@master_shifu said in Question Bank - 100 Algebra Questions From Previous CAT Papers (Solved): Q17. (CAT 2003)If 1/3 log_3M + 3 log_3N = 1 + log_0.0008 (5), then:(1) M^9 = N/9(2) N^9 = 9/M(3) M^3 = 3/N(4) N^9 = 3/M Correction:log_0.008(5)

@swati-jha Thanks Swati. Corrected the solution. Mistake was in distance values and is now clean, hopefully :) Happy learning!

f(7)^2 - f(6)^2 = 517 (f(7) + f(6)) (f(7) - f(6)) = 517 = 11 x 47 As 11 and 47 cannot be further factorized and f(7) or f(6) should be natural numbers, we can say f(7) + f(6) = 47 (Largest prime factor should come from their sum) f(7) - f(6) = 11 (smallest prime factor should come from their difference) solving, f(7) = 29 and f(6) = 18 f(10) = f(8) + f(9) = f(7) + f(6) + f(7) + f(8) = f(7) + f(6) + f(7) + f(7) + f(6) 3f(7) + 2f(6) = 3 x 29 + 2 x 18 = 123.