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Aptitudes and mathematical kill:

Quantitative  aptitude includes operations related to logic and expressions whereas numerical ability(mathematical skill) relates to mathematical calculation. A particular problem can be solved by both quantitative aptitude and numerical ability which depends on the skill set of the solver.
Let us suppose a simple problem where it is given to compute (M^2-N^2)/(M-N).and it is given M=1 and N=2.
there are two possible ways to work this out...
1.If we put the respective values of M and N we get (1^2-2^2)/(1-2) which yields 3 as the answer. This approach is from numerical ability view point
2.Or we may solve it as 
(M^2-N^2)/(M-N)
=M+N ..substituting the values of M and N we get 3.This approach comprises of Quantitative aptitude first and then numerical ability
 
Numerical ability can also be under the set of quantitative aptitude. The reason is for quantitative aptitude we require both logical thinking and numerical aptitude.
Problems on numbers, profit and loss, work, interest, falls under numerical ability
Problems on progressions, calculus, probability, logarithm falls under quantitative aptitude where numerical ability is required to some extent

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