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At a certain store, books are sold. Books are hard cover or

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At a certain store, books are sold. Books are hard cover or

by Max@Math Revolution » Tue Feb 16, 2016 5:44 pm
At a certain store, books are sold. Books are hard cover or soft cover and hard cover books are sold at $10 each and soft cover books are sold at $6. Is the number of hard cover books are sold greater than that of soft cover books?

1) The average price sold of total books is $9
2) The number of hard cover books sold is 100


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Source: — Data Sufficiency |
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by Max@Math Revolution » Sat Feb 20, 2016 10:28 pm
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.

At a certain store, books are sold. Books are hard cover or soft cover and hard cover books are sold at $10 each and soft cover books are sold at $6. Is the number of hard cover books are sold greater than that of soft cover books?

1) The average price sold of total books is $9
2) The number of hard cover books sold is 100


In the original condition, the number of hard cover books is h and the number of soft cover books is b, which makes 2 variables. In order to match with the number of equations, you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. In fact, the answer is C.
However, this is also an integer question, which is one of the key questions.(the number of books is hidden integer). Apply the mistake type 4(A). if one con is number and the other con is ratio, it is most likely that ratio is an answer. If you look at ratio 1), (10h+6s)/(h+s)=9, 10h+6s=9h+9s, h=3s -> h>s, which is yes and sufficient.
Therefore, the answer is A.


� For cases where we need 2 more equations, such as original conditions with "2 variables", or "3 variables and 1 equation", or "4 variables and 2 equations", we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% 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 C 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, D or E.

� from con 1) and con 2), if one of the conditions is given by numbers and the other is given by ratio (percent,fraction), then the condition with ratio (percent,fraction) value has higher chance of being the answer.
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