surds and indices aptitude questions – Free Online Questions and Answers

(17)^3.5 x (17)^? = 17⁸

A.	2.29	B.	2.75
C.	4.25	D.	4.5

Answer: Option D

Explanation:

Let (17)^3.5 x (17)^x = 17⁸.

Then, (17)^{3.5 + x} = 17⁸.

3.5 + x = 8

x = (8 – 3.5)

x = 4.5

If		a		x – 1	=		b		x – 3	, then the value of x is:
		b					a

Answer: Option C

Explanation:

Given	a		x – 1	=		b		x – 3
	b					a

x – 1

-(x – 3)

(3 – x)

x – 1 = 3 – x

2x = 4

x = 2.

Given that 10^0.48 = x, 10^0.70 = y and x^z = y², then the value of z is close to:

A.	1.45	B.	1.88
C.	2.9	D.	3.7

Answer: Option C

Explanation:

x^z = y² 10^(0.48z) = 10^{(2 x 0.70)} = 10^1.40

0.48z = 1.40

z =	140	=	35	= 2.9 (approx.)
	48		12

If 5^a = 3125, then the value of 5^{(a – 3)} is:

A.	25	B.	125
C.	625	D.	1625

Answer: Option A

Explanation:

5^a = 3125 5^a = 5⁵

a = 5.

5^{(a – 3)} = 5^{(5 – 3)} = 5² = 25.

If 3^{(x – y)} = 27 and 3^{(x + y)} = 243, then x is equal to:

A.	0	B.	2
C.	4	D.	6

Answer: Option C

Explanation:

3^{x – y} = 27 = 3³ x – y = 3 ….(i)

3^{x + y} = 243 = 3⁵ x + y = 5 ….(ii)

On solving (i) and (ii), we get x = 4.