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iwantroca
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In a garden, there are flowers of two colors, blue and red. The ratio 19 Feb 2024, 05:38
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95% (hard)

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52% (03:14) correct 48% (03:18) wrong based on 100 sessions

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­In a garden, there are flowers of two colors, blue and red. The ratio of the number of blue roses to the number of red tulips is 3 : 7. The ratio of red roses to the number of blue tulips is 2 : 1. If the ratio of the number of blue flowers to the number of red flowers is 35 : 76, then what is the ratio of the number of roses to the number of tulips?

A. 47 : 51
B. 41 : 43
C. 52 : 59 
D. 59 : 52
E. None of these   ­­­­­
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C
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In a garden, there are flowers of two colors, blue and red. The ratio 19 Feb 2024, 11:01
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iwantroca
­In a garden, there are flowers of two colors, blue and red. The ratio of the number of blue roses to the number of red tulips is 3 : 7. The ratio of red roses to the number of blue tulips is 2 : 1. If the ratio of the number of blue flowers to the number of red flowers is 35 : 76, then what is the ratio of the number of roses to the number of tulips?

A. 47 : 51
B. 41 : 43
C. 52 : 59 
D. None of these   ­­­­
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­Blue rose : Red tulip = 3 : 7 => Blue rose = 3x and Red tulip = 7x
Red rose : Blue tulip = 2 : 1 => Red rose = 2y and Blue tulip = y
Total blue = 3x+y
Total red = 7x+2y
So: (3x+y)/(7x+2y) = 35/76
=> 228x + 76y = 245x + 70y
=> 17x = 6y
=> x/y = 6/17 
=> Say x = 6k and y = 17k
=> Rose : Tulip = (3x+2y) : (7x+y) = (18k+34k) : (42k+17k) = 52 : 59
Answer C
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In a garden, there are flowers of two colors, blue and red. The ratio 20 Feb 2024, 23:06
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@iwantrocaGiven: In a garden, there are flowers of two colors, blue and red. The ratio of the number of blue roses to the number of red tulips is 3 : 7. The ratio of red roses to the number of blue tulips is 2 : 1.

Asked: If the ratio of the number of blue flowers to the number of red flowers is 35 : 76, then what is the ratio of the number of roses to the number of tulips?
Let the number of blue roses & red tulips be 3x & 7x respectively
Let the number of red roses & blue tulips be 2y & y respectively

(3x + y)/(7x+2y) = 35/76
76(3x + y) = 35(7x+2y) 
228x + 76y = 245x + 70y
6y = 17x ; x = 6y/17

The ratio of the number of roses to the number of tulips = (3x + 2y)/(7x+y) = (18y/17 + 2y)/(42y/17 + y) = (52/17)/(59/17) = 52/59

IMO C­
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In a garden, there are flowers of two colors, blue and red. The ratio 04 Mar 2024, 19:02
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iwantroca
­In a garden, there are flowers of two colors, blue and red. The ratio of the number of blue roses to the number of red tulips is 3 : 7. The ratio of red roses to the number of blue tulips is 2 : 1. If the ratio of the number of blue flowers to the number of red flowers is 35 : 76, then what is the ratio of the number of roses to the number of tulips?

A. 47 : 51
B. 41 : 43
C. 52 : 59 
D. 59 : 52
E. None of these   ­­­­­
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­Bunuel, can you please guide me to more questions like these? On ratio and proportion?
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In a garden, there are flowers of two colors, blue and red. The ratio 04 Mar 2024, 23:55
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RenB

iwantroca
­In a garden, there are flowers of two colors, blue and red. The ratio of the number of blue roses to the number of red tulips is 3 : 7. The ratio of red roses to the number of blue tulips is 2 : 1. If the ratio of the number of blue flowers to the number of red flowers is 35 : 76, then what is the ratio of the number of roses to the number of tulips?

A. 47 : 51
B. 41 : 43
C. 52 : 59 
D. 59 : 52
E. None of these   ­­­­­
­Bunuel, can you please guide me to more questions like these? On ratio and proportion?
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­Hi Bunuel

Thanks for the explanation and extra practice questions you posted. I struggle a lot with questions of this type (where something is added or subtracted from another ratio). Is there a post on the theoretical concepts that I can use to learn this? I would like to get my concepts clear before diving into difficult problems of this nature. Thanks a lot in advance![/quote]

3. Fractions, Decimals, Ratios and Proportions



For other topics check Ultimate GMAT Quantitative Megathread

Hope it helps.­
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In a garden, there are flowers of two colors, blue and red. The ratio 09 Nov 2025, 19:15
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iwantroca

In a garden, there are flowers of two colors, blue and red. The ratio of the number of blue roses to the number of red tulips is 3 : 7. The ratio of red roses to the number of blue tulips is 2 : 1.

If the ratio of the number of blue flowers to the number of red flowers is 35 : 76, then what is the ratio of the number of roses to the number of tulips?

Let the number of blue roses and the number of red tulips be 3k & 7k respectively.

Let the number of red roses and the number of blue tulips is be 2m & m respectively

The number of Blue roses = 3k
The number of Blue tulips = m
The number of Blue flowers = 3k + m

The number of Red roses = 2m
The number of Red tulips = 7k
The number of Red flowers = 7k + 2m

The ratio of the number of blue flowers to the number of red flowers is 35 : 76
3k + m : 7k + 3m = 35: 76

35 (7k + 2m) = 76 (3k + m)
245k + 70m = 228k + 76m
17k = 6m
Let k = 6x ; m = 17x

The ratio of the number of roses to the number of tulips = 3k + 2m : 7k + m = 18x + 34x : 42x + 17x = 52 : 59

IMO C
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In a garden, there are flowers of two colors, blue and red. The ratio 09 Nov 2025, 22:02
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I think the question should mention that there are no flower types apart from roses and tulips, for clarity.

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Harsha
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