Quantitative Aptitude: Simplification Mastery Quiz (Set 3)

Question 1

Evaluate the expression: $$\sqrt{7 + 4\sqrt{3}} - \sqrt{7 - 4\sqrt{3}}$$

Accepted Answer

C) $2\sqrt{3}$

Answer

A) $\sqrt{3}$

Answer

B) 2

Answer

D) 4

Question 2

Find the value of $x$ if: $$x = 1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \dots}}}$$

Accepted Answer

B) $\frac{1 + \sqrt{5}}{2}$

Answer

A) $\frac{1 + \sqrt{3}}{2}$

Answer

C) $\sqrt{2}$

Answer

D) 1.62

Question 3

Simplify the following telescoping series: $$\frac{1}{1 imes 3} + \frac{1}{3 imes 5} + \frac{1}{5 imes 7} + \dots + \frac{1}{19 imes 21}$$

Accepted Answer

D) $\frac{10}{21}$

Answer

A) $\frac{20}{21}$

Answer

B) $\frac{19}{21}$

Answer

C) $\frac{5}{21}$

Question 4

Simplify the expression: $$\frac{(0.7)^3 + (0.3)^3}{(0.7)^2 - 0.21 + (0.3)^2}$$

Accepted Answer

A) 1

Answer

B) 0.4

Answer

C) 0.1

Answer

D) 0.49

Question 5

If $3^x - 3^{x-1} = 162$, find the value of $x^2 - x$.

Accepted Answer

C) 20

Answer

A) 12

Answer

B) 30

Answer

D) 25

Question 6

Find the value of $$\sqrt{12 + \sqrt{12 + \sqrt{12 + \dots \infty}}}$$

Accepted Answer

A) 4

Answer

B) 3

Answer

C) 6

Answer

D) 12

Question 7

Which of the following is the largest? $$2^{60}, 3^{48}, 4^{36}, 5^{24}$$

Accepted Answer

B) $3^{48}$

Answer

A) $2^{60}$

Answer

C) $4^{36}$

Answer

D) $5^{24}$

Question 8

Simplify: $$\frac{1}{1 + a^{m-n}} + \frac{1}{1 + a^{n-m}}$$

Accepted Answer

D) 1

Answer

A) 0

Answer

B) $a^{m+n}$

Answer

C) $a$

Question 9

If $x + y + z = 0$, what is the value of $$\frac{x^2}{yz} + \frac{y^2}{zx} + \frac{z^2}{xy}$$

Accepted Answer

B) 3

Answer

A) 0

Answer

C) 1

Answer

D) -3

Question 10

Simplify: $$\left(1 - \frac{1}{3}\right)\left(1 - \frac{1}{4}\right)\left(1 - \frac{1}{5}\right)\dots\left(1 - \frac{1}{n}\right)$$

Accepted Answer

C) $\frac{2}{n}$

Answer

A) $\frac{1}{n}$

Answer

B) $\frac{2(n-1)}{n}$

Answer

D) $\frac{n-1}{n}$