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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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
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.
20 Jan 2025, 10:25
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AVMachine
I think the fraction required is 2r/2w and not 2r/8x
