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An unpainted wall with a total area of 100 square feet needed to be pa

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Sajjad1994
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An unpainted wall with a total area of 100 square feet needed to be pa [#permalink] New post   29 Oct 2020, 10:40
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An unpainted wall with a total area of 100 square feet needed to be painted with three coats of paint. Nelson began the job by painting an area of 60 square feet. Then, Jamaica painted a total area of 70 square feet. Finally, Bryan painted a total area of 80 square feet. Aȇer Bryan finished painting, an area of q square feet of the wall was covered in three coats of paint. If the entire surface area of the wall had received at least one coat of paint, which of the following specifies all the possible values of q ?

(A) 0 ≤ q ≤ 50

(B) 0 ≤ q ≤ 60

(C) 10 ≤ q ≤ 50

(D) 10 ≤ q ≤ 55

(E) 10 ≤ q ≤ 60
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Re: An unpainted wall with a total area of 100 square feet needed to be pa [#permalink] New post   31 Oct 2020, 21:18
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Total area to be painted= 300 square feet (3 coats on a wall of 100 square feet)
3 of them painted 60+70+80 square feet= 210 square feet

Entire surface area was painted with one coat atleast once
If the entire surface was covered once that means 100 square feet was covered and then 2 more coats were applied. The 2 coats covered 210-100=110 square feet and one coat covered 110/2=55 square feet. Hence, area with 3 coats was 55.

If the entire surface was covered twice that means 200 square feet was covered and then 1 more coat was applied on 210-200=10square feet. Hence, area with 3 coats was 10 square feet.

I know I did not articulate it well, still I hope the explanation was helpful.
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An unpainted wall with a total area of 100 square feet needed to be pa [#permalink] New post   17 May 2021, 03:43
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Sajjad1994 wrote:
An unpainted wall with a total area of 100 square feet needed to be painted with three coats of paint. Nelson began the job by painting an area of 60 square feet. Then, Jamaica painted a total area of 70 square feet. Finally, Bryan painted a total area of 80 square feet. Aȇer Bryan finished painting, an area of q square feet of the wall was covered in three coats of paint. If the entire surface area of the wall had received at least one coat of paint, which of the following specifies all the possible values of q ?

(A) 0 ≤ q ≤ 50

(B) 0 ≤ q ≤ 60

(C) 10 ≤ q ≤ 50

(D) 10 ≤ q ≤ 55

(E) 10 ≤ q ≤ 60


We can PLUG IN THE ANSWERS, which represent the area painted by all 3 workers.
Start with the largest value among the answer choices -- 60 square feet -- to determine the maximum area that can be painted by all 3 workers.
When the correct answer is plugged in, the total area painted = 100 square feet

Case 1: 60 square feet painted by all 3 workers
Of the 70 square feet painted by Jamaica, the area that receives 3 coats of paint = 60, implying that the area painted by Jamaica that could receive 1 coat of paint = 70-60 = 10
Of the 80 square feet painted by Bryan, the area that receives 3 coats of paint = 60, implying that the area painted by Bryan that could receive 1 coat of paint = 80-60 = 20
Total area that receives paint = sum of the blue values above = 60+10+20 = 90
The total area painted is too small.
Since it is not possible that q=60, eliminate B and E.

Among the remaining answer choices, the next largest option = 55 square feet

Case 2: 55 square feet painted by all 3 workers
Of the 60 square feet painted by Nelson, the area that receives 3 coats of paint = 55, implying that the area painted by Nelson that could receive 1 coat of paint = 60-55 = 5
Of the 70 square feet painted by Jamaica, the area that receives 3 coats of paint = 55, implying that the area painted by Jamaica that could receive 1 coat of paint = 70-55 = 15
Of the 80 square feet painted by Bryan, the area that receives 3 coats of paint = 55, implying that the area painted by Bryan that could receive 1 coat of paint = 80-55 = 25
Total area that receives paint = sum of the blue values above = 55+5+15+25 = 100
Success!
Since it is possible that q=55, eliminate A and C.

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Re: An unpainted wall with a total area of 100 square feet needed to be pa [#permalink] New post   29 Oct 2020, 14:52
Minm possible value of q = 100-[(100-60)+(100-70)+(100-80)] = 10

Also, Suppose double coated area = x

60+70+80-2q-x=100
2q+x=110

Max possible value of q = 110/2 =55 (when x=0)

Sajjad1994 wrote:
An unpainted wall with a total area of 100 square feet needed to be painted with three coats of paint. Nelson began the job by painting an area of 60 square feet. Then, Jamaica painted a total area of 70 square feet. Finally, Bryan painted a total area of 80 square feet. Aȇer Bryan finished painting, an area of q square feet of the wall was covered in three coats of paint. If the entire surface area of the wall had received at least one coat of paint, which of the following specifies all the possible values of q ?

(A) 0 ≤ q ≤ 50

(B) 0 ≤ q ≤ 60

(C) 10 ≤ q ≤ 50

(D) 10 ≤ q ≤ 55

(E) 10 ≤ q ≤ 60
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An unpainted wall with a total area of 100 square feet needed to be pa [#permalink] New post   31 Oct 2020, 11:11
Where did i get the answer wrong? Please help me.

Case 1 - Nelson Coat 1 - 60sq.ft ... Jamaica continued to paint 70 sq.ft (40 as coat 1 and 30 as coat 2).. Bryan continued 80sq.ft ( 70 as Coat 2 and 10 as Coat 3 ).. So Bryan would have painted 10sq.feet in coat 3.

Case 2 - Nelson Coat 1 - 60sq.ft .. Jamaica painted of 60sq.ft on Coat 1 + 10Sq.ft extra (As Nelson didnt complete the 100sq.ft, The extra 10sq.ft of jamaica's job would be coat 1)... Bryan painted 60sq.ft on Coat 2 = 60 sq.ft of 3 coats + 10 sq.ft of coat2 and 10 sq.ft of coat 1.

Hence i selected 10<=q<=60.
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Re: An unpainted wall with a total area of 100 square feet needed to be pa [#permalink] New post   31 Oct 2020, 23:29
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nishg13 wrote:
Where did i get the answer wrong? Please help me.

Case 1 - Nelson Coat 1 - 60sq.ft ... Jamaica continued to paint 70 sq.ft (40 as coat 1 and 30 as coat 2).. Bryan continued 80sq.ft ( 70 as Coat 2 and 10 as Coat 3 ).. So Bryan would have painted 10sq.feet in coat 3.

Case 2 - Nelson Coat 1 - 60sq.ft .. Jamaica painted of 60sq.ft on Coat 1 + 10Sq.ft extra (As Nelson didnt complete the 100sq.ft, The extra 10sq.ft of jamaica's job would be coat 1)... Bryan painted 60sq.ft on Coat 2 = 60 sq.ft of 3 coats + 10 sq.ft of coat2 and 10 sq.ft of coat 1.

Hence i selected 10<=q<=60.


In case 2, you are total area that has been painted
60sqft(thrice)+10sqft(twice)+10sqft(once)=80sqft
This means 100-80=20sqft is untouched but question says that entire 100sqft has been done at least once
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Re: An unpainted wall with a total area of 100 square feet needed to be pa [#permalink] New post   31 Oct 2020, 23:33
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Sajjad1994 wrote:
An unpainted wall with a total area of 100 square feet needed to be painted with three coats of paint. Nelson began the job by painting an area of 60 square feet. Then, Jamaica painted a total area of 70 square feet. Finally, Bryan painted a total area of 80 square feet. Aȇer Bryan finished painting, an area of q square feet of the wall was covered in three coats of paint. If the entire surface area of the wall had received at least one coat of paint, which of the following specifies all the possible values of q ?

(A) 0 ≤ q ≤ 50

(B) 0 ≤ q ≤ 60

(C) 10 ≤ q ≤ 50

(D) 10 ≤ q ≤ 55

(E) 10 ≤ q ≤ 60


So total area painted is 60+70+80=210 sqft.
However entire 100sqft is painted at least once, so we have 210-100 or 110 sqft to cater for.

q is the area painted thrice,
Minimum value, when we paint everything twice and remaining becomes the value of q =110-100=10 sqft
Maximum value, when we utilise the entire 110 to paint a surface two times more, so that the surface becomes painted thrice, q=110/2=55

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Re: An unpainted wall with a total area of 100 square feet needed to be pa [#permalink] New post   17 May 2021, 03:12
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Looking it as an inequality problem

Total Area Painted = 210
Total area painted once= 100 sq feet

Remaining area painted went in coat 2 and coat 3
Let them be p( coat 2) and q (coat3)

p+q=210-100=110 ----1
p<=100 -----2 ( a second coat cant cover more than the wall)
q<=p -----3 ( as we cant paint a 3rd coat before a 2nd coat is painted)



From 1 and 2 q>=10
From 1 ,2 and 3 q<=55
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Re: An unpainted wall with a total area of 100 square feet needed to be pa [#permalink]
17 May 2021, 03:12
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