Surds and Indices - Arithmetic Aptitude Questions and Answers

Share

Whatsapp
Facebook
Copy
Copy Text
Copy
Copy URL
Share as Image
As Image

If $[\frac { a } { b }]^X-1$ = $[\frac { b} { a }] ^X-3$ , then the value of x is

A.

$[\frac { 1 } { 2 } ]$

B.

1

C.

2

D.

$[\frac { 7 } { 2 } ]$

Share

Whatsapp
Facebook
Copy
Copy Text
Copy
Copy URL
Share as Image
As Image

Answer : Option C

Explanation :

Given ^{$[\frac { a } { b } ]^X-1$ = _{$[\frac {b} {a}]^X-3$}}

^{$[\frac { a } { b } ]^X-1$}^{= $[\frac { a } { b }]^(X-3)$}= $[\frac {a } { b } ]^(3-X)$

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

Share

Whatsapp
Facebook
Copy
Copy Text
Copy
Copy URL
Share as Image
As Image

Answer : Option C

Explanation :

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

0.48z = 1.40

z = $\frac { 140 } { 48 }$ = $\frac { 35 } {12 }=$ 2.9(approx.)

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

A.

25

B.

125

C.

625

D.

1625

Share

Whatsapp
Facebook
Copy
Copy Text
Copy
Copy URL
Share as Image
As Image

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

A.

0

B.

2

C.

4

D.

6

Share

Whatsapp
Facebook
Copy
Copy Text
Copy
Copy URL
Share as Image
As Image

(256)^0.16 x (256)^0.09 = ?

A.

4

B.

16

C.

64

D.

256.25

Share

Whatsapp
Facebook
Copy
Copy Text
Copy
Copy URL
Share as Image
As Image

The value of [(10)¹⁵⁰ ÃƒÆ’· (10)¹⁴⁶]

A.

1000

B.

10000

C.

100000

D.

10⁶

Share

Whatsapp
Facebook
Copy
Copy Text
Copy
Copy URL
Share as Image
As Image

Answer : Option B

Explanation :

= 10^{150 - 146}

= 10⁴

= 10000.

(10)¹⁵⁰ ÃƒÆ’· (10)¹⁴⁶ =^{$\frac { 1 0^150} { 10^146 }$}

(25)^7.5 x (5)^2.5 Ã· (125)^1.5 = 5^?

A.

8.5

B.

13

C.

16

D.

17.5

E.

None of these

Share

Whatsapp
Facebook
Copy
Copy Text
Copy
Copy URL
Share as Image
As Image

Answer : Option B

Explanation :

Let (25)^7.5 x (5)^2.5 Ã· (125)^1.5 = 5^x.

Then,(5^2)*(5)2.5/(5^3)^1.5=5X

$\frac { 5(2*7.5)*5^2.5} { 5(3*1.5) } =5^X$

5^x = 5^{(15 + 2.5 - 4.5)}

5^x = 5¹³

x = 13.

$\frac { 1 } {1+X(b-a)+X(c-a) }$ + $\frac { 1 } { 1+X(a-b)+X(c-b) }+$ $\frac { 1 } {1+X(b-c)+X(a-c)}=?$

A.

0

B.

1

C.

x^{a - b - c}

D.

None of these

Share

Whatsapp
Facebook
Copy
Copy Text
Copy
Copy URL
Share as Image
As Image

Answer : Option B

Explanation :

Given Exp $= \frac {1} { (1+ \frac { x^b } { x^a } + \frac { x^c } { x^a }) } + \frac {1} { (1+ \frac { x^a } { x^b } + \frac { x^c } { x^b }) } +\frac {1} { (1+ \frac { x^b } { x^c } + \frac { x^a } { x^c }) }$

= $\frac { X^a } {(X^a+X^b+X^c) }+$ $\frac { X^b } {(X^a+X^b+X^c) }+$ $\frac { X^c } {(X^a+X^b+X^c) }$

= $\frac { (X^a+X^b+X^c)} {€‹€‹(X^a+X^b+X^c )}$

=1

(0.04)^-1.5 = ?

A.

25

B.

125

C.

250

D.

625

Share

Whatsapp
Facebook
Copy
Copy Text
Copy
Copy URL
Share as Image
As Image