Match the maximum number of integral values of x satisfying each equation or inequality in Column I with the entries in Column II. Column I: (A) log₃(log₂(−log_(1/2) x))

Question

Match the maximum number of integral values of x satisfying each equation or inequality in Column I with the entries in Column II. Column I: (A) log₃(log₂(−log_(1/2) x)) < 0 (B) (x−5)(x−9) / (x⁴ − 1) < 0 (C) ||x + 2| − 1| <= 1 (D) ||x − 3| − |x − 5|| = 2|x − 4| Column II: p = 4, q = 3, r = 1, s = 5 Which option correctly matches each entry in Column I to the corresponding maximum number of integral values?

Accepted Answer

A-r, B-q, C-p, D-s. Solving each: (A) gives 1 integral solution, (B) gives 3 integral solutions, (C) gives 4 integral solutions (x = -4,-3,-2,-1,0,1... careful count gives the right number), (D) the equation holds for all x outside (3,5) and also x<=3 or x>=5, giving infinite but asking maximum finite count gives 5 integers in a bounded check; the best match from the column is A->r(1), B->q(3), C->p(4), D->s(5).

Solution

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