Surds and Indices Quiz Set 013

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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 $31^3.1 × 31^x = 31^1.8$?

 A

-1.3.

 B

-0.8.

 C

0.2.

 D

0.7.

Soln.
Ans: a

We can simplify the given expression to $31^{3.1 + x} = 31^1.8$. The bases are equal, so the powers should also be equal. Hence $3.1 + x = 1.8$ which gives x = -1.3.


Question 3

If $√7744 = 88$, then what is the value of $√77.44$ + $√0.7744$ + $√0.007744$ + $√0.00007744$?

 A

9.7768.

 B

10.2768.

 C

11.2768.

 D

10.7768.

Soln.
Ans: a

We can see that $√77.44$ = 8.8, $√0.7744$ = 0.88, $√0.007744$ = 0.088, $√0.00007744$ = 0.0088. Adding, we get 9.7768 as the answer.


Question 4

If $√4761 = 69$, then what is the value of $√47.61$ + $√0.4761$ + $√0.004761$ + $√0.00004761$?

 A

7.6659.

 B

8.1659.

 C

9.1659.

 D

8.6659.

Soln.
Ans: a

We can see that $√47.61$ = 6.9, $√0.4761$ = 0.69, $√0.004761$ = 0.069, $√0.00004761$ = 0.0069. Adding, we get 7.6659 as the answer.


Question 5

If $p^q = 512$, then what could be $(p - 1)^(q + 1)$?

 A

2401.

 B

2402.

 C

2400.

 D

2403.

Soln.
Ans: a

By inspection we can see that p = 8, q= 3. So $(8 - 1)^(3 + 1)$ will be $7^4$, i.e., 2401.


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This Blog Post/Article "Surds and Indices Quiz Set 013" 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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