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A garden has only red, green and yellow flowers

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A garden has only red, green and yellow flowers  [#permalink]

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New post 24 Apr 2017, 03:25
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  25% (medium)

Question Stats:

77% (01:37) correct 23% (01:17) wrong based on 99 sessions

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A garden has only red, green and yellow flowers, 57% of the flowers have red colour, 35% have green colour and 50% have yellow colour. If no flower has all three colors, what percentage of the flowers has only one colour?

A. 32
B. 50
C. 55
D. 58
E. 82

Can someone please explain how to approach these kinds of problems? I am at a loss when especially 'at least one, two' category questions arise. Kindly suggest some reasoning or method for these questions along with more questions on the same line. thanks!

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Re: A garden has only red, green and yellow flowers  [#permalink]

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New post Updated on: 28 Apr 2017, 10:12
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ashikaverma13 wrote:
A garden has only red, green and yellow flowers, 57% of the flowers have red colour, 35% have green colour and 50% have yellow colour. If no flower has all three colors, what percentage of the flowers has only one colour?

A. 32
B. 50
C. 55
D. 58
E. 82

Can someone please explain how to approach these kinds of problems? I am at a loss when especially 'at least one, two' category questions arise. Kindly suggest some reasoning or method for these questions along with more questions on the same line. thanks!


Let the total number of flowers be 100. Let number of red and green be "x", number of green and yellow be "Z" and number of red and yellow be "y" (refer the venn diagram). Also number of flowers with all three combinations will be 0 in this case
Now, only red = 57-(x+y)
only green = 35-(x+z)
only yellow = 50-(y+z)
Thus, 57-(x+y)+35-(x+z)+50-(y+z) + x+y+z = 100
or, x+y+z = 42. Hence total number of flowers that have two colours are 42.
So total number of flowers that have only one colour = 100-42 = 58
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Originally posted by niks18 on 24 Apr 2017, 03:49.
Last edited by niks18 on 28 Apr 2017, 10:12, edited 1 time in total.
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Re: A garden has only red, green and yellow flowers  [#permalink]

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New post 24 Apr 2017, 10:39
niks18 wrote:
ashikaverma13 wrote:
A garden has only red, green and yellow flowers, 57% of the flowers have red colour, 35% have green colour and 50% have yellow colour. If no flower has all three colors, what percentage of the flowers has only one colour?

A. 32
B. 50
C. 55
D. 58
E. 82

Can someone please explain how to approach these kinds of problems? I am at a loss when especially 'at least one, two' category questions arise. Kindly suggest some reasoning or method for these questions along with more questions on the same line. thanks!


Let the total number of flowers be 100. Let number of red and green be "x" and number of green and yellow be "y" (refer the venn diagram)
Now, only red = 57-x
only green = 35-(x+y)
only yellow = 50-y
Thus, 57-x+35-(x+y)+50-y + x+y = 100
or, x+y = 42. Hence total number of flowers that have two colours are 42.
So total number of flowers that have only one colour = 100-42 = 58


Hey, thanks for the explanation. I was making the mistake of trying to subtract 142-100 considering the combined ones must be taking the total more than 100. It is clear now. Thanks!
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Re: A garden has only red, green and yellow flowers  [#permalink]

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New post 27 Apr 2017, 17:14
2
1
ashikaverma13 wrote:
A garden has only red, green and yellow flowers, 57% of the flowers have red colour, 35% have green colour and 50% have yellow colour. If no flower has all three colors, what percentage of the flowers has only one colour?

A. 32
B. 50
C. 55
D. 58
E. 82


We can use the following formula:

100% = percent of red flowers + percent of green flowers + percent of yellow flowers - percent of flowers with 2 colors - 2(percent of flowers with all 3 colors) + percent of flowers with neither color.

We are given that a garden has only red, green and yellow flowers, 57% of the flowers have red color, 35% have green color, 50% have yellow color, and no flower has all three colors. Thus:

100 = 57 + 35 + 50 - D - 2(0) + 0

100 = 142 - D

D = 42

We can use one final equation:

100% = percent of flowers with 1 color + percent of flowers with 2 colors + percent of flowers with 3 colors + percent of flowers with 0 colors

100 = x + 42 + 0 + 0

x = 58

58% of the flowers have only one color.

Answer: D
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Re: A garden has only red, green and yellow flowers  [#permalink]

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New post 16 Jun 2018, 22:24
S=57+35+50=142;X=100; III=0
S-X=42=II + 2 III
II=42
S=I +2 II + 3III
142= I + 2X42
I=58
Re: A garden has only red, green and yellow flowers &nbs [#permalink] 16 Jun 2018, 22:24
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