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Fuji vs Gala

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by AIM TO CRACK GMAT » Sun Jan 20, 2013 1:28 am
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]
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by GMATGuruNY » Sun Jan 20, 2013 5:28 am
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.
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by saurabh s » Sun Jan 20, 2013 6:01 am
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.
Hi, Can you please brief more on "Based on 10% as cross polinated - How we can assume that total must be multiple of 10 ?" This will a nice way to guess the Ans :)

I solved it based on Venn Diag Approach:

Taken : a/b/c as Fuji/Gala/Fuji n Gala Cross-polinated(Mix) and T as Total. Here , n=0 as we know the orchard has either mix or one type of tress.

Given are :
a= 3/4T
a+c= 187
c= T/10

Also we can deduce that , 3/4T+1/10T= 187
we get, T=220

Thus, we can get b (from a+b+c= T ) as 33.
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by GMATGuruNY » Sun Jan 20, 2013 7:14 pm
saurabh s wrote:
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.
Hi, Can you please brief more on "Based on 10% as cross polinated - How we can assume that total must be multiple of 10 ?" This will a nice way to guess the Ans :)
10% = 1/10.
Since 1/10 of the total number of trees are cross-pollinated, the total number of trees MUST be a multiple of 10.
Otherwise, the number of cross-pollinated trees will not be an integer value.
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My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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by Lifetron » Sun Jan 27, 2013 9:56 pm
Given :
F = 3/4 * T
C = 1/10 * T
F + C = 187

F + C + G = T

3T/4 + T/10 + T-187 = T
T = 220

Hence, G = 33 !
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by digvijay.rajput » Tue Aug 06, 2013 4:19 am
There is another approach to this question's answer..

3/4 of the trees are pure fuji,
when converted into percentage it gives = 75%

Also given 10% of the trees cross-pollinated.
Therefore, the percentage of gala apples = 100 - fuji + cross-pollinated
= 100 - (75+10)
= 100 - 85 = 15%
So, according to the question..
85% OF total = 187
1% of total = 187/85
So, 15% of total = 187/85*15
= 33

Number of gala trees = 33
answer is option b


Correct me if iam wrong.
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