A farmer has an apple orchard consisting of Fuji and Gala

[Pia]

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

in the explanation it is mentioned (1) C = 0.1(F + G + C), y wld we include C on the Rt hand side of the equation??? Question says C = .1 (F+G) not C = 0.1 (F+G+C)

Thanks

[GMAT 2007]

Is (B) the correct answer?

GMAT 2007

[Pia]

Yes

[GMAT 2007]

Here is how I solved it: -

Lets assume the total no. of apple trees be 'X'.

From the question we know the following: -

1/10(X) + 3/4(X) = 187

Solving the above question X = 220. Hence pure Gala trees = 220-187 = 33

Hope it helps

GMAT 2007

[StaceyKoprince]

The total number of trees = Gala + Fuji + Gala/Fuji mix (those are the cross-pollinated ones)
10% of the total number of trees = the cross-pollinated ones.
Therefore, c = 0.1(G+F+C).

I agree, though, that the question is a little bit fuzzy and could be read as total = Gala + Fuji and no cross-pollinated ones. I'll pass on to our curriculum director for his review.
Thanks! :)

[Guest]

yes! i totally agree with pia. i was solving for 0.1 (F+G) = C as well.
in order for the soln to work according to mgmat, the qustion should be re-worded as to read, "10% of his trees are cross pollinates" rather than "cross pollinated"...

[RJ]

hi Stacy,

This problem is still the same, no change yet in the language. I spent a lot of time trying to figure out the question before i thought of posting about it, and I find that i am not alone..:-)

So jsut thought of updating so that something can be done to rectify this and save future mgmat students time adn efforts.

thanks

RJ

[esledge]

Since this one is the subject of some debate, I will weigh in: I think it is clear as is.

It is established that the farmer had some total # of trees. We can all agree that whether they started as Fuji or Gala trees, stayed that way, or became cross pollinated, no extra trees were added, right? The total # of trees is constant.

We know that some cross pollinated (past tense!), so there are clearly 3 different types of trees after that event: pure Fuji, pure Gala, and the mix. But the total # of trees is constant, so we have to understand that "10% of his trees cross pollinated" means that if total = T = sum of all 3 types, then cross pollinated = 0.1T, and pure Fuji + pure Gala = 0.9T.

Also, note that the problem very consistently refers to "pure Gala" and "pure Fuji" when referencing the ones that weren't mixed, to further emphasize the 3 different categories of trees.

[benkriger]

Agreed, wording is terrible. Anyway, is there a way to solve this problem using Venn Diagrams? if so, please show the work and explain. I am very curious.

[cyber_office]

This question seems fine and so does the wording. I agree with the individual who posted in 2007:

Let all apple trees = X

X/10 + 3/4*X= 187

You can cacluate the total number of apple trees and determine the pure Gala trees.

Regards.

[Ben Ku]

yup

[nachikett13]

hi Stacy,

This problem is still the same, no change yet in the language. I spent a lot of time trying to figure out the question before i thought of posting about it, and I find that i am not alone..:-)

So jsut thought of updating so that something can be done to rectify this and save future mgmat students time adn efforts.

thanks

RJ

Hi Stacy and esledge,

I am still not convinced with this explanation. The problem is that it is difficult to assume that C=0.1(F+C+G). My thought process goes as follows: The C trees are added only after the F+G cross-pollinate. That means if the author says that '10% of the trees cross-pollinated' we cant assume that there already were C trees before the cross-pollination happened. According to me, it should be C=0.1(F+G). The case would have changed had the author mentioned pure Gala and pure Fiji right from the start, sadly he doesn't.

Can you please clarify my doubt? I am not trying to question an official solution; I'm just trying to get my interpretations correct.

[nachikett13]

Also, the question talks about 10% trees having pollinated after mentioning that the farmer's orchard consisted of Fiji and Gala trees. Following that line, it's pretty clear that 10% of THOSE (F+G) cross pollinated.

Regards,
N

[jnelson0612]

hi Stacy,

This problem is still the same, no change yet in the language. I spent a lot of time trying to figure out the question before i thought of posting about it, and I find that i am not alone..:-)

So jsut thought of updating so that something can be done to rectify this and save future mgmat students time adn efforts.

thanks

RJ

Hi Stacy and esledge,

I am still not convinced with this explanation. The problem is that it is difficult to assume that C=0.1(F+C+G). My thought process goes as follows: The C trees are added only after the F+G cross-pollinate. That means if the author says that '10% of the trees cross-pollinated' we cant assume that there already were C trees before the cross-pollination happened. According to me, it should be C=0.1(F+G). The case would have changed had the author mentioned pure Gala and pure Fiji right from the start, sadly he doesn't.

Can you please clarify my doubt? I am not trying to question an official solution; I'm just trying to get my interpretations correct.

Emily explains it above about as well as anyone could. I'm not sure I'm reading your comment exactly the way you meant it, but I think the mistake that you are making is here: thinking that the C trees are "added" after the cross-pollination. That is not correct; these trees do not join the sample (as in, new trees don't sprout). I am just changing the status of some of my existing F and G trees to the status of C. Let me give an example that I hope will help make it more clear:

10 people are standing with wet blue paint on their hands.
10 people are standing with wet red paint on their hands.
10% of this sample touches someone with the opposite color paint, creating purple hands (blue + red = purple). This is the cross-pollination.

Thus, of the 20 people, 2 people touch hands with someone of the other color. Thus, 1 red handed and 1 blue handed person must touch each other.

I now have 9 blue, 9 red, and 2 purple, but notice that my sample stayed the same. I just changed the color status of some of the sample.

I hope this helps at all.

[jnelson0612]

Also, the question talks about 10% trees having pollinated after mentioning that the farmer's orchard consisted of Fiji and Gala trees. Following that line, it's pretty clear that 10% of THOSE (F+G) cross pollinated.

Regards,
N

Right, but remember that the original F + G equals the same number of the later F + G + C. You are just taking some of the original F + G and converting them to C.