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.
For any positive integer x, the 2-height of x is defined to be the greatest non-negative integer n such that 2^n is a factor of x. If k and m are positive integers, is the 2-height of k greater than the 2-height of m?
1. k>m
2. k/m is an even integer
2-height is a unique type of question in gmat math. In other words, 40=(2^3)5, therefore the 2 height of 40 is 3 while 16=2^4 thus the 2 height of 16 is 4. Therefore, greater number does not guarantee greater 2 height.
In the original condition, we have 2 variables (k,m) and we need 2 equations to match the number of variables and equations. Since there is 1 each in 1) and 2), there is high probability that C is the answer. Using both 1) & 2), from k/m=2integer we get k=(2integer)m, therefore k always has 2 on top of m. Thus the 2height of k is always 1 greater than that of m, and C becomes the answer. The key question is the integer question, therefore we should apply common mistake type 4(A) and therefore using just 2) already gives us the answer. 2 height of k is 1 greater than that of m. Therefore the answer is B.
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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