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

Question

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

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

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PKN · Answer

d

Question stem: Will the total cost incurred to put grass only in the field be more than $7100? (Y/N)

Statement 1
Area of the portion of rectangular field where grass to be covered= Area of rectangular field-(Area of horizontal restricted rectangular path+Area of vertical restricted rectangular path)

=100*80- 
=8000-875
=7125 sq. m
The cost of implementing artificial grass is at least $1 per sq. m.
So, (cost of implementing artificial grass in 7125 sq. m)  \geq{$7125}

Therefore, st1 is sufficient.( Answer to question stem is Yes)

Statement 2:-
25% of grass area= \frac{1}{4} *total area= \frac{1}{4} *80*100=2000 sq. m

(cost of covering grass in 2000 sq. m)  \leq{1800} =X (say)-----(a)

(Cost of covering grass in the rest portion of field i.e, 6000 sq. m)  \geq{$6000} =Y(say)...........(b)

from (a) and (b), we can have

when X=1000 & Y=6000, X+Y=7000, answer to question is No
when X=1800 & Y=6100, X+Y=7900,answer to question is Yes
Therefore, St2 is not sufficient.

Ans. A

Azedenkae · Answer

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

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

Firstly, let's figure out the area of the field. I always like to figure out values that may be used throughout the question. So 100 x 80 = 8000m^2. It is also valuable to think before hand how this would relate to potential answers. Since the minimum cost of the artificial grass is $1 per m^2, we know then that to cover the entire field, it would be at least $8000. Whether this will be the case after considering statements (1) and (2) is a different matter, but it is good to think of it beforehand.

Statement (1): We now have restricted paths, where there will be no grass. The wording is a bit confusing, but it could be understood that the paths intersect and form a cross. There's two ways to figure this out. Either calculate the parts of each path that does not intersect, and then add on the intersected area; or calculate the areas for both path, then subtracting the area of the intersect once (because of the intersection, calculating the areas for both path would have doubled up on the intersected area, hence we need to subtract that area once). First method: 5*(100-5) + 5*(80-5) + 5*5 = 5*95 + 5*75 + 5*5 = 5*(95+75+5) = 5*(175) = 875m^2. Second method: 5*100 + 5*80 - 5*5 = 5*(100+80-5) = 5*175 = 875m^2. Both give us the same answer. Note that I kept the '5' as is for as long as possible. Always avoid making calculations where not necessary. Anywayssss let's figure out the area to be grassed. 8000 - 875 = 7125m^2. Because the minimum cost is $1 per m^2, then 7125m^2 is AT LEAST $7,125. Which is >$7,100. So, sufficient.

Statement (2): This is really, really, really confusing. The cost of covering 25% of the field (i.e. 2,000m^2) is <=$1,800, although somehow this is less than the 'at least $1 per sq. m' thing in the question... but okay. I assume then, that specifically for that 25%, the cost can be any positive number less than or equal to $1,800. If that's the case, we now just need to test to see if various costs of the 25% combined with the cost of the remainder can a.) be <= $7,100 and b.) be > $7,100. So let's get started testing! With extremes. What if 25% of the field costed $1 to cover with grass, and the remainder $6,000? Then the total cost would be $6,001. Now what if 25% of the field costed $1,800? Then even if the remaining 75% cost $6,000, that'd be $7,800. To be honest, even if 25% of the field costed $1, the remaining 75% can still cost $7,101 on its own, and in and of itself make the cost of covering the field with grass be > $7,100. So (2) is not sufficient.

Thus, answer is A.

EgmatQuantExpert · Answer

Solution

Given:  
 • A rectangular field of dimension 100 m x 80 m is to be covered by artificial grass
• Cost of implementing artificial grass is at least $1 per sq. m.

To find:  
 • Whether the total cost incurred to put grass only in the field will be more than $7100

Analysing Statement 1  
 • As per the information given in statement 1, there are two restricted paths in the field – of uniform width 5 m – which spread along the centre of the field, and parallel to the length and breadth of the field respectively

• As the paths are parallel to the edges, the dimensions of the parks are 100 m x 5 m and 80 m x 5 m
 o We can find the area covered by both the paths

• Also, total area of the field including the paths = 100 x 80 sq. m
• Therefore, we can find the area where artificial grass to be put
 o As the cost per sq. m is given, we can find out the total cost, and hence, can conclude whether the total cost is more than $7100 or not

Hence, statement 1 is sufficient to answer

Analysing Statement 2  
 • As per the information given in statement 2, the cost of putting grass in 25% of the total field is not more than $1800
 o It means to cover 100%, the cost will be less than $7200

• But, from this we can’t say whether the cost is more than $7100 or not

Hence, statement 2 is not sufficient to answer

Hence, the correct answer is option A.

Answer: A

Azedenkae · Answer

I have a query - in this case here the cost of covering 25% of the field with grass is less than $1 per square meter, which contradicts what is given in the question, that the cost per square meter  must be at least $1 . In the actual GMAT test, could the statement contradict the question that way?

Additionally, in a real GMAT test, can we really make the assumption that the cost of covering the remaining 75% of the total field would be the same (per square meter) as covering 25% of the field? People can always argue that because $1800 for 25% of the field is less than the minimum as required by the question itself, that it in and of itself is a special case and the remaining 75% of the field should follow the question's at least $1 per square meter requirement.

EgmatQuantExpert · Answer

Hey  Azedenkae ,
The second part of your query actually answers the first question - the other 75% can actually change the cost.
From the statement "The cost of putting grass in 25% of the total field is not more than $1800", when we are saying that the total cost would be not more than $7200, we are taking one possible case into account. As the possible case itself is not giving us unique solution, we can say statement 2 is not sufficient to answer, without checking the other possibilities.

Azedenkae · Answer

The part that I still want to figure out the logic behind is still how 'It means to cover 100%, the cost will be less than $7200' could be deduced from 'As per the information given in statement 2, the cost of putting grass in 25% of the total field is not more than $1800'. I understand the whole point is that it is not giving us a unique solution, but why specifically did we manage to get 'the cost will be less than $7200' out of that statement? Why 'will', implying we don't have any other possible outcome from that statement, as you suggested? Am I just being pedantic?

EgmatQuantExpert · Answer

As mentioned, this is  one of the possible cases  when the cost of putting grass remains uniform. And there are other cases, which is not considered as the statement is unable to provide unique answer in this case, and hence, becomes insufficient.

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

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