Surds and Indices Quiz Set 006

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Question 1

What is the value of x if $(15625)^1.5 × 5^5$ ÷ $625^4.5$ = $5^x$?

 A

-4.

 B

2.

 C

8.

 D

14.

Soln.
Ans: a

Simplifying, we get $(5^6)^1.5 × 5^5$ ÷ $(5 ^ 4)^4.5$ = $5^x$, which simplifies to $5^9 × 5^5$ ÷ $5^18$ = $5^x.$ Equating the powers x = 9 + 5 - 18 = -4.


Question 2

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 3

If $2^3.4 = p, and 2^2.6 = q$ and $p^m = q^3$ then what is the value of m?

 A

2.29.

 B

2.53.

 C

2.43.

 D

2.83.

Soln.
Ans: a

Substituting in $p^m = q^3$, we get $2^{3.4m} = 2^{2.6 × 3}$. Bases are same so powers should be same. Hence, $3.4m = {2.6 × 3}$, which gives m = 2.29.


Question 4

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 5

If $2^x = 16$, then what is the value of $2^{x - 1}$?

 A

8.

 B

9.

 C

7.

 D

10.

Soln.
Ans: a

We can write the given expression as $2^x = 2^4$. The bases are same so powers should be same. Comparing we get x = 4. So x - 1 = 3, we get $2^3 = 8$.


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This Blog Post/Article "Surds and Indices Quiz Set 006" 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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