Surds and Indices Quiz Set 012

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Question 1

If $4^{m + n} = 4096$, and $4^{m - n} = 64$, then what is m?

 A

4.5.

 B

5.0.

 C

6.0.

 D

7.0.

Soln.
Ans: a

By inspection, both the expressions can be simplified to $4^{m + n} = 4^6$ and $4^{m - n} = 4^3$. The bases are same, so powers should be same as well. So these expressions lead us to two simultaneous equations $m + n = 6$ and $m - n = 3$. Solving, we get $m = {6 + 3}/2$ = 4.5. Note: The trick in such type of questions is to keep an eye on the "bases".


Question 2

What is $81^0.11 × 81^0.14$?

 A

3.

 B

4.

 C

2.

 D

5.

Soln.
Ans: a

By inspection, we get $(3^4)^0.11 × (3^4)^0.14$, which equals $(3^4)^(0.11 + 0.14)$, which equals $(3^4)^0.25$, which equals $3^1$, or 3. Note: The trick in such type of questions is to keep an eye on the "bases".


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

What is x if $8^x = 512$?

 A

3.

 B

4.

 C

2.

 D

5.

Soln.
Ans: a

We can write the given expression as $8^x = 8^3$. The bases are same so powers should be same. Comparing we get x = 3.


Question 5

What is ${7^499}/{7^496}$?

 A

343.

 B

344.

 C

342.

 D

345.

Soln.
Ans: a

Simplifying, we get $7^{499 - 496}$ which equals$7^3$, or 343.


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This Blog Post/Article "Surds and Indices Quiz Set 012" 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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