Sets

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dhairya275: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Mon Jun 18, 2012 11:53 am; Thanked: 2 times

by dhairya275 » Sun Sep 09, 2012 6:34 am

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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Source: Beat The GMAT — Problem Solving | Sun Sep 09, 2012 6:34 am

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Sun Sep 09, 2012 8:30 am

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: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Aug 12, 2012 9:30 pmFollowed by: 1 member; Thanked: 2 times

by subhash.sonu39 » Sat Sep 15, 2012 12:45 am

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.
Linear Equations

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Sep 15, 2012 3:20 am

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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subhash.sonu39: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Sun Aug 12, 2012 9:30 pmFollowed by: 1 member; Thanked: 2 times

by subhash.sonu39 » Thu Sep 20, 2012 8:54 pm

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Dec 13, 2017 5:19 pm

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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