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 n is a positive integer and r is the remainder when 4+7n is divided by 3 what is the value of r ?
(1) n+1 is divisible by 3
(2) n >20
We solve remainder problems by directly substituting in values. Looking at the original condition, we can see that there is only 1 variable (n) We therefore need 1 equation, and 2 equations are given, so there is high chance (D) will be our answer.
From condition 1, n+1=3t(t is a positive integer), So n=3t-1=2,5,8,11,.......(directly substituted) Then 4+7n=18, 39, 60... All these values divided by 3 leave remainders of 0, so this is a sufficient condition.
For condition 2, n=21,22 and 4+7n=151, 158, and 151=3*50+1, so the remainder is 1, but for 158=3*52+2, the remainder is 2, and this is not unique, so this condition is insufficient and therefore the answer is (A).
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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