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10 Nov 2012, 14:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (02:17) correct
27%
(02:20)
wrong
based on 343
sessions
History
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Not Attempted Yet
Two teams, working jointly, complete harvesting a plot in 4 days. In how many days would each team complete the job, working separately, if one of the teams might do the work six days earlier than the other team?
A. 2 and 8
B. 3 and 9
C. 4 and 10
D. 5 and 11
E. 6 and 12
A. 2 and 8
B. 3 and 9
C. 4 and 10
D. 5 and 11
E. 6 and 12
11 Nov 2012, 04:44
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derekgmat
First of all notice that A, B and C just cannot be correct. The time needed for any of the teams to complete the job working alone must be more than the time needed for both of them to complete the job working together. Thus, the time needed for any of the teams to complete the job alone must be more than 4. So, the answer is either D or E.
If one team need 5 and another 11 days to complete the job, then their combined rate is 1/5+1/11=16/55 job/day, but since we are told that working together they can do the job in 4 days, then their combined rate must be 1/4 job/day. So, D is not correct. Only E is left.
Answer: E.
Algebraic approach:
Say one team needs x and another x+6 days to complete the job separately.
The rate of the first team would be 1/x job/day and the rate of another would be 1/(x+6) job/day, thus their combined rate would be 1/x+1/(x+6) job/day.
We are told that working together they can do the job in 4 days, so their combined rate is 1/4 job/day.
Therefore, we have that 1/x+1/(x+6)=1/4. At this point it's better to substitute the values for x. Answer choice E works, if x=6, then 1/6+1/(6+6)=1/4.
Answer: E.
Hope it helps.
General Discussion
22 May 2013, 02:50
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Team I Team II Total Days
==================================
x y 4
x - d
- y d+6
From the table above, we draw 3 equations:
1/x + 1/y = 1/4,
1/x = 1/d &
1/y = 1/(d+6)
Equating the above, d = 6 & 12 Answer = E
==================================
x y 4
x - d
- y d+6
From the table above, we draw 3 equations:
1/x + 1/y = 1/4,
1/x = 1/d &
1/y = 1/(d+6)
Equating the above, d = 6 & 12 Answer = E
