Let f(x) be defined for any positive integer x greater than 2 as the sum of all prime numbers less than x. For example, f(4)=2+3=5 and f(8)=2+3+5+7=17. What is the value of f(86)−f(82)? (A) 3 (B) 4 (C) 47 (D) 59 (E) 83

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answer: the correct option is d.

explanation:

it is given that the triangle j'k'l' shown on the grid below is a dilation of triangle jkl using the origin as the center of dilation.

from the given graph it is noticed that k(4,8) and k'(2,4). let origin is defined by o and scale factor is defined by k, then

    (1)

distance formula,

put these values in equation (1).

therefore scale factor is     and option d is correct.