Surds and Indices Quiz Set 001

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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".


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Creative Commons License
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 2017-04-07.

Posted by Parveen(Hoven),
Aptitude Trainer


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