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

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Intern
Joined: 07 Aug 2013
Posts: 18
WE: Engineering (Aerospace and Defense)
Re: A farmer has an apple orchard consisting of Fuji and Gala  [#permalink]

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10 Oct 2013, 21:58
1
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]

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05 Jul 2014, 13:17
can we use double set matrix method for this?
I was trying to do that , but could not. anyone can help?

Arthur1000 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

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]

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24 Jul 2014, 02:36
Let total trees = x

Pure Fuji$$= \frac{3x}{4}$$

Cross pollinated $$= \frac{x}{10}$$

$$\frac{3x}{4} + \frac{x}{10} = 187$$

x = 220

Pure Gala = 220 - 187 = 33
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Re: A farmer has an apple orchard consisting of Fuji and Gala  [#permalink]

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28 Oct 2014, 23:46
Silvers 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 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.

I like the simplicity of the way u dealt with this problem.
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Re: A farmer has an apple orchard consisting of Fuji and Gala  [#permalink]

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20 Nov 2014, 12:25
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

sol: I first thought I can do it using double matrix. But with in first 25 sec, I realized venn is better.

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

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22 Mar 2016, 12:24
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, creating trees that are part Fuji and part Gala. 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

See edited text in red above.

Question: if the question is re-worded as edited above, would we interpret instead that the 10% of trees that are cross pollinated are actually 10% of the total existing trees before pollination (meaning Pure Fuji + Pure Gala)? I would think that in this case 33 should no longer be the answer.

Disclosure: The CAT exam has the edited wording above.
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Re: A farmer has an apple orchard consisting of Fuji and Gala  [#permalink]

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13 Jul 2017, 18:33
$$f+g = x$$
$$0.1x$$ cross pollinated

$$f+0.1x = 187$$
$$f = 0.75x$$

$$0.75+0.1x = 187$$
$$x = \frac{187}{0.85} = 220$$

No. of cross pollinated trees = $$0.1(220) = 22$$.

No. of Fuji = $$\frac{3}{4}(220) = 165$$, so no. of Gala = $$220-165-22 = 33$$. Ans - B.
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Re: A farmer has an apple orchard consisting of Fuji and Gala  [#permalink]

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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]

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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]

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16 Feb 2019, 11:50
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

Let the total number of trees be x.

We are given that P(Both) = $$0.1x$$ -> P(PF) + $$0.1x = 187$$

Since P(PF) = $$0.75x$$, $$0.1x + 0.75x = 0.85x = 187$$ -> $$\frac{17x}{20} = 187$$

Solving for x, we get x = $$187*\frac{20}{17} = 220$$

Therefore, the total number of pure Gala trees is 220 - 187 = 33(Option B)(because P(Not PG) = 187)
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Re: A farmer has an apple orchard consisting of Fuji and Gala  [#permalink]

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16 Feb 2019, 13:37
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

Total = PURE FUGI + PURE GALA + CROSS-POLLINATED.
Since the number of his trees that are PURE FUGI plus the CROSS-POLLINATED ones totals 187, we get:
Total = 187 + PURE GALA..
Since 10% of the trees are cross-pollinated, the total number of trees must be a MULTIPLE OF 10.
Of the five answer choices, only 33 will yield a multiple of 10 when added to 187.

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Re: A farmer has an apple orchard consisting of Fuji and Gala   [#permalink] 16 Feb 2019, 13:37

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