sana.noor wrote:By what percent is the time taken by 12 men to complete a particular task greater than the time taken by 10 women to complete the same task?
(1) The time taken by 6 men to complete a particular task is 25% more than the time taken by 5 women to complete the same task.
(2) The time taken by 10 men to complete a particular task is 10% less than the time taken by 6 women to complete the same task.
OA is D
Time and rate are RECIPROCALS.
To determine (time for 12 men) : (time for 10 women), we need to know (rate for 12 men) : (rate for 10 women).
In other words, we need to know the RELATIVE SPEEDS of the men and the women.
Since each statement on its own gives the relative speeds of the men and the women, each is sufficient.
The correct answer is
D.
One way to verify that each statement is sufficient is to try TWO CASES.
Statement 1: The time taken by 6 men to complete a particular task is 25% more than the time taken by 5 women to complete the same task.
Case 1:
Let the rate per woman = 6 units per day.
Thus, the rate for 5 women = 30 units per day.
Let the time for 5 women = 4 days.
Task = r*t = 30*4 = 120 units.
Time for 6 men = 4 + .25(4) = 5 days.
Thus, the rate for 6 men = w/t = 120/5 = 24 units per day.
Thus, the rate per man = 24/6 = 4 units per day.
In this case:
(rate per man) : (rate per woman) = 4:6 = 2:3.
Case 2:
Let the rate per woman = 12 units per day.
Thus, the rate for 5 women = 60 units per day.
Let the time for 5 women = 12 days.
Task = r*t = 60*12 = 720 units.
Time for 6 men = 12 + .25(12) = 15 days.
Thus, the rate for 6 men = w/t = 720/15 = 48 units per day.
Thus, the rate per man = 48/6 = 8 units per day.
In this case:
(rate per man) : (rate per woman) = 8:12 = 2:3.
Since the rate ratio is the same in each case, SUFFICIENT.
Statement 2: The time taken by 10 men to complete a particular task is 10% less than the time taken by 6 women to complete the same task.
Case 1:
Let the rate per woman = 3 units per day.
Thus, the rate for 6 women = 18 units per day.
Let the time for 5 women = 10 days.
Task = r*t = 18*10 = 180 units.
Time for 10 men = 10 - .1(10) = 9 days.
Thus, the rate for 10 men = w/t = 180/9 = 20 units per day.
Thus, the rate per man = 20/10 = 2 units per day.
In this case:
(rate per man) : (rate per woman) = 2:3.
Case 2:
Let the rate per woman = 6 units per day.
Thus, the rate for 6 women = 36 units per day.
Let the time for 5 women = 100 days.
Task = r*t = 36*100 = 3600 units.
Time for 10 men = 100 - .1(10) = 90 days.
Thus, the rate for 10 men = w/t = 3600/90 = 40 units per day.
Thus, the rate per man = 40/10 = 4 units per day.
In this case:
(rate per man) : (rate per woman) = 4:6 = 2:3.
Since the rate ratio is the same in each case, SUFFICIENT.
The correct answer is
D.
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