Surds and Indices Quiz Set 008

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Question 1

What is $({2/9})^{x - 0.05} × ({2/9})^x = ({2/9})^2.3$?

 A

1.175.

 B

1.675.

 C

2.675.

 D

3.175.

Soln.
Ans: a

We can simplify the given expression to $({2/9})^{2x - 0.05} = ({2/9})^2.3$. The bases are equal, so the powers should also be equal. Hence $2x - 0.05 = 2.3$ which gives x = 1.175.


Question 2

If $p^q = 5$, then what could be $(p - 1)^(q + 1)$?

 A

16.

 B

17.

 C

15.

 D

18.

Soln.
Ans: a

By inspection we can see that p = 5, q= 1. So $(5 - 1)^(1 + 1)$ will be $4^2$, i.e., 16.


Question 3

If $√86$ is approximately $9$, then what is $86^3$?

 A

531441.

 B

531442.

 C

531440.

 D

531443.

Soln.
Ans: a

Since $√x = x^{1/2}$, we can see that $86^3$ is same as $(√86)^6$ which gives $9^6$ = 531441.


Question 4

What is $({11/12})^{x - 0.27} × ({11/12})^x = ({11/12})^0.32$?

 A

0.295.

 B

0.795.

 C

1.795.

 D

2.295.

Soln.
Ans: a

We can simplify the given expression to $({11/12})^{2x - 0.27} = ({11/12})^0.32$. The bases are equal, so the powers should also be equal. Hence $2x - 0.27 = 0.32$ which gives x = 0.295.


Question 5

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.


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This Blog Post/Article "Surds and Indices Quiz Set 008" 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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