Surds and Indices Quiz Set 002

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Wrong Answers:
Unattempted:

Question 1

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 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

If $7^{m + n} = 117649$, and $7^{m - n} = 49$, then what is m?

 A

4.

 B

4.5.

 C

5.5.

 D

6.5.

Soln.
Ans: a

By inspection, both the expressions can be simplified to $7^{m + n} = 7^6$ and $7^{m - n} = 7^2$. The bases are same, so powers should be same as well. So these expressions lead us to two simultaneous equations $m + n = 6$ and $m - n = 2$. Solving, we get $m = {6 + 2}/2$ = 4. Note: The trick in such type of questions is to keep an eye on the "bases".


Question 4

What is x if $3^x = 27$?

 A

3.

 B

4.

 C

2.

 D

5.

Soln.
Ans: a

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


Question 5

What is $6561^0.12 × 6561^0.13$?

 A

9.

 B

10.

 C

8.

 D

11.

Soln.
Ans: a

By inspection, we get $(3^8)^0.12 × (3^8)^0.13$, which equals $(3^8)^(0.12 + 0.13)$, which equals $(3^8)^0.25$, which equals $3^2$, or 9. Note: The trick in such type of questions is to keep an eye on the "bases".


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This Blog Post/Article "Surds and Indices Quiz Set 002" 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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