A garden has only red, green and yellow flowers

Question

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

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!

niks18 · Accepted Answer

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

ScottTargetTestPrep · Answer

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

ashikaverma13 · Answer

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!

apurva908 · Answer

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

StressTest · Answer

can you please explain why you multiply the "percent of flowers with all 3 colors" by 2 in your first equation?

ScottTargetTestPrep · Answer

Because the circle representing “percent of flowers with all 3 colors” in the Venn Diagram overlaps 3 times. By subtracting out two of those “overlaps” we are left with the actual value.

TheMongoose · Answer

Assume T=100
Also note that N=0

T-N= A+B+C - (exactly 2) - 2(all 3)

A - 57
B - 35
C - 50
Exactly 2 - X
All 3 - 0 {Given}

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

100 = 142 - X

X = 42

But we are not done yet!

So there are exactly 42 flowers that have 2 colours.

We need flowers that have only one colour 
For that

flowers that have exactly one colour = (Total flowers) - (flowers that have exactly two colours)

=> 100-42 = 58

So 58 is your answer

OA : D

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A garden has only red, green and yellow flowers

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