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# A farmer has an apple orchard consisting of Fuji and Gala

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A farmer has an apple orchard consisting of Fuji and Gala  [#permalink]

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Updated on: 12 Aug 2012, 07:01
3
12
00:00

Difficulty:

65% (hard)

Question Stats:

70% (02:56) correct 30% (03:10) wrong based on 696 sessions

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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 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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Originally posted by iamseer on 26 Apr 2010, 15:13.
Last edited by Bunuel on 12 Aug 2012, 07:01, edited 1 time in total.
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Re: A farmer has an apple orchard: MGMAT, PS  [#permalink]

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02 Apr 2011, 07:04
3
3
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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26 Apr 2010, 15:17
3
1
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]

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Updated on: 26 Apr 2010, 15:21
1
2
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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Originally posted by gurpreetsingh on 26 Apr 2010, 15:19.
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 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]

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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 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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04 Jul 2010, 11:16
1
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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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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05 Jul 2010, 13:10
2
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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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 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

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 cross-pollinated fuji(not including cross-pollinated 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
1
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]

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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 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*Total
The number of his trees that are pure Fuji plus the cross-pollinated ones totals 187 i.e. Pure Fuji+ Cross Pollinated=187
3/4 of all his trees are pure Fuji i.e. Pure Fuji=0.75*Total

Pure 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]

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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]

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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----.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]

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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]

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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]

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05 Oct 2012, 00:45
2
1
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 &nbs [#permalink] 05 Oct 2012, 00:45

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