Data Sufficiency

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.


If K is a positive 3 digit integer, what is value of hundreds digit of K?

1. Hundredth digit of K+150 is 4
2. Tens digit of K+25 is 7

Transforming the original condition and the question, we have k=100a+10b+c and thus there are 4 variables (k,a,b,c), and 1 equation (k=100a+10b+c). Therefore we need 3 more equations to match the number of variables and equations. since there is 1 each in 1) and 2), E has high probability of being the answer.

Using both 1) & 2) together, k=254, 345 thus k has value starting with 2 and 3. The answer is not unique, therefore the conditions are not sufficient. Thus the answer is E.


Normally for cases where we need 3 more equations, 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 E has a high chance of being the answer (especially about 90% of 2by2 questions where there are more than 3 variables), which is why we attempt to solve the question using 1) and 2) together. Here, there is 80% chance that E is the answer, while C has 15% 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 E is most likely to be the answer according to DS definition, we solve the question assuming E would be our answer hence using ) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

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