Cross Pollination

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Cross Pollination

by alivapriyada » Tue Sep 14, 2010 1:42 pm
A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?

22

33

55

77

88
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by goyalsau » Tue Sep 14, 2010 2:13 pm
alivapriyada wrote:A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?

22

33

55

77

88
33 trees are pure Gala.

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by klmehta03 » Tue Sep 14, 2010 6:22 pm
Assume the total number of trees is x
pure fuji trees is y
pure gala tress is z
cross pollinated is 0.1x
so first equation y+0.1x=187....(1)
second equation is y=0.75x....(2)
From 1) and 2) eqn
x=220 ; y=165
total trees y+z+0.1x=220
z= 33.
Hope this helps

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by GMATGuruNY » Tue Sep 14, 2010 7:35 pm
alivapriyada wrote:A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?

22

33

55

77

88
Let c = cross pollinated, f = fuji, g=gala

c+f = 10% + 3/4 = 85%
So g = 15%
So (c+f):g = 85:15 = 17:3
c+f = 187
So 187/g = 17/3
g = (3*187)/17 = 33.

The correct answer is B.
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by alivapriyada » Tue Sep 14, 2010 11:43 pm
@All...thanks a lot!!!
got the doubt cleared.
ans is 33

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by minkathebest » Sat Nov 03, 2012 2:23 pm
I tried doing this using the double matrix method and got stuck until I figured out that there is a hidden constraint here. The Number of Non-Gala trees and Non-Fuji trees is 0. This makes the 33 easily. I did not have that as a zero first in my matrix for this problem and wondered what to do with it when I got 33.