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.
x and y are positive integers such that x=8y+12, what is the greatest common divisor of x and y?
(1) X=12u, where u is an integer.
(2) Y=12z, where z is an integer.
There are 2 variables (x,y), one equation (x=8y+12), and 2 more equations are given from the 2 conditions; there is high chance (D) will be our answer.
From condition 1, 12u=8y+12, 8y=12(u-1), 2y=3(u-1), from x=4(2y+3), this has to be a multiple of y=3, but x is a multiple of 4, so we cannot decide the GCD; this is insufficient.
From condition 2, x=8(12z)+12=12(8z+1), z cannot equal 8z+1, the GCD(x,y)=12, so this is sufficient, and the answer becomes (B).
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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