Surds and Indices Quiz Set 011

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Question 1

What is the value of x if $(625)^1.5 × 5^5$ ÷ $25^2.5$ = $5^x$?

 A

6.

 B

10.

 C

14.

 D

18.

Soln.
Ans: a

Simplifying, we get $(5^4)^1.5 × 5^5$ ÷ $(5 ^ 2)^2.5$ = $5^x$, which simplifies to $5^6 × 5^5$ ÷ $5^5$ = $5^x.$ Equating the powers x = 6 + 5 - 5 = 6.


Question 2

If $8^{m + n} = 2097152$, and $8^{m - n} = 4096$, 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 $8^{m + n} = 8^7$ and $8^{m - n} = 8^4$. 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".


Question 3

If $p^q = 36$, then what could be $(p - 1)^(q + 1)$?

 A

125.

 B

126.

 C

124.

 D

127.

Soln.
Ans: a

By inspection we can see that p = 6, q= 2. So $(6 - 1)^(2 + 1)$ will be $5^3$, i.e., 125.


Question 4

If $√54$ is approximately $7$, then what is $54^1.5$?

 A

343.

 B

344.

 C

342.

 D

345.

Soln.
Ans: a

Since $√x = x^{1/2}$, we can see that $54^1.5$ is same as $(√54)^3$ which gives $7^3$ = 343.


Question 5

If $√5329 = 73$, then what is the value of $√53.29$ + $√0.5329$ + $√0.005329$ + $√0.00005329$?

 A

8.1103.

 B

8.6103.

 C

9.6103.

 D

9.1103.

Soln.
Ans: a

We can see that $√53.29$ = 7.3, $√0.5329$ = 0.73, $√0.005329$ = 0.073, $√0.00005329$ = 0.0073. Adding, we get 8.1103 as the answer.


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This Blog Post/Article "Surds and Indices Quiz Set 011" by Parveen (Hoven) is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Updated on 2019-08-18.

Posted by Parveen(Hoven),
Aptitude Trainer


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