Surds and Indices Quiz Set 007

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Question 1

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 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

What is the value of x if $(64)^3 × 2^3$ ÷ $16^1.5$ = $2^x$?

 A

15.

 B

21.

 C

27.

 D

33.

Soln.
Ans: a

Simplifying, we get $(2^6)^3 × 2^3$ ÷ $(2 ^ 4)^1.5$ = $2^x$, which simplifies to $2^18 × 2^3$ ÷ $2^6$ = $2^x.$ Equating the powers x = 18 + 3 - 6 = 15.


Question 4

What is $({4/34})^{x - 0.18} × ({4/34})^x = ({4/34})^0.23$?

 A

0.205.

 B

0.705.

 C

1.705.

 D

2.205.

Soln.
Ans: a

We can simplify the given expression to $({4/34})^{2x - 0.18} = ({4/34})^0.23$. The bases are equal, so the powers should also be equal. Hence $2x - 0.18 = 0.23$ which gives x = 0.205.


Question 5

What is the value of x if $(117649)^3.5 × 7^8$ ÷ $49^2.5$ = $7^x$?

 A

24.

 B

30.

 C

36.

 D

42.

Soln.
Ans: a

Simplifying, we get $(7^6)^3.5 × 7^8$ ÷ $(7 ^ 2)^2.5$ = $7^x$, which simplifies to $7^21 × 7^8$ ÷ $7^5$ = $7^x.$ Equating the powers x = 21 + 8 - 5 = 24.


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This Blog Post/Article "Surds and Indices Quiz Set 007" 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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