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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
An unpainted wall with a total area of 100 square feet needed to be pa
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18 May 2021, 01:03
18 May 2021, 01:03
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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
(A) 0 ≤ q ≤ 50
(B) 0 ≤ q ≤ 60
(C) 10 ≤ q ≤ 50
(D) 10 ≤ q ≤ 55
(E) 10 ≤ q ≤ 60
Re: An unpainted wall with a total area of 100 square feet needed to be pa
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20 May 2021, 07:05
20 May 2021, 07:05
hi can I have the answer to this please?
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: An unpainted wall with a total area of 100 square feet needed to be pa
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20 May 2021, 08:07
20 May 2021, 08:07
Expert Reply
Anushka123 wrote:
hi can I have the answer to this please?
Here is the explanation from a GMAT expert.
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.
Show: ::
D
