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 a number N is decreased by p percent and then the resulting value is increased by q percent, the final result is equal to N. If both p and q are positive integers, what is the value of p ?
(1) p is not a multiple of 10.
(2) q is not a multiple of 10.
If we modify the question by multiplying both sides by 100 and dividing by n, we get (100-p)(100+q)=10,000
There are 2 variables (p,q) and one equation (100-p)(100+q)=10,000. There are 2 more equations given from the 2 conditions, so there is high chance (D) will be our answer.
From condition 1, p=98, q=4,900/ p=84, q=525. This is insufficient, as there is no unique answer.
For condition 2, p=20, q=25/ p=84, q=525. This is also insufficient for the same reason.
Looking at the condition together, however, we get p=84, q=525, which is a unique answer.
The answer is therefore (C).
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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