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29 Oct 2020, 10:40
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
41% (02:41) correct
59%
(02:59)
wrong
based on 337
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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
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.
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.
17 May 2021, 03:43
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Sajjad1994
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.
