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A farmer has an apple orchard consisting of Fuji and Gala

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Director
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A farmer has an apple orchard consisting of Fuji and Gala [#permalink] New post 16 Nov 2007, 06:26
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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

Solution :

F = Fuji
G = Gala
x = Total no. of trees

x/10 - pollinate


F + x/10 = 187
F = 3x/4 - Pure Figi
3x/4 + x/10 = 187

30x + 4x/40 = 187 * 40
x = 187 * 40 /17 = 220

3/4 * 220 = 54 * 3 = 165 - 187 = 22. --- I'm getting A

Any more takers ??
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Manager
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Re: PS - MGMT [#permalink] New post 16 Nov 2007, 07:09
alimad 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

Solution :

F = Fuji
G = Gala
x = Total no. of trees

x/10 - pollinate


F + x/10 = 187
F = 3x/4 - Pure Figi
3x/4 + x/10 = 187

30x + 4x/40 = 187 * 40
x = 187 * 40 /17 = 220

3/4 * 220 = 54 * 3 = 165 - 187 = 22. --- I'm getting A

Any more takers ??


If the number of pure fuji + number of cross pollinated trees = 187 and the total number of trees = 220. Then isn't the number of pure gala trees = total number of trees - total number of non-gala trees = 220 - 187 = 33 ? Or am i missing something here?
Manager
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Re: PS - MGMT [#permalink] New post 16 Nov 2007, 07:17
alimad 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

Solution :

F = Fuji
G = Gala
x = Total no. of trees

x/10 - pollinate


F + x/10 = 187
F = 3x/4 - Pure Figi
3x/4 + x/10 = 187

30x + 4x/40 = 187 * 40
x = 187 * 40 /17 = 220

3/4 * 220 = 54 * 3 = 165 - 187 = 22. --- I'm getting A

Any more takers ??


Ans B.

3x/4 + x/10 = 187
x=220

Pure Gala = 220 - 187 = 33

However if I do
Gala = Total - Pure Fuji - Cross poolinated
= Total - 3/4(Total) - 1/10(Total) = 35

So I am not 100% sure of my answer.
Manager
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Posts: 108
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Re: PS - MGMT [#permalink] New post 16 Nov 2007, 07:22
saviop wrote:
alimad 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

Solution :

F = Fuji
G = Gala
x = Total no. of trees

x/10 - pollinate


F + x/10 = 187
F = 3x/4 - Pure Figi
3x/4 + x/10 = 187

30x + 4x/40 = 187 * 40
x = 187 * 40 /17 = 220

3/4 * 220 = 54 * 3 = 165 - 187 = 22. --- I'm getting A

Any more takers ??


Ans B.

3x/4 + x/10 = 187
x=220

Pure Gala = 220 - 187 = 33

However if I do
Gala = Total - Pure Fuji - Cross poolinated
= Total - 3/4(Total) - 1/10(Total) = 35

= 220 - (3/4(220)) - 1/10(220)
= 220 - 165 - 22
= 33
Director
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Re: PS - MGMT [#permalink] New post 16 Nov 2007, 07:32
alimad 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

Solution :

F = Fuji
G = Gala
x = Total no. of trees

x/10 - pollinate


F + x/10 = 187
F = 3x/4 - Pure Figi
3x/4 + x/10 = 187

30x + 4x/40 = 187 * 40
x = 187 * 40 /17 = 220

3/4 * 220 = 54 * 3 = 165 - 187 = 22. --- I'm getting A

Any more takers ??


I'm getting 33 using backsolving.

G= gala F = fuji C = cross
Start w/ choice B, G = 33
F + C = 187 (given)
F + C = Total - Gala
Total - Gala = 187
Total = 187 + 33 = 220
F = 3/4 (220) = 165
C = 187 - (165+33) = 22
C = 10% of total --> given
C = 22 = 10% of 220.
Therefore, B is correct.
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 [#permalink] New post 16 Nov 2007, 08:56
Pure Gala ---> (187/0.85)*0.15 = 33

:)
Manager
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 [#permalink] New post 16 Nov 2007, 13:34
85/100 * x = 187

15/100 x = 187*15/85
= 33


Answer B
  [#permalink] 16 Nov 2007, 13:34
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