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Surds and Indices - General Aptitude

Q1:

(25)7.5 x (5)2.5 ÷ (125)1.5 = 5?

A 8.5

B 13

C 16

D 17.5

E None of these

ANS:B - 13

Let (25)7.5 x (5)2.5 ÷ (125)1.5 = 5x.

Then, (52)7.5 x (5)2.5 = 5x
(53)1.5
5(2 x 7.5) x 52.5 = 5x
5(3 x 1.5)
515 x 52.5 = 5x
54.5
 5x = 5(15 + 2.5 - 4.5)  5x = 513  x = 13.