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A farmer has an apple orchard consisting of Fuji and Gala [#permalink]
 26 Apr 2010, 15:13
Question Stats:
58% (03:24) correct
41% (02:48) wrong based on 3 sessions
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
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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]
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 cross-pollinated 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 cross-pollinated ones totals 187 3x/4 + x/10 = 187 solve this x = 220 220-187 = 33 are the pure Gala trees.
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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
26 Apr 2010, 15:19
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 cross-pollinated 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]
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 cross-pollinated 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]
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 cross-pollinated 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: A farmer has an apple orchard: MGMAT, PS [#permalink]
26 Apr 2010, 15:24
haha
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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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]
01 Apr 2011, 21:35
Let x be the number of apple trees 0.1x of apple trees are cross-pollinated 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]
02 Apr 2011, 07:04
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 = 187Now 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*1717 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]
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]
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 cross-pollinated 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 cross-pollinated 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) = 187/0.85-187=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]
01 May 2011, 23:35
0.1x + 0.75x = 187 x = 220 number of G trees = 220-187 = 33 Hence B
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Re: A farmer has an apple orchard: MGMAT, PS [#permalink]
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]
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----.1x-----y nG---.75x---0 ------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]
04 Oct 2012, 15:48
this is the explanatio i understood can anyone explain y it should be 55-22 Thank subhashghosh wrote: Let x be the number of apple trees
0.1x of apple trees are cross-pollinated
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]
04 Oct 2012, 21:16
venmic wrote: this is the explanatio i understood can anyone explain y it should be 55-22 Thank subhashghosh wrote: Let x be the number of apple trees
0.1x of apple trees are cross-pollinated
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]
05 Oct 2012, 00:45
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 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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05 Oct 2012, 00:45
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