Surds and Indices Quiz Set 008

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Question 1

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.


Question 2

If $√65$ is approximately $8$, then what is $65^3.5$?

 A

2097152.

 B

2097153.

 C

2097151.

 D

2097154.

Soln.
Ans: a

Since $√x = x^{1/2}$, we can see that $65^3.5$ is same as $(√65)^7$ which gives $8^7$ = 2097152.


Question 3

What is ${4^513}/{4^511}$?

 A

16.

 B

17.

 C

15.

 D

18.

Soln.
Ans: a

Simplifying, we get $4^{513 - 511}$ which equals$4^2$, or 16.


Question 4

If $√47$ is approximately $6$, then what is $47^2$?

 A

1296.

 B

1297.

 C

1295.

 D

1298.

Soln.
Ans: a

Since $√x = x^{1/2}$, we can see that $47^2$ is same as $(√47)^4$ which gives $6^4$ = 1296.


Question 5

If $4^{m + n} = 16384$, and $4^{m - n} = 256$, then what is m?

 A

5.5.

 B

6.0.

 C

7.0.

 D

8.0.

Soln.
Ans: a

By inspection, both the expressions can be simplified to $4^{m + n} = 4^7$ and $4^{m - n} = 4^4$. The bases are same, so powers should be same as well. So these expressions lead us to two simultaneous equations $m + n = 7$ and $m - n = 4$. Solving, we get $m = {7 + 4}/2$ = 5.5. 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 008" 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


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