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01 May 2026, 07:16
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
74% (02:40) correct
26%
(02:39)
wrong
based on 80
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On the last day of a certain month, Casey tallies how many cars she has sold so far this year. If she sells 20 cars next month, her average monthly sales for the year to date will be 17. On the other hand, if she sells 20 cars in each of the next two months, her average monthly sales for the year to date will be 17.5. What is today’s date?
(A) January 31
(B) February 28
(C) March 31
(D) April 30
(E) May 31
(A) January 31
(B) February 28
(C) March 31
(D) April 30
(E) May 31
01 May 2026, 09:27
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On the last day of a certain month, Casey tallies how many cars she has sold so far this year. If she sells 20 cars next month, her average monthly sales for the year to date will be 17. On the other hand, if she sells 20 cars in each of the next two months, her average monthly sales for the year to date will be 17.5.
What is today’s date?
Algebraic Approach
Let the number of months that have passed so far be M.
Total for Past Months and Next 1 month + 20 = Total for Past Months and Next 2 Months
17(M + 1) + 20 = 17.5(M + 2)
17M + 37 = 17.5M + 35
2 = .5M
4 = M
The fourth month is April.
Alternative Approach
Adding 20 sales for the second month ahead to the previous total increased the average from 17 sales per month to 17.5, an increase of 0.5.
So, the difference of 3 between 17 and 20 must have been divided over 6 months since 0.5 = 3/6.
Thus, after 2 more months, she will have sold for 6 months total.
So, 4 months have passed so far.
The fourth month is April.
(A) January 31
(B) February 28
(C) March 31
(D) April 30
(E) May 31
Correct answer: D
What is today’s date?
Algebraic Approach
Let the number of months that have passed so far be M.
Total for Past Months and Next 1 month + 20 = Total for Past Months and Next 2 Months
17(M + 1) + 20 = 17.5(M + 2)
17M + 37 = 17.5M + 35
2 = .5M
4 = M
The fourth month is April.
Alternative Approach
Adding 20 sales for the second month ahead to the previous total increased the average from 17 sales per month to 17.5, an increase of 0.5.
So, the difference of 3 between 17 and 20 must have been divided over 6 months since 0.5 = 3/6.
Thus, after 2 more months, she will have sold for 6 months total.
So, 4 months have passed so far.
The fourth month is April.
(A) January 31
(B) February 28
(C) March 31
(D) April 30
(E) May 31
Correct answer: D
adipisfugat
06 Jun 2026, 01:13
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Let m be the number of months that have passed so far this year, and let S be the total number of cars Casey has sold so far.
Clue 1: If she sells 20 cars next month
• Months passed: The months will increase by 1, so it becomes m + 1.
• Total cars sold: Her total sales will increase by 20, so it becomes S + 20.
• The average: We are told her average monthly sales will be 17.
Since Average = (Total Sales) / Months, we can write:
(S + 20) / (m + 1) = 17
If we multiply both sides by (m + 1), we get:
S + 20 = 17(m + 1)
S + 20 = 17m + 17
S = 17m - 3 --- (Equation 1)
Clue 2: If she sells 20 cars in each of the next two months
• Months passed: The months will increase by 2, so it becomes m + 2.
• Total cars sold: She sells 20 cars twice (20 + 20 = 40), so her total sales become S + 40.
• The average: We are told her average monthly sales will be 17.5.
Using the average formula again:
(S + 40) / (m + 2) = 17.5
If we multiply both sides by (m + 2), we get:
S + 40 = 17.5(m + 2)
S + 40 = 17.5m + 35
S = 17.5m - 5 --- (Equation 2)
Step 3: Find the number of months (m)
Since both equations equal S, we can set them equal to each other:
17m - 3 = 17.5m - 5
Let's move the m's to one side and the numbers to the other:
5 - 3 = 17.5m - 17m
2 = 0.5m
To find m, divide 2 by 0.5 (which is the same as multiplying by 2):
m = 4
Conclusion
The value m = 4 means that 4 months have passed so far this year.
The first 4 months of the year are January, February, March, and April. Since Casey is tallying her sales on the last day of that 4th month, today must be the last day of April.
Correct Answer: (D) April 30
Clue 1: If she sells 20 cars next month
• Months passed: The months will increase by 1, so it becomes m + 1.
• Total cars sold: Her total sales will increase by 20, so it becomes S + 20.
• The average: We are told her average monthly sales will be 17.
Since Average = (Total Sales) / Months, we can write:
(S + 20) / (m + 1) = 17
If we multiply both sides by (m + 1), we get:
S + 20 = 17(m + 1)
S + 20 = 17m + 17
S = 17m - 3 --- (Equation 1)
Clue 2: If she sells 20 cars in each of the next two months
• Months passed: The months will increase by 2, so it becomes m + 2.
• Total cars sold: She sells 20 cars twice (20 + 20 = 40), so her total sales become S + 40.
• The average: We are told her average monthly sales will be 17.5.
Using the average formula again:
(S + 40) / (m + 2) = 17.5
If we multiply both sides by (m + 2), we get:
S + 40 = 17.5(m + 2)
S + 40 = 17.5m + 35
S = 17.5m - 5 --- (Equation 2)
Step 3: Find the number of months (m)
Since both equations equal S, we can set them equal to each other:
17m - 3 = 17.5m - 5
Let's move the m's to one side and the numbers to the other:
5 - 3 = 17.5m - 17m
2 = 0.5m
To find m, divide 2 by 0.5 (which is the same as multiplying by 2):
m = 4
Conclusion
The value m = 4 means that 4 months have passed so far this year.
The first 4 months of the year are January, February, March, and April. Since Casey is tallying her sales on the last day of that 4th month, today must be the last day of April.
Correct Answer: (D) April 30
