A farmer has an apple orchard consisting of Fuji and Gala

Question

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

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

Silvers · Accepted Answer

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.

KarishmaB · Answer

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

gurpreetsingh · Answer

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.

YourDreamTheater · Answer

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?

surjoy · Answer

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.

jay121 · Answer

Please tell me how should I calculate 187*0.85=220 within 30 seconds? :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

subhashghosh · Answer

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

rocketscience · Answer

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!

honggil · Answer

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.

venmic · Answer

this is the explanatio i understood

can anyone explain y it should be 55-22

Thank

KarishmaB · Answer

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)

Arthur1000 · Answer

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

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

missil3 · Answer

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

ShekharRavi · Answer

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!

gulyaa · Answer

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

GMATGuruNY · Answer

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

B

proddnav · Answer

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

kkannan2 · Answer

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.

Bunuel · Answer

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

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

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