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A and B can complete a task in 20 days. B and C can complete

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A and B can complete a task in 20 days. B and C can complete

by BTGmoderatorLU » Wed Sep 05, 2018 1:42 pm

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Source: e-GMAT

A and B can complete a task in 20 days. B and C can complete the same task in 30 days. If A and C can complete the task in 40 days, arrange the efficiencies of A, B, and C in descending order.

A. A>B>C
B. A>C>B
C. B>A>C
D. B>C>A
E. C>A>B

The OA is C.
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by Jay@ManhattanReview » Wed Sep 05, 2018 8:35 pm
BTGmoderatorLU wrote:Source: e-GMAT

A and B can complete a task in 20 days. B and C can complete the same task in 30 days. If A and C can complete the task in 40 days, arrange the efficiencies of A, B, and C in descending order.

A. A>B>C
B. A>C>B
C. B>A>C
D. B>C>A
E. C>A>B

The OA is C.
We have

1. A and B can complete a task in 20 days.
2. B and C can complete the same task in 30 days.
3. A and C can complete the task in 40 days.

From (1) and (2), we see that when A is replaced by C, the number of days to complete the same task increases (30 - 20 = 10 days more). This implies that A is more efficient than C. A > C.

From (1) and (3), we see that when B is replaced by C, the number of days to complete the same task increases (40 - 20 = 20 days more). This implies that B is more efficient than C. B > C.

Similarly, From (2) and (3), we see that when B is replaced by A, the number of days to complete the same task increases (40 - 30 = 10 days more). This implies that B is more efficient than A. B > A.

From A > C, B > C, and B > A, we see that B > A > C.

The correct answer: C

Hope this helps!

-Jay
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by GMATGuruNY » Thu Sep 06, 2018 4:27 am
BTGmoderatorLU wrote:Source: e-GMAT

A and B can complete a task in 20 days. B and C can complete the same task in 30 days. If A and C can complete the task in 40 days, arrange the efficiencies of A, B, and C in descending order.

A. A>B>C
B. A>C>B
C. B>A>C
D. B>C>A
E. C>A>B
Alternate approach:

Let the job = 240 units.
Since A+B take 20 days to complete the 240-unit job, A+B = 240/20 = 12 units per day.
Since B+C take 30 days to complete the 240-unit job, B+C = 240/30 = 8 units per day.
Since A+C take 40 days to complete the 240-unit job, A+C = 240/40 = 6 units per day.

Thus:

(A+B) - (B+C) = 12-8.
A-C = 4 units per day.

(A-C) + (A+C) = 4+6
2A = 10
A = 5 units per day.

Since A-C = 4 units per day, and A = 5 units per day, C = 1 unit per day.
Since B+C = 8 units per day, and C = 1 unit per day, B = 7 units per day.
Since B=7, A=5 and C=1, B>A>C.

The correct answer is C.
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by Scott@TargetTestPrep » Sat Sep 29, 2018 5:09 pm
BTGmoderatorLU wrote:Source: e-GMAT

A and B can complete a task in 20 days. B and C can complete the same task in 30 days. If A and C can complete the task in 40 days, arrange the efficiencies of A, B, and C in descending order.

A. A>B>C
B. A>C>B
C. B>A>C
D. B>C>A
E. C>A>B
Since A and B can complete a task in 20 days but B and C can complete the same task in 30 days, A must be more efficient than C.

Since B and C can complete the same task in 30 days but A and C can complete the task in 40 days, B must be more efficient than A.

Therefore, their efficiencies in descending order is B, followed by A, followed by C.

Answer: C

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by [email protected] » Sun Sep 30, 2018 3:26 pm
Hi All,

We're told that A and B can complete a task in 20 days. B and C can complete the same task in 30 days and A and C can complete the task in 40 days. We're asked to arrange the 'efficiencies' of A, B, and C in descending order. This is actually more of a 'logic question' than a 'math question' - and you can solve it with some basic logical comparisons.

To start, we know:
A and B take 20 days to do a task
B and C take 30 days to do a task
Thus, 'swapping' A for C makes the job take 10 days LONGER, meaning that A is MORE efficient than C (re: A > C).

Next, we know:
A and B take 20 days to do a task
A and C take 40 days to do a task
Thus, 'swapping' B for C makes the job take 20 days LONGER, meaning that B is MORE efficient than C (re: B > C).

Finally, we know:
B and C take 30 days to do a task
A and C take 40 days to do a task
Thus, 'swapping' B for A makes the job take 10 days LONGER, meaning that B is MORE efficient than A (re: B > A).

Combining the three inequalities, we have B > A > C

Final Answer: C

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