Surds and Indices Quiz Set 012

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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

What is $16^0.15 × 16^0.1$?

 A

2.

 B

3.

 C

5.

 D

4.

Soln.
Ans: a

By inspection, we get $(2^4)^0.15 × (2^4)^0.1$, which equals $(2^4)^(0.15 + 0.1)$, which equals $(2^4)^0.25$, which equals $2^1$, or 2. Note: The trick in such type of questions is to keep an eye on the "bases".


Question 3

If $3^x = 729$, then what is the value of $3^{x - 1}$?

 A

243.

 B

244.

 C

242.

 D

245.

Soln.
Ans: a

We can write the given expression as $3^x = 3^6$. The bases are same so powers should be same. Comparing we get x = 6. So x - 1 = 5, we get $3^5 = 243$.


Question 4

What is $({19/28})^0.12 × ({19/28})^x = ({19/28})^0.11$?

 A

-0.00999999999999998.

 B

0.49.

 C

1.49.

 D

1.99.

Soln.
Ans: a

We can simplify the given expression to $({19/28})^{0.12 + x} = ({19/28})^0.11$. The bases are equal, so the powers should also be equal. Hence $0.12 + x = 0.11$ which gives x = -0.00999999999999998.


Question 5

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".


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This Blog Post/Article "Surds and Indices Quiz Set 012" 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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