Problem Solving

A farmer has an apple orchard consisting of F=uji and Gala apple trees.10% of his trees cross pollinated. Now the Fuji trees plus the cross pollinated equals: 187,
While ¾ of his trees are pure fuji..
Number of pure gala trees=?

A. 22
B. 33
C. 55
D. 77
E. 88

[spoiler]OA: B
IMO: C
Pls explain if you got the OA. �[/spoiler]

heymayank08 wrote:A farmer has an apple orchard consisting of F=uji and Gala apple trees.10% of his trees cross pollinated. Now the Fuji trees plus the cross pollinated equals: 187,
While ¾ of his trees are pure fuji..
Number of pure gala trees=?

A. 22
B. 33
C. 55
D. 77
E. 88

F= Fuji trees , C= cross pollinated trees & G = Gala trees

Let F+C+G = x
given that
F+C = 187
also
F = 3/4*x
so 3/4*(F+C+G) = F
=> 3/4*(187+G) = F
Now for F to be an integer (187+G) must be a multiple of 4.
Looking at the options
Option A & E will give an odd value when added to 187, so they can be eliminated.
a)187+22 = odd
e)187+88 = odd

Now option B, C & D
b)187+33 = 220 (divisible by 4)
c)187+55 = 242 (not divisible by 4)
d)187+77 = 264 (divisible by 4)

so eliminate option C

Now we know that 10% of the trees were cross pollinated
b) 220*10% = 22 = C
F+C = 187 => 165
c) 264*10% = 26.4 ( not an integer)

Hence the answer is B

P.S we can also cross check the answer
3/4*220 = 165 = F

F+x+G = Total Trees

F+x = 187
F/(F+x+G) = 3/4
x/(F+x+G) = 1/10
Solving for G we get G = 33

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

We can plug in the answers, which represent the number of pure Gala trees.
Since 10% of all the trees cross pollinated, the total number of trees must be a multiple of 10.
Thus, when the correct answer choice (the number of pure gala trees) is added to 187 (the number of pure Fuji trees plus the number of cross-polinated trees), the sum must be a multiple of 10.

Only B works: 33+187 = 220.

The correct answer is B.

Appreciate the out of box approach to solve this question.
Just wanted to understand how do you get such approaches. I mean this was a very smart and time saving way to do the question. There is no way to do this question in 2 minutes by solving all the equations.

GMATGuruNY 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

We can plug in the answers, which represent the number of pure Gala trees.
Since 10% of all the trees cross pollinated, the total number of trees must be a multiple of 10.
Thus, when the correct answer choice (the number of pure gala trees) is added to 187 (the number of pure Fuji trees plus the number of cross-polinated trees), the sum must be a multiple of 10.

Only B works: 33+187 = 220.

The correct answer is B.