To clarify the problem's intent, I've added the phrase in red to Statement 1:
canbtg wrote:What percentage of his bills did Stanley pay before their due dates last month?
(1) Last month Stanley would have paid 70 percent of his bills before their due dates if he had paid 40 percent more bills before their due dates than he actually did.
(2) Last month the ratio of total bills to bills paid before their due dates was 2 : 1.
(2) Last month the ratio of total bills to bills paid before their due dates was 2:1.
Case 1: Total number of bills = 20, bills paid before their due dates = 10.
In this case, (paid before due date)/(total bills) = 10/20 = 1/2 = 50%.
Case 2: Total number of bills = 40, bills paid before their due dates = 20.
In this case, (paid before due date)/(total bills) = 20/40 = 1/2 = 50%.
Since the percentage in each case is the same, SUFFICIENT.
(1) Last month Stanley would have paid 70 percent of his bills before their due dates if he had paid 40 percent more bills before their due date than he actually did.
Check whether Cases 1 and 2 also satisfy statement 1.
Case 1: Total number of bills = 20, bills paid before their due dates = 10.
Increased by 40%, bills paid before their due dates = 10 + 40% of 10 = 10+4 = 14.
(increased number of bills paid before their due dates)/(total bills) = 14/20 = 70/100 = 70%.
The resulting percentage is 70%, as required by statement 1.
Case 2: Total number of bills = 40, bills paid before their due dates = 20.
Increased by 40%, bills paid before their due dates = 20 + 40% of 20 = 20+8 = 28.
(increased number of bills paid before their due dates)/(total bills) = 28/40 = 14/20 = 70/100 = 70%.
The resulting percentage is 70%, as required by statement 1.
Since Cases 1 and 2 also satisfy Statement 1, Statement 1 implies the same ratio as described in Statement 2:
(total bills)/(bills paid before their due dates) = 2:1.
Thus, like Statement 2, Statement 1 implies that 50% of the bills were paid on time.
SUFFICIENT.
The correct answer is
D.
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