At the end of the day, February 14th, a florist had 120 : GMAT Problem Solving (PS)
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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]

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27 Dec 2005, 12:46
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Question Stats:

63% (06:42) correct 37% (02:56) wrong based on 539 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!
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27 Dec 2005, 13:47
I get E.

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%
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27 Dec 2005, 13:56
believe2 wrote:
I get E.

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).
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27 Dec 2005, 14:12
I also got 25 %.

40 SS
120 LS
20W + 15P + 5 R = 40

also we know that

15/X*100 = 5/80-X*100
X = 60 which is the number of pink roses. so 20 is the number of red roses. 25 percent of LS roses were red.
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27 Dec 2005, 14:29
Well on the second thought

15/(X + 15) = 5/(80 - X + 5) I missed the total flowers. Just counted LS
X = 60

So the answer is again 25.
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At the end of the day, February 14th, a florist had 120 [#permalink]

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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%

Last edited by GMATT73 on 01 Sep 2006, 06:29, edited 2 times in total.
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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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01 Sep 2006, 00:53
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
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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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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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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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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.
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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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Red_White_Pink_Roses_Set.PNG [ 22.75 KiB | Viewed 10581 times ]

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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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27 Mar 2011, 01:28
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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%

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

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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]

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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]

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07 Sep 2012, 06:29
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?
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Re: At the end of the day, February 14th, a florist had 120 [#permalink]

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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]

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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)
Re: At the end of the day, February 14th, a florist had 120   [#permalink] 04 Nov 2013, 09:52

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