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A farmer has an apple orchard consisting of Fuji and Gala

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iamseer
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A farmer has an apple orchard consisting of Fuji and Gala [#permalink] New post   Updated on: 12 Aug 2012, 07:01
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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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B

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.
Added the answer choices and the OA.
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Re: A farmer has an apple orchard: MGMAT, PS [#permalink] New post   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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KarishmaB
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Re: A farmer has an apple orchard: MGMAT, PS [#permalink] New post   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? :roll: :roll: :roll:

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] New post   Updated on: 26 Apr 2010, 15:21
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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 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.

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: Apple trees [#permalink] New post   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] New post   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: A farmer has an apple orchard: MGMAT, PS [#permalink] New post   01 Apr 2011, 21:04
Please tell me how should I calculate 187*0.85=220 within 30 seconds? :roll: :roll: :roll:

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] New post   01 Apr 2011, 21:35
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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] New post   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] New post   22 Sep 2012, 14:17
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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] New post   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] New post   04 Oct 2012, 21:16
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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] New post   05 Oct 2012, 00:45
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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

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 [#permalink] New post   10 Oct 2013, 21:58
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An easy way to solve this without having to do any lengthy calculations:

The total number of trees must be divisible by 10, as 0.1*Total number of trees = Number of trees that have cross pollinated (integer). A quick look at the answers show that only when 33 is added to 187 the total will be divisible by 10.

Once you get 33 you can quickly back check the 3/4 condition to confirm your answer
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Re: A farmer has an apple orchard consisting of Fuji and Gala [#permalink] New post   13 Mar 2018, 01:18
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?

A. 22
B. 33
C. 55
D. 77
E. 88





For those who prefer 100 rather than X



Let total tree be 100
Total pollinated = 10
Pure Fuji = 75
Pure Gala = 15

when Pure Fuji + pollinated = 85 (75+10) then Pure Gala = 15
Apply Unitary method

85 -> 15
1. -> 15/85
187 -> 15/85*187 = 33

Keep it simple!
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A farmer has an apple orchard consisting of Fuji and Gala [#permalink] New post   15 Jan 2019, 21:54
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?

A. 22
B. 33
C. 55
D. 77
E. 88


We can solve using 2x2 Matrix fairly quickly:

_________gala__not gala___total
fuji______0.1x___0.15x____0.25x
not fuji __0.75x___0_______0.75x
total_____187____0.15x______x

187 = 0.85x = 85/100x = 17/20
11*17 = 17/20x
>> x = 220 >> 0.15x = 33
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A farmer has an apple orchard consisting of Fuji and Gala [#permalink] New post   Updated on: 25 Feb 2021, 07:31
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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?

A. 22
B. 33
C. 55
D. 77
E. 88

Since 10% of the trees are cross-pollinated, the total number of trees must be a MULTIPLE OF 10.
Almost no work is needed here if we pay attention to the answer choices, which represent the number of trees that are pure gala.

Total number of trees = Pure Fuji + Cross-Pollinated + Pure Gala
Since the number of trees that are pure Fuji plus the cross-pollinated ones totals 187. we get:
Total number of trees = 187 + Pure Gala

Of the five answer choices, only B will yield a multiple of 10 for the total number of trees:
187 + 33 = 220

Show Spoiler
B

Originally posted by GMATGuruNY on 16 Feb 2019, 13:37.
Last edited by GMATGuruNY on 25 Feb 2021, 07:31, edited 2 times in total.
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Re: A farmer has an apple orchard consisting of Fuji and Gala [#permalink] New post   04 May 2023, 23:43
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?

A. 22
B. 33
C. 55
D. 77
E. 88


Hi it is easier to resolve this in an algebraic form.

Let's assume Trees as T
Cross Pollinated as CP
Fuji as F
Gala as G

CP=(10/100)*T
F=(3/4)*T
F+CP=187
(3T/4)+(10T/100)=187
75T+10T=187*100
85T=187*100
T=187*100/85
T=220
T=G+F+CP
220=G+187
G=33

Option B

Hope this is clear
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Re: A farmer has an apple orchard consisting of Fuji and Gala [#permalink] New post   25 Apr 2024, 23:24
Hi Bunuel and KarishmaB, how do we interpret the meaning of "cross pollinated" here? For some reason, I interpreted "cross pollinated" as saying that 10% of the apples are of both the Fuji and Gala varieties, and tried to solve using overlapping sets. I got the wrong answer, since I didn't set this up properly, but was wondering if that's the right or wrong way to interpret this one since there's no additional context provided.
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Re: A farmer has an apple orchard consisting of Fuji and Gala [#permalink] New post   26 Apr 2024, 00:14
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kkannan2 wrote:
Hi Bunuel and KarishmaB, how do we interpret the meaning of "cross pollinated" here? For some reason, I interpreted "cross pollinated" as saying that 10% of the apples are of both the Fuji and Gala varieties, and tried to solve using overlapping sets. I got the wrong answer, since I didn't set this up properly, but was wondering if that's the right or wrong way to interpret this one since there's no additional context provided.

­In this problem, 'cross pollinated' means that 10% of the trees are both Fuji and Gala. Hence:

Total number of trees = Pure Fuji + Pure Gala + Cross-Pollinated
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Re: A farmer has an apple orchard consisting of Fuji and Gala [#permalink]
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