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Let set A={all the integer between 1 and k inclusively such

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Let set A={all the integer between 1 and k inclusively such

by Max@Math Revolution » Sun Feb 21, 2016 9:09 pm
Let set A={all the integer between 1 and k inclusively such that k is less than 50}. If m is '0s' number A and n is '4s' number in set A, n=?

1) n>m
2) n=m+11


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Source: — Data Sufficiency |
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by Max@Math Revolution » Wed Feb 24, 2016 9:08 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.

Let set A={all the integer between 1 and k inclusively such that k is less than 50}. If m is '0s' number A and n is '4s' number in set A, n=?

1) n>m
2) n=m+11


In the original condition, there are 2 variables(m,n), which should match with the number of equations. So you need 2 equations. For 1) 1 equation for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), just only for 2), n>m is valid and k=49 when substituting, which makes m=4, n=15. Thus, it is unique and sufficient. Then, the answer is B. This kind of integer question, one of the key questions, is a very critical question, which can lead you to score 50-51.
Therefore, the answer is B.


� 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.
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