February 14th, a florist had 120 [#permalink] New post 13 Nov 2014, 13:23
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Re: At the end of the day, February 14th, a florist had 120   [#permalink] 13 Nov 2014, 13:23
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