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A flower bouquet has roses and tulips only and each of them is in two color variants, i.e. white and yellow. If the number of yellow-colored flowers is double the number of white-colored flowers for both roses and tulips. What fraction of the yellow-colored flowers in the bouquet are roses?
(1) In the bouquet, the ratio of the number of roses to the number of tulips is 3:5.
(2) In the bouquet, 20 roses are yellow-colored.
(1) In the bouquet, the ratio of the number of roses to the number of tulips is 3:5.
(2) In the bouquet, 20 roses are yellow-colored.
Updated on: 20 Jan 2025, 07:45
Originally posted by Whoisdmx15 on 20 Jan 2025, 02:53.
Last edited by Whoisdmx15 on 20 Jan 2025, 07:45, edited 1 time in total.
Last edited by Whoisdmx15 on 20 Jan 2025, 07:45, edited 1 time in total.
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A flower bouquet has roses and tulips only and each of them is in two color variants, i.e. white and yellow. If the number of yellow-colored flowers is double the number of white-colored flowers for both roses and tulips. What fraction of the yellow-colored flowers in the bouquet are roses?
(1) In the bouquet, the ratio of the number of roses to the number of tulips is 3:5.
Given the nature of 2X 2 Variables, we can solve it using a Matrix:
We have been given :
We are also given that for both flowers, yellows are double that of red.
Therefore Yellow= 2/3of Flower
Hence:
Hence the required fraction is \(\frac{(1\4) }{ (2\3)})\)=\(\frac{3}{8}\)
Hence Sufficient
(2) In the bouquet, 20 roses are yellow-colored.
As doe not tell us about the distribution amongst Roses and Tulips, we cannot determineany other parameter.
Hence insufficient.
IMO Ans A
(1) In the bouquet, the ratio of the number of roses to the number of tulips is 3:5.
Given the nature of 2X 2 Variables, we can solve it using a Matrix:
We have been given :
| Roses | Tulips | ||
| White | |||
| Yellow | |||
| \((\frac{3}{5})*T\) | \((\frac{2}{5})*T\) | Total=T |
We are also given that for both flowers, yellows are double that of red.
Therefore Yellow= 2/3of Flower
Hence:
| Roses | Tulips | ||
| White | \(\frac{1}{8}*T\) | \(\frac{5}{24}*T\) | \(\frac{1}{3}*T\) |
| Yellow | \(\frac{1}{4}*T\) | \(\frac{5}{12}*T\) | \(\frac{2}{3}*T\) |
| \(\frac{3}{5}*T\) | \(\frac{2}{5}*T\) | Total=T |
Hence the required fraction is \(\frac{(1\4) }{ (2\3)})\)=\(\frac{3}{8}\)
Hence Sufficient
(2) In the bouquet, 20 roses are yellow-colored.
As doe not tell us about the distribution amongst Roses and Tulips, we cannot determineany other parameter.
Hence insufficient.
IMO Ans A
| W | Y | ||
| Ro | r | 2r | |
| Tu | t | 2t | |
| w | 2w |
1.
| W | Y | ||
| Ro | r | 2r | 3x |
| Tu | t | 2t | 5x |
| w | 2w | 8x |
3r=3x; r=x
3t=5x; t=5x/3
2w = 2r+2r = 2x+10x/3
Required Fraction = 2r/2w; Sufficient.
2.20 roses are yellow colored.
| W | Y | ||
| Ro | r | 2r | |
| Tu | t | 2t | |
| w | 2w |
2r=20; 3r=30;
Still, we don't know 3t.
Not sufficient.
