Of the land owned by a farmer, 90 percent was cleared for planting. Of

Percentage cleared for planting = 90
Soybean = 40% of 90 = 36 % of total
Wheat = 50 % of 90 =45 % of total
Corn = 10 % of 90 = 9 % of total

Since 9% of total = 720 acres
Therefore , total land = 720/9 * 100 = 8000 acres

Answer D

Attached is a visual that should help.

Let farmer has X land;
Cleaned =.9 x
out of .9 x 10% is 720 ; therefore .09x=720 => x=8000

Hence answer is D

Thanks

I understand it the following way:
0.40(90)+0.50(90)+720=0.90x
2880+3600+720=0.90x
7200=0.90x
\(\frac{7200}{0.90}\)=x
8000=x

Of the land owned by a farmer, 90 percent was cleared for planting. Of the cleared land, 40 percent was planted with soybeans and 50 percent of the cleared land was planted with wheat. If the remaining 720 acres of cleared land was planted with corn, how many acres did the farmer own?

(A) 5,832
(B) 6,480
(C) 7,200
(D) 8,000
(E) 8,889

For this type of Question its always better to go by option and elimination plays a key role here .

As per the Q -- out of the total land -- 90% was cleared for planting .

now see the option --- only B,C, D will give you a integer value .When we do 90% of total Area.

hence A,E can be eliminated .

Option B -- 6480 * (90/100) = 5832
5832 * ( 40/100 ) = wont give us a integer value . Hence can be eliminated .

Option C and D left .
Now see option D is good number to start with because its value .( 8000)

When we apply 8000( 90/100) = 7200 (50/100) = 3600
7200(40/100)= 2880

Now sum them = 2880 + 3600 = 6480

If the remaining 720 acres of cleared land was planted with corn .

This remaining area comes from 7200 - 6480 = 720 .

Hence the condition got satisfied .

Ans is D .

(10% of (90% of total land)) is 720

\(0.1 * 0.9 * X = 720\)

\(X = 8000\)

Option D

Hi All,

This question can be solved by TESTing THE ANSWERS. From the prompt, we know that we're going to be doing a number of small calculations AND we're going to end with 720 acres remaining for corn. Since we're asked for the total number of acres, and the answers are all numbers, we just have to work until we find the one that matches what we've been told. In these situations, it's often best to start with Answer B or D. Between those 2 options, D looks 'nicer'/easier, so let's start there.

IF....there were 8000 total acres...

90% was cleared for planting = (.9)(8000) = 7200 acres for planting

Of that land,
40% was soybeans = (4.)(7200) = 2880 acres
50% was wheat = (.5)(7200) = 3600

2880 + 3600 = 6480

7200 - 6480 = 720 --> this is an exact match for what we were told, so this MUST be the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Another approach is to recognize that 720 = 10% of the cleared land and the cleared land is 90% of the total acreage (A).

Cleared land= 720/0.1= 7,200
Acreage= 7,200/0.9 = 8,000

The answer is D

IMO 8000

9 out of 100 corresponds to 720 out of 8000.

Suppose the total land was 100. Then, 90% of 100 = 90.

Of the 90, 40%(36) of land was used for soyabeans, 50%(45) was for wheat. Remaining land portion of 90 is 9.

According to question 9 equals 720.

By unitary method.
If;
9(land) = 720
then;
100(land) =x(what).

By cross multiplication.

x = \(720*100/9\)

= 8000.

D.

Hi,

Is this a right approach [or an unnecessarily longer one?]

In the cleared land : 720 is 10%
Hence, 720*4 = 2880 is 40%
and, 720*5 = 3600 is 50%

Adding all these the 90% cleared land turns out to be 7200, the remaining has to be 800. Hence 7200+800 = 8000 -> Answer D.

36+45 =81x
now remaining cleared land = 90-81 = 9x
Now 9x = 720: x =80
So total land = 100x = 8000

Quick Soln

given) 10% of 90% =720
So 100%=7200

if 90% of x =7200 ( X is the total acre of land farmer has)
90/100*x =7200
x=7200*100/90
x=8000

Ans choice D
DReam if! Achieve it

Answer: Option D

Video solution by GMATinsight



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Usually in percentage problems, do not we take final value as 100 and back solve?

Eg: Say total acres of farm owned = 100

Cleared for farming: 90 acres
Of cleared farm: 40% ie 36 acres planted with SB
Of cleared farm: 50% ie 45 acres planted with W
Total SB + W : 91 acres

Remaining 9 acres: planted with corn.

Now 9x= 720 or x = 60

Let us set up a proportion: SB : W: C = 36 : 45 : 9
or 4 :5 : 1 or 10 * x = 600

What is incorrect about this approach ?

Video solution from Quant Reasoning:
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One of the quickest ways to solve this question is to visualize the problem. Please refer to the illustration attached.

Black circle => Total farm area
Red circle => Cleared farm area

90% of the black circle = 100% of the red circle = 7200 acres
Therefore, 100% of black circle = \((7200*100)/90 = 8000 acres\)

The answer is (D)