Data Sufficiency

In a retail store, the average (arithmetic mean) sale for month M was d dollars. Was the average (arithmetic mean) sale for month J at least 20 percent higher than that for month M?
(1) For month M, total revenue from sales was $3,500.
(2) For month J, total revenue from sales was $6,000.

In the solution, it is mentioned that

This statement provides no information as to the number of sales so there is no way to determine the size of average scale.

My confusion is whether the fact that no of days of a month can be 28 or 30 or 31 is the main culprit or any other reason is present because of which we are not able to solve the problem.

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Remember equal number of variables and independent equations ensures a solution.

In a retail store, the average (arithmetic mean) sale for month M was d dollars. Was the average (arithmetic mean) sale for month J at least 20 percent higher than that for month M?
(1) For month M, total revenue from sales was $3,500.
(2) For month J, total revenue from sales was $6,000.

from the original condition we can acquire the below table, a typical 2by2 question in GMAT test.


There are 4 variables (a,b,c,d) therefore we need 4 equations to match the number of variables and equations. Since there is 1 each in 1) and 2), there is high probability that E is the answer. But since the number of days in a month is 28, 29, 30 or 31, month J avg sale has the least value and the greatest avg sale is 6,000/31=193, 3,500/28=125 thus 125*1.2=150 and 193>150. The answer is yes, therefore the answer is C.

Normally for cases where we need 2 more equation, such as original conditions with 2 variable, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

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Mechmeera wrote:In a retail store, the average (arithmetic mean) sale for month M was d dollars. Was the average (arithmetic mean) sale for month J at least 20 percent higher than that for month M?
(1) For month M, total revenue from sales was $3,500.
(2) For month J, total revenue from sales was $6,000.

In the solution, it is mentioned that

This statement provides no information as to the number of sales so there is no way to determine the size of average scale.

My confusion is whether the fact that no of days of a month can be 28 or 30 or 31 is the main culprit or any other reason is present because of which we are not able to solve the problem.

That's definitely part of it, but I don't think the question is asking for the average DAILY sale, but the average sale itself.

For instance, suppose that in Month M we sell 100 items. Then d = 3500/100 = $35. Now suppose that in Month J we only sell 20 items, but they're all very expensive. Then the average J sale = 6000/20 = $300.

But of course we don't know either of these numbers of items, so we can't answer.