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# In her backyard, Florry grows only yellow roses and white roses. Some

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Manager
Joined: 06 Jul 2011
Posts: 95
In her backyard, Florry grows only yellow roses and white roses. Some  [#permalink]

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06 May 2015, 15:49
5
00:00

Difficulty:

55% (hard)

Question Stats:

67% (02:51) correct 33% (03:04) wrong based on 113 sessions

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In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent of her bushes have only yellow roses?

A) 20
B) 30
C) 50
D) 70
E) 80
Intern
Joined: 09 Oct 2014
Posts: 20
Re: In her backyard, Florry grows only yellow roses and white roses. Some  [#permalink]

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06 May 2015, 18:17
1
let, the number of bushes with only yellow flowers be x
so, number of bushes with only yellow flowers will be 1.5x

if total number of bushes of flowers= T
then total number of bushes with yellow flowers= 0.8T

we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers
so, 0.8T+x=T
x=0.2T
so, 1.5x=0.3T
30% flowers are yellow flowers

OA B
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Manager
Joined: 12 Nov 2014
Posts: 63
Re: In her backyard, Florry grows only yellow roses and white roses. Some  [#permalink]

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06 May 2015, 18:20
See the attachment. This is a overlapping sets problem.
Let the number of only White roses be X.
Then the number of only Yellow roses would be 1.5X (50% greater than X)
Let the number of both yellow and white roses be Y.
So the total number of roses in the bush is X+1.5X + Y
Also we are given the information that 1.5X +Y = 0.8(1.5X+X+Y)
i.e. 0.2Y = 0.5X or Y = 2.5X

And we are asked to find (1.5X / 1.5X+X+Y)*100 which is (1.5X/ 5X)*100 = 30%

Ambarish
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rose.jpg [ 30.97 KiB | Viewed 1932 times ]

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Intern
Joined: 09 Nov 2015
Posts: 32
Re: In her backyard, Florry grows only yellow roses and white roses. Some  [#permalink]

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29 Jan 2018, 00:03
1
Quick and simple method:

Let the total number of rose bushes be 100.
80 bushes have yellow roses so it follows that 20 bushes have only white roses.
Therefore, the number of bushes with only yellow roses is 20x1.5=30.
Ans: B
Re: In her backyard, Florry grows only yellow roses and white roses. Some &nbs [#permalink] 29 Jan 2018, 00:03
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