Quantitative Aptitude: Simplification (Set 5) - Concept of Maths

Question 1

Find the value of $x$ in the following continued fraction: $$1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{x}}} = \frac{8}{5}$$

Accepted Answer

C) 2

Answer

A) 1

Answer

B) 1.5

Answer

D) 2.5

Question 2

Simplify the expression: $$\frac{(0.1)^2 + (0.01)^2 + (0.001)^2}{(0.01)^2 + (0.001)^2 + (0.0001)^2}$$

Accepted Answer

D) 100

Answer

A) 10

Answer

B) 0.1

Answer

C) 0.01

Question 3

What is the value of $\sqrt{7 + 4\sqrt{3}} + \sqrt{7 - 4\sqrt{3}}$?

Accepted Answer

B) 4

Answer

A) $2\sqrt{3}$

Answer

C) $4\sqrt{3}$

Answer

D) 2

Question 4

Simplify: $$\frac{x^3 - y^3}{x^2 + xy + y^2} \div \frac{x^2 - y^2}{x + y}$$

Accepted Answer

A) 1

Answer

B) $x-y$

Answer

C) $x+y$

Answer

D) 0

Question 5

If $a + b + c = 0$, find the value of $\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab}$.

Accepted Answer

C) 3

Answer

A) 1

Answer

B) 0

Answer

D) -3

Question 6

Find the value of $999 \frac{995}{999} imes 999$.

Accepted Answer

B) 998996

Answer

A) 999000

Answer

C) 998999

Answer

D) 999995

Question 7

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

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

Answer

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

Answer

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

Answer

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

Question 8

Find $x$ if $\sqrt{x + 2\sqrt{x + 2\sqrt{x + 2\sqrt{\dots}}}} = x$.

Accepted Answer

A) $x$ can be any positive value that satisfies $x^2 - x - 2\sqrt{x...} = 0$, specifically if we let the nested part be $x$, then $x=2$

Answer

B) 0

Answer

C) 4

Answer

D) 1

Question 9

If $x = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$ and $y = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$, find $x^2 + xy + y^2$.

Accepted Answer

B) 63

Answer

A) 62

Answer

C) 64

Answer

D) 65

Question 10

Simplify: $$\frac{1}{1 imes 2} + \frac{1}{2 imes 3} + \frac{1}{3 imes 4} + \dots + \frac{1}{99 imes 100}$$

Accepted Answer

C) $\frac{99}{100}$

Answer

A) $\frac{1}{100}$

Answer

B) $\frac{98}{100}$

Answer

D) 1