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Re: An unpainted wall with a total area of 100 square feet needed to be pa [#permalink]
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
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]
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]
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nishg13
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]
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Sajjad1994
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]
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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]
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Re: An unpainted wall with a total area of 100 square feet needed to be pa [#permalink]
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