Surds and Indices Quiz Set 006

Question 1

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 2

If \$7^x = 16807\$, then what is the value of \$7^{x - 3}\$?

A

49.

B

50.

C

48.

D

51.

Soln.
Ans: a

We can write the given expression as \$7^x = 7^5\$. The bases are same so powers should be same. Comparing we get x = 5. So x - 3 = 2, we get \$7^2 = 49\$.

Question 3

If \$13^1.1 = p, and 13^2.5 = q\$ and \$p^m = q^4\$ then what is the value of m?

A

9.09.

B

9.33.

C

9.23.

D

9.63.

Soln.
Ans: a

Substituting in \$p^m = q^4\$, we get \$13^{1.1m} = 13^{2.5 × 4}\$. Bases are same so powers should be same. Hence, \$1.1m = {2.5 × 4}\$, which gives m = 9.09.

Question 4

What is \$29^0.8 × 29^x = 29^1.4\$?

A

0.6.

B

1.1.

C

2.1.

D

2.6.

Soln.
Ans: a

We can simplify the given expression to \$29^{0.8 + x} = 29^1.4\$. The bases are equal, so the powers should also be equal. Hence \$0.8 + x = 1.4\$ which gives x = 0.6.

Question 5

What is \$26^0.24 × 26^x = 26^0.15\$?

A

-0.09.

B

0.41.

C

1.41.

D

1.91.

Soln.
Ans: a

We can simplify the given expression to \$26^{0.24 + x} = 26^0.15\$. The bases are equal, so the powers should also be equal. Hence \$0.24 + x = 0.15\$ which gives x = -0.09.

Updated on 2017-05-17.

Posted by Parveen(Hoven),
Aptitude Trainer