Surds and Indices Quiz Set 005

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Question 1

If $2^{m + n} = 32$, and $2^{m - n} = 4$, then what is m?

 A

3.5.

 B

4.0.

 C

5.0.

 D

6.0.

Soln.
Ans: a

By inspection, both the expressions can be simplified to $2^{m + n} = 2^5$ and $2^{m - n} = 2^2$. The bases are same, so powers should be same as well. So these expressions lead us to two simultaneous equations $m + n = 5$ and $m - n = 2$. Solving, we get $m = {5 + 2}/2$ = 3.5. Note: The trick in such type of questions is to keep an eye on the "bases".


Question 2

What is ${4^584}/{4^581}$?

 A

64.

 B

65.

 C

63.

 D

66.

Soln.
Ans: a

Simplifying, we get $4^{584 - 581}$ which equals$4^3$, or 64.


Question 3

If $√4489 = 67$, then what is the value of $√44.89$ + $√0.4489$ + $√0.004489$ + $√0.00004489$?

 A

7.4437.

 B

7.9437.

 C

8.9437.

 D

8.4437.

Soln.
Ans: a

We can see that $√44.89$ = 6.7, $√0.4489$ = 0.67, $√0.004489$ = 0.067, $√0.00004489$ = 0.0067. Adding, we get 7.4437 as the answer.


Question 4

What is the value of x if $(64)^3 × 2^3$ ÷ $16^1.5$ = $2^x$?

 A

15.

 B

21.

 C

27.

 D

33.

Soln.
Ans: a

Simplifying, we get $(2^6)^3 × 2^3$ ÷ $(2 ^ 4)^1.5$ = $2^x$, which simplifies to $2^18 × 2^3$ ÷ $2^6$ = $2^x.$ Equating the powers x = 18 + 3 - 6 = 15.


Question 5

If $13^1.1 = p, and 13^2.5 = q$ and $p^m = q^4$ then what is the value of m?

 A

9.09.

 B

9.33.

 C

9.23.

 D

9.63.

Soln.
Ans: a

Substituting in $p^m = q^4$, we get $13^{1.1m} = 13^{2.5 × 4}$. Bases are same so powers should be same. Hence, $1.1m = {2.5 × 4}$, which gives m = 9.09.


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This Blog Post/Article "Surds and Indices Quiz Set 005" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2017-08-12.

Posted by Parveen(Hoven),
Aptitude Trainer


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