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
50
[C] 55
[D] 58
[E] 82
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dhairya275
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rijul007
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dhairya275 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
50
[C] 55
[D] 58
[E] 82
g = 0
a+b+c+d+e+f = 100
a+d+e = 57
b+e+f = 35
c+d+f = 50
add the three equations:
a+b+c+2(d+e+f) = 142
a+b+c+2(d+e+f) - (a+b+c+d+e+f) = 142-100
d+e+f = 42
42% flowers have exactly 2 colors
Hence, 58% flowers have only one color.
Option D
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subhash.sonu39
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The elements or members of a set can be anything, likely numbers, people, letters of the alphabet, other sets, and so on. Sets are conventionally denoted with capital letters. Sets A and B are equal if and only if they have precisely the same elements.
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dhairya275 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
50
[C] 55
[D] 58
[E] 82
100% = R + G + Y - (RG + RY + GY)
SUBTRACT THE OVERLAP.
In the equation above, when we count all of the red flowers (R), all of the green flowers (G), and all of the yellow flowers (Y), the OVERLAP -- every flower that has exactly TWO colors -- gets counted TWICE.
Thus, we SUBTRACT these flowers (RG + RY + GY) from the total so that they are not double-counted.
Plugging the given percentages into the equation above, we get:
100 = 57 + 35 + 50 - (RG + RY + GY)
RG + RY + GY = 42.
Since 42% of the flowers have exactly two colors, the percentage that have only one color = 58%.
The correct answer is D.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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subhash.sonu39
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Solved perfectly and what I know about set is, Set is a gathering together into a whole of definite, distinct objects of our perception and of our thought, which are called elements of the set. though a set is a well defined collection of objects.
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dhairya275 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
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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