# Surds and Indices Quiz Set 001

### Question 1

If \$p^q = 512\$, then what could be \$(p - 1)^(q + 1)\$?

A

2401.

B

2402.

C

2400.

D

2403.

Soln.
Ans: a

By inspection we can see that p = 8, q= 3. So \$(8 - 1)^(3 + 1)\$ will be \$7^4\$, i.e., 2401.

### Question 2

What is \$24^0.06 × 24^x = 24^2.3\$?

A

2.24.

B

2.74.

C

3.74.

D

4.24.

Soln.
Ans: a

We can simplify the given expression to \$24^{0.06 + x} = 24^2.3\$. The bases are equal, so the powers should also be equal. Hence \$0.06 + x = 2.3\$ which gives x = 2.24.

### Question 3

What is \$({33/18})^0.18 × ({33/18})^x = ({33/18})^0.3\$?

A

0.12.

B

0.62.

C

1.62.

D

2.12.

Soln.
Ans: a

We can simplify the given expression to \$({33/18})^{0.18 + x} = ({33/18})^0.3\$. The bases are equal, so the powers should also be equal. Hence \$0.18 + x = 0.3\$ which gives x = 0.12.

### Question 4

If \$p^q = 36\$, then what could be \$(p - 1)^(q + 1)\$?

A

125.

B

126.

C

124.

D

127.

Soln.
Ans: a

By inspection we can see that p = 6, q= 2. So \$(6 - 1)^(2 + 1)\$ will be \$5^3\$, i.e., 125.

### Question 5

What is \$4096^0.15 × 4096^0.1\$?

A

8.

B

9.

C

7.

D

10.

Soln.
Ans: a

By inspection, we get \$(2^12)^0.15 × (2^12)^0.1\$, which equals \$(2^12)^(0.15 + 0.1)\$, which equals \$(2^12)^0.25\$, which equals \$2^3\$, or 8. Note: The trick in such type of questions is to keep an eye on the "bases".

This Blog Post/Article "Surds and Indices Quiz Set 001" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-05-17.

Posted by Parveen(Hoven),
Aptitude Trainer