MathRevolution
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 r and s are each greater than 0, is (r + n)/(s + n) > r/s?
(1) n > 0
(2) r < s
If we modify the question, we want to know whether (r+n)/(s+n)>r/s, so s(r+n)>r(s+n), sr+sn>rs+rn, and sn-rn>0, and ultimately we want to know whether (s-r)n>0.
There are 3 variables (r,s,n) and we are given 2 equations from the 2 conditions, making (E) our likely answer.
Looking at the conditions together, the answer to the question becomes 'yes' 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.
Hi,
MathRevolutionIn text highlighted in
Blue , I don't think without knowing about the sign of variable n we can cross multiply. could you please explain?