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08 Oct 2024, 01:30
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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:
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Question Stats:
67% (02:21) correct
33%
(02:40)
wrong
based on 347
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Emma and Deep are painting a wall. Emma started painting the wall alone and worked for 3 hours. Then she left and Deep completed painting the rest of the wall in 4 hours. Sam alone can paint the wall in 4.5 hours completely. How long would it take to paint the wall, if Emma and Deep worked together?
(1) Emma, Deep, and Sam together can finish the painting of the wall in 2 hours.
(2) In 4 hours, Deep painted twice the area as Emma did in 3 hours.
(1) Emma, Deep, and Sam together can finish the painting of the wall in 2 hours.
(2) In 4 hours, Deep painted twice the area as Emma did in 3 hours.
This is a Data Sufficiency Butler Question
Check the links to other Butler Projects:
Check the links to other Butler Projects:
- Data Sufficiency Butler
- Problem Solving Butler
- Sentence Correction Butler
- Reading Comprehension Butler
- Integrated Reasoning Butler
08 Oct 2024, 08:44
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Emma took 3 hours
Deep took 4 to finish
Sam alone would take 4.5
How long would emma and deep take together
S1: 1/e+1/d+1/s=1/2 bc rates add up
and we know 1/s1/4.5
hence sufficient
S2: if paint twice the area that means he painted 2/3 in 4 hours and emma painted 1/3 in 3 hours
hence emma would take 9 hours alone and deep 6
1/e+1/d=1/9+1/6 is their rate, inverse of which is total time
Deep took 4 to finish
Sam alone would take 4.5
How long would emma and deep take together
S1: 1/e+1/d+1/s=1/2 bc rates add up
and we know 1/s1/4.5
hence sufficient
S2: if paint twice the area that means he painted 2/3 in 4 hours and emma painted 1/3 in 3 hours
hence emma would take 9 hours alone and deep 6
1/e+1/d=1/9+1/6 is their rate, inverse of which is total time
08 Oct 2024, 16:19
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Let t be the total work i.e. work to complete the wall
Emma completed e in 3 hrs, Deep completed t-e in 4 hours, and Sam can complete t in 4.5 hours
We need to find, \((\frac{e}{3} + \frac{t-e}{4}) * k = t\) ; where k is the time taken by Emma and Deep to paint the wall working together
\(k = \frac{12t}{e+3t}\) .................(1)
Statement 1
\((\frac{e}{3} + \frac{t-e}{4} + \frac{2t}{9})*2 = t\)
3e = t
Subs. in 1, we get k = 3.6 SUFFICIENT
Statement 2
\(\frac{2t}{9} * 4 = 2e\)
4t = 9e
Subs. in 1 also gives k SUFFICIENT
Answer D.
However, I'm skeptical because in a DS question the answers of St. 1 and 2 should match, here the value of k differs. Can someone please help me in case I went wrong somewhere above?
Emma completed e in 3 hrs, Deep completed t-e in 4 hours, and Sam can complete t in 4.5 hours
We need to find, \((\frac{e}{3} + \frac{t-e}{4}) * k = t\) ; where k is the time taken by Emma and Deep to paint the wall working together
\(k = \frac{12t}{e+3t}\) .................(1)
Statement 1
\((\frac{e}{3} + \frac{t-e}{4} + \frac{2t}{9})*2 = t\)
3e = t
Subs. in 1, we get k = 3.6 SUFFICIENT
Statement 2
\(\frac{2t}{9} * 4 = 2e\)
4t = 9e
Subs. in 1 also gives k SUFFICIENT
Answer D.
However, I'm skeptical because in a DS question the answers of St. 1 and 2 should match, here the value of k differs. Can someone please help me in case I went wrong somewhere above?
