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A rectangular field of dimension 100m x 80m is to be covered

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A rectangular field of dimension 100m x 80m is to be covered

by AAPL » Mon Feb 04, 2019 3:54 am

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A rectangular field of dimension 100m x 80m is to be covered by artificial grass. The cost of implementing artificial grass is at least $1 per square meter. Will the total cost incurred to put grass only in the filed be more than $7100?

1) In the filed are two restricted paths - of uniform width 5 m - which spread along the center of the field, and parallel to the length and breadth of the filed respectively.
2) The cost of putting grass in 25% of the total filed is not more than $1800.

OA A
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Source: — Data Sufficiency |
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by deloitte247 » Sun Feb 10, 2019 7:20 am

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Statement 1
In the field are two restricted paths of uniform width 5m which spread along the center of the field and parallel to the length and breadth of the field respective area of the position of the rectangular field to be covered with grass.
= Area of rectangular field - (Area of horizontally restricted rectangular path + Area of vertical restricted path)
$$=\left(100\cdot80\right)-\left\{\left(100\cdot5\right)+\left(5\cdot\left(80-5\right)\right)\right\}$$
$$=\left(100\cdot80\right)-\left\{\left(100\cdot5\right)+\left(5\cdot\left(75\right)\right)\right\}$$
$$=\left(8000\right)-\left\{\left(500\right)+\left(375\right)\right\}$$
$$=8000-875$$
$$=7125sq.m$$
cost of implementing artificial grass at least 1 dollar per sq.m
So cost of implementing artificial grass is 7125 sq.m is at least
$$\ge7125$$
Total cost incurred to put grass on the field is > 7,100 .
Hence, statement 1 is INSUFFICIENT.

Statement 2
The cost of putting grass on 25% of the total field is more than 1800 dollars
25% of grass area = 1/4 of total area = 1/4 * 80 * 100 = 2000 sq.m
Let cost of covering grass in 2000 sq.m = x
$$x\le1800dollar$$
If x= 1800 dollars ; cost of covering remaining 75% (6000 sq.m) = 5,400 dollars and Total = 5400 +1800 = 7200 dollars
If x < 1,800 dollars, lets say x = 10,000 dollars
25% = 1000
75% = 3000
Total =3000 +1000 = 4000 dollars
Statement 2 is INSUFFICIENT.

$$answer\ is\ Option\ A$$
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