Sets

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
50
[C] 55
[D] 58
[E] 82

rijul007 · Answer

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

subhash.sonu39 · Answer

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

GMATGuruNY · Answer

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

subhash.sonu39 · Answer

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.

Scott@TargetTestPrep · Answer

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

Sets

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER