Surds and Indices Quiz Set 007

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Question 1

If $3^x = 729$, then what is the value of $3^{x - 1}$?

 A

243.

 B

244.

 C

242.

 D

245.

Soln.
Ans: a

We can write the given expression as $3^x = 3^6$. The bases are same so powers should be same. Comparing we get x = 6. So x - 1 = 5, we get $3^5 = 243$.


Question 2

What is $({27/28})^{x - 1.5} × ({27/28})^x = ({27/28})^0.29$?

 A

0.895.

 B

1.395.

 C

2.395.

 D

2.895.

Soln.
Ans: a

We can simplify the given expression to $({27/28})^{2x - 1.5} = ({27/28})^0.29$. The bases are equal, so the powers should also be equal. Hence $2x - 1.5 = 0.29$ which gives x = 0.895.


Question 3

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".


Question 4

What is ${7^364}/{7^360}$?

 A

2401.

 B

2402.

 C

2400.

 D

2403.

Soln.
Ans: a

Simplifying, we get $7^{364 - 360}$ which equals$7^4$, or 2401.


Question 5

What is $({5/23})^0.05 × ({5/23})^x = ({5/23})^3.2$?

 A

3.15.

 B

3.65.

 C

4.65.

 D

5.15.

Soln.
Ans: a

We can simplify the given expression to $({5/23})^{0.05 + x} = ({5/23})^3.2$. The bases are equal, so the powers should also be equal. Hence $0.05 + x = 3.2$ which gives x = 3.15.


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This Blog Post/Article "Surds and Indices Quiz Set 007" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-06-24.

Posted by Parveen(Hoven),
Aptitude Trainer


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