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A farmer has an apple orchard consisting of Fuji and Gala [#permalink]
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26 Apr 2010, 15:13
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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 crosspollinated 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
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Last edited by Bunuel on 12 Aug 2012, 07:01, edited 1 time in total.
Added the answer choices and the OA.



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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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26 Apr 2010, 15:17
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iamseer 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 crosspollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala? Let the total trees be x 3/4 are pure Fuji = 3x/4 10% cross pollinated = x/10 now The number of his trees that are pure Fuji plus the crosspollinated ones totals 187 3x/4 + x/10 = 187 solve this x = 220 220187 = 33 are the pure Gala trees.
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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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26 Apr 2010, 15:19
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iamseer 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 crosspollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala? Let f = pure fuji , g = pure gala and c  cross pollinated. c = 10% of x where x is total trees. c = .1x also 3x/4 = f and c+f = 187 => .1x + 3/4x = 187 => x = 220 220  187 = pure gala = 33. PS: While posting the questions please post options and source.
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Last edited by gurpreetsingh on 26 Apr 2010, 15:21, edited 1 time in total.



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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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26 Apr 2010, 15:21
gurpreetsingh wrote: iamseer 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 crosspollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala? Let f = pure fuji , g = pure gala and c  cross pollinated. c = 10% of x where x is total trees. c = .1x also 3x/4 = f and c+f = 187 => .1x + 3/4x = 187 => x = 220 220  187 = pure gala = 33. Hi shouldnt it be 33, since 187 includes the fuji and the ones that cross pollinated???
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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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26 Apr 2010, 15:23
Silvers wrote: gurpreetsingh wrote: iamseer 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 crosspollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala? Let f = pure fuji , g = pure gala and c  cross pollinated. c = 10% of x where x is total trees. c = .1x also 3x/4 = f and c+f = 187 => .1x + 3/4x = 187 => x = 220 220  187 = pure gala = 33. Hi shouldnt it be 33, since 187 includes the fuji and the ones that cross pollinated??? Its 33 only check again what you have quoted.
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Re: Apple trees [#permalink]
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04 Jul 2010, 11:16
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First  I want to point out the fact that the Google ad on this particular thread is an advertisement that says, "Apple trees are on sale now!" Classic.
I'm not sure how to do this without simply setting up the formulas and hacking your way through the algebra. I'm guessing from your post ("need to understand the easiest way to solve this one") that you don't want this method.
Anyone else?



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Re: Apple trees [#permalink]
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04 Jul 2010, 11:52
yup....no need for the 4 equations method f+g= T 0.1T = c 0.75T = F f+c= 187 you can figure out the rest.....i hope there is a simpler way of doing it....



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Re: Apple trees [#permalink]
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05 Jul 2010, 13:10
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Gala apples  G Fuji apples  F C  Cross Pollinated apples Total apples  X Given: F = 3/4X X = G + F + cross pollinated Fuji + Cross pollinated (10 % of all apples) = 187
Solution: 3/4X + 1/10X = 187 Hence X = 220 X = G + F + cross pollinated 220 = G + 187 Hence G = 33.



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Re: Apple trees [#permalink]
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05 Jul 2010, 14:05
zisis 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 crosspollinated 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 OA: please explain method.....need to understand the easiest way to solve this one I got confused with the highlighted part; how would the question be framed if the part in bold where to mean pure fuji plus crosspollinated fuji(not including crosspollinated Gala)? Am I reading too much meaning to the question?
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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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01 Apr 2011, 21:04
Please tell me how should I calculate 187*0.85=220 within 30 seconds? Is there any specific trick for that? Even if i split it up and say: 0.1x +0.75x = 187 I have difficulties to solve it fast? Any tipps? Thanks



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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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01 Apr 2011, 21:35
Let x be the number of apple trees 0.1x of apple trees are crosspollinated 3x/4 = Fuji 3x/4 + 0.1x = 187 => 0.85x = 187 => 0.05x = 11 => x = 1100/5 = 220 Now x/4  0.1x = Pure Gala = 55  22 = 33
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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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02 Apr 2011, 07:04
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jay121 wrote: Please tell me how should I calculate 187*0.85=220 within 30 seconds? Is there any specific trick for that? Even if i split it up and say: 0.1x +0.75x = 187 I have difficulties to solve it fast? Any tipps? Thanks 10% are cross pollinated and 75% are pure Fuji so 85% are Fuji which gives you \((\frac{85}{100})*x = 187\) Now it is obvious that number of trees has to be an integer so 85 and 187 need to have come common factor. 187 isn't divisible by 2 (not even), by 3(1+8+7 = 16 so not divisible by 3), by 7 (since 7*2 = 14, you have 47 left which will not go by 7) but it is divisible by 11 (11*1 = 11 and 11*7 = 77). So you split 187 into 11*17. Now 85 is 17*5. Now the equation becomes: \((\frac{17*5}{100})*x = 11*17\) 17 gets canceled and 5 gets canceled with 100 leaving a 20. So you get x = 220
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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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02 Apr 2011, 13:24
Lets assume F stands for pure Fuji, G for pure Gala , CP for cross pollinated and T for total trees.
F + CP = 187
=> 3T/4 + 10T/100 = 187 = > T = 220
T = F+G+CP = > G = 33



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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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02 Apr 2011, 13:48
iamseer 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 crosspollinated ones totals 187, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala? 10% of his trees cross pollinated i.e. Cross Pollinated = 0.1*TotalThe number of his trees that are pure Fuji plus the crosspollinated ones totals 187 i.e. Pure Fuji+ Cross Pollinated=1873/4 of all his trees are pure Fuji i.e. Pure Fuji=0.75*TotalPure Fuji+ Cross Pollinated=0.75*Total+0.1*Total=0.85*Total 0.85*Total=187 Total=187/0.85 Pure Gala = Total  (Pure Fuji+ Cross Pollinated) = 187/0.85187=187((1/0.85)1)=187(0.15/0.85)=187(3/17)=11*3=33 Ans: 33 Pure Gala Apples
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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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01 May 2011, 23:35
0.1x + 0.75x = 187 x = 220 number of G trees = 220187 = 33 Hence B
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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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12 Aug 2012, 05:53
Hello,
I got this question today on my MGMAT CAT and tried first to solve it through a chart for overlapping sets, but then realized that this is not possible. I solved the question afterwards as in the posts here equation system). How can I identify that the chart won't work here?
Thanks!



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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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22 Sep 2012, 14:17
rocketscience wrote: Hello,
I got this question today on my MGMAT CAT and tried first to solve it through a chart for overlapping sets, but then realized that this is not possible. I solved the question afterwards as in the posts here equation system). How can I identify that the chart won't work here?
Thanks! 2X2 works as well. You just need to set "neither" as 0 because apples have to be either G or F. F nF G.1xy nG.75x0 187?x From here solve for x and y will be the difference between x and 187.



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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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04 Oct 2012, 15:48
this is the explanatio i understood can anyone explain y it should be 5522 Thank subhashghosh wrote: Let x be the number of apple trees
0.1x of apple trees are crosspollinated
3x/4 = Fuji
3x/4 + 0.1x = 187
=> 0.85x = 187
=> 0.05x = 11
=> x = 1100/5 = 220
Now x/4  0.1x = Pure Gala
= 55  22 = 33



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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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04 Oct 2012, 21:16
venmic wrote: this is the explanatio i understood can anyone explain y it should be 5522 Thank subhashghosh wrote: Let x be the number of apple trees
0.1x of apple trees are crosspollinated
3x/4 = Fuji
3x/4 + 0.1x = 187
=> 0.85x = 187
=> 0.05x = 11
=> x = 1100/5 = 220
Now x/4  0.1x = Pure Gala
= 55  22 = 33 3/4 (i.e. 75%) are pure Fuji and 10% are cross so 15% are pure Gala. So once you get x, you can calculate pure Gala as 15% of x = 15/100 * 220 = 33 or you can say Pure Gala = 25% of x (Gala apples)  10% of x (cross) = 55  22 = 33 (as done above)
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Re: A farmer has an apple orchard consisting of Fuji and Gala [#permalink]
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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 crosspollinated 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 THE QUICK METHOD... Fuji + Cross = 187 10% are cross 75% are Fuji so 85% = 187 We want to know what the 15% is Divide our percent by 10, 8.5% = 18.7 Double it, 17% = 38 We need 15 percent and it is pretty obvious 33 fits the bill
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Re: A farmer has an apple orchard consisting of Fuji and Gala
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