VJesus12 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?
A. 22
B. 33
C. 55
D. 77
E. 88
[spoiler]OA=B[/spoiler]
Source: Manhattan GMAT
We can let x = total number of trees in the orchard. So 3x/4 = the number of pure Fuji apple trees and x/10 = the number of cross-pollinated trees. We can create the equation:
3x/4 + x/10 = 187
Multiply the equation by 20, we have:
15x + 2x = 187(20)
17x = 187(20)
x = 11(20) = 220
Now let y = the number of pure Gala apple trees, we have:
3x/4 + x/10 + y = x
187 + y = 220
y = 33
Alternate Solution:
Since 3/4 of all trees are pure Fuji and 10% = 1/10 of all trees are cross-pollinated, 3/4 + 1/10 = 34/40 = 17/20 of all trees are either Fuji or cross-pollinated. Thus, the remaining 1 - 17/20 = 3/20 of all trees are pure Gala. If x is the total number of trees, the number of pure Gala trees are 3x/20, which we observe is a multiple of 3 (since the number of any kind or combination of kinds of trees must be an integer). Of the given answer choices, only 33 is a multiple of 3.
Answer: B
