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

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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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

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

GMAT assassins aren't born, they're made,
Rich