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 than he actually did.
(2) Last month the ratio of total bills to bills paid before their due dates was 2 : 1.
OA
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What percentage of his bills did Stanley pay before their
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To clarify the problem's intent, I've added the phrase in red to Statement 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.
(2) Last month the ratio of total bills to bills paid before their due dates was 2:1.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.
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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Target question: What percentage of his bills did Stanley pay before their due dates last month?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.
This is a great candidate for rephrasing the target question.
Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Let P = # of bills PAID before due date
Let T = TOTAL # of bills
IMPORTANT: If we can determine the ratio P/T then we can calculate the required percent. For example, if P/T = 3/4, then Stanley paid 75% of his bills.
So, we can rephrase the target question as....
REPHRASED target question: What is the value of P/T?
Statement 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.
If Stanley had paid 40 percent more bills before their due dates than he actually did, then he would have paid 1.4P bills.
We're told that this would have resulted in Stanley paying 70% (i.e., 7/10) of his bills.
So, we can write 1.4P/T = 7/10
If we take this equation and divide both sides by 1.4, we get P/T = 1/2
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT
Aside: This means that Stanley paid 50% of his bills on time.
Statement 2: Last month the ratio of total bills to bills paid before their due dates was 2 : 1
In other words, T/P = 2/1
Or we can write: P/T = 1/2
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent