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.

What is the value of the three-digit number SSS if SSS is the sum of the three-digit numbers ABC and XYZ, where each letter represents a distinct digit from 0 to 9, inclusive?

1) S = 1.75 X

2) S^2 = 49zx/8

There are 6 variables (x,y,z,a,b,c), but only 2 equations are given by the 2 conditions, so there is high chance (E) will be the answer.

Looking at the conditions together,

From condition 1, S=175x/100=7x/4, S and x are all integers, and x=4, S=7.

From condition 2, S^2=49zx/8, z=sqrt (49zx/8)=7sqrt(zx/8)=7 (because S is 1-digit integer)

Condition 1 = condition 2, and the answer becomes (D).

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, 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.

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