Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A souvenir stand began the day Wednesday with a ratio of 13 hats for every 7 shirts. If the stand received no new hats or shirts during the day Wednesday, and the only items that left the stand were those that were sold, did the stand end the day Wednesday with more shirts than hats?

(1) During the day Wednesday, the stand sold a total of 10 hats.

(2) The stand began the day Wednesday with an even number of hats.

This is a '2by2' question, most common type of question in GMAT math.

Attachment:

GCDS Thoughtosphere souvenir stand (20151107).jpg [ 23.05 KiB | Viewed 1689 times ]
There are 3 variables (k,b,c) but only 2 equations are given from the 2 conditions, so there is high chance (E) will be our answer.

Looking at the conditions together,

13k:7k=13:7=26:14=39:21=52:28.. From this the situations in which the numbers become even are 26:14=52:28... In all of these cases, even if 10 hats are sold, the answer becomes 'no' so this is sufficient, and the answer becomes (C).

For cases where we need 3 more equation, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

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