Practice MCQ Questions and Answer on Simplification

1.

Find the value of $$225-\left[42-\left\{25-\left(18-\overline{18+13}\right)\right\}\right].$$

• (A) 222
• (B) 221
• (C) 223
• (D) 244

Show Answer

 $$\eqalign{ & 225 - \left[ {42 - \left\{ {25 - \left( {18 - \overline {18 + 13} } \right)} \right\}} \right] \cr & = 225 - \left[ {42 - \left\{ {25 - \left( {18 - 18 - 13} \right)} \right\}} \right] \cr & = 225 - \left[ {42 - \left\{ {25 + 13} \right\}} \right] \cr & = 225 - \left[ {42 - 38} \right] \cr & = 221 \cr} $$

2.

The value of $$\frac{2}{3}\times \frac{3}{\frac{5}{6}÷\frac{2}{3}\text{ of 1}\frac{1}{4}}=?$$

• (A) 2
• (B) 1
• (C) $$\frac{1}{2}$$
• (D) $$\frac{2}{3}$$

Show Answer

 $$\eqalign{ & {\text{According to question,}} \cr & \,\,\,\,\,\,\frac{2}{3} \times \frac{3}{{\frac{5}{6} \div \frac{2}{3}{\text{of 1}}\frac{1}{4}}} \cr & \Rightarrow \frac{2}{3} \times \frac{3}{{\frac{5}{6} \div \left( {\frac{2}{3} \times \frac{5}{4}} \right)}} \cr & \Rightarrow \frac{2}{3} \times \frac{3}{{\frac{5}{6} \div \frac{5}{6}}} \cr & \Rightarrow \frac{2}{3} \times \frac{3}{1} \cr & \Rightarrow 2 \cr} $$

3.

Simplify : $$\frac{\frac{1}{3}+\frac{1}{4}\left[\frac{2}{5}-\frac{1}{2}\right]}{1\frac{2}{3}\text{of }\frac{3}{4}-\frac{3}{4}\text{of }\frac{4}{5}}=?$$

• (A) $$\frac{37}{78}$$
• (B) $$\frac{37}{13}$$
• (C) $$\frac{74}{78}$$
• (D) $$\frac{74}{13}$$

Show Answer

 $$\eqalign{ & {\text{According to question,}} \cr & \frac{{\frac{1}{3} + \frac{1}{4}\left[ {\frac{2}{5} - \frac{1}{2}} \right]}}{{1\frac{2}{3}\,{\text{of }}\frac{3}{4} - \frac{3}{4}\,{\text{of }}\frac{4}{5}}} \cr & \Rightarrow \frac{{\frac{1}{3} + \frac{1}{4}\left[ {\frac{{4 - 5}}{{10}}} \right]}}{{\frac{5}{3}\, \times \frac{3}{4} - \frac{3}{4}\, \times \frac{4}{5}}} \cr & \Rightarrow \frac{{\frac{1}{3} - \frac{1}{4} \times \frac{1}{{10}}}}{{\frac{5}{4} - \frac{3}{5}}} \cr & \Rightarrow \frac{{\frac{{40 - 3}}{{120}}}}{{\frac{{25 - 12}}{{20}}}} \cr & \Rightarrow \frac{{37}}{{120}} \times \frac{{20}}{{13}} \cr & \Rightarrow \frac{{37}}{{78}} \cr} $$

4.

Find the value of 2.1 + 2.25 ÷ [63 - {7.5 × 8 + (13 - 2.5 × 5)}].

• (A) 2.8
• (B) 2.9
• (C) 3.0
• (D) 3.1

Show Answer

 2.1 + 2.25 ÷ [63 - {7.5 × 8 + (13 - 2.5 × 5)}] = 2.1 + 2.25 ÷ [63 - {60 + 0.5}] = 2.1 + 2.25 ÷ [63 - 60.5] = 2.1 + $$\frac{{2.25}}{{2.50}}$$ = 2.1 + 0.9 = 3.0

5.

$$\sqrt{\frac{0.25}{0.0009}}\times \sqrt{\frac{0.09}{0.36}}$$     is equal to ?

• (A) $$\frac{5}{6}$$
• (B) $$\text{7}\frac{1}{6}$$
• (C) $$\text{7}\frac{1}{3}$$
• (D) $$\text{8}\frac{1}{3}$$

Show Answer

 $$\eqalign{ & {\text{According to question,}} \cr & \sqrt {\frac{{0.25}}{{0.0009}}} \times \sqrt {\frac{{0.09}}{{0.36}}\,\,} \cr & \Rightarrow \sqrt {\frac{{25}}{9} \times 100} \times \sqrt {\frac{9}{{36}}\,\,} \cr & \Rightarrow \frac{{5 \times 10}}{3} \times \frac{3}{6} \cr & \Rightarrow \frac{{25}}{3} \cr & \Rightarrow 8\frac{1}{3} \cr} $$

6.

(98764 + 89881 + 99763 + 66342) ÷ (1186 + ? + 1040 + 1870) = 55

• (A) 2254
• (B) 2354
• (C) 2368
• (D) 2404

Show Answer

 Let the missing number is x. then, $$\frac{{354750}}{{4096 + x}}$$   = 55 ⇒ 55( 4096 + x ) = 354750 ⇒ 55x = 354750 - 225280 ⇒ 55x = 129470 ⇒ x = 2354

7.

The value of $$\frac{40+\frac{3}{4}\text{ of }32}{37+\frac{3}{4}\text{ of }\left(34-6\right)}$$    is:

• (A) $$-1\frac{3}{29}$$
• (B) $$1\frac{9}{29}$$
• (C) $$2\frac{3}{29}$$
• (D) $$1\frac{3}{29}$$

Show Answer

 $$\eqalign{ & \frac{{40 + \frac{3}{4}{\text{ of }}32}}{{37 + \frac{3}{4}{\text{ of }}\left( {34 - 6} \right)}} \cr & = \frac{{40 + 24}}{{37 + 21}} \cr & = \frac{{64}}{{58}} \cr & = \frac{{32}}{{29}} \cr & = 1\frac{3}{{29}} \cr} $$

8.

The value of $$\sqrt{32}$$  - $$\sqrt{128}$$  + $$\sqrt{50}$$ correct to 3 places of decimal is $$\sqrt{32}$$  - $$\sqrt{128}$$  + $$\sqrt{50}$$  = ?

• (A) 1.732
• (B) 1.141
• (C) 1.414
• (D) 1.441

Show Answer

 $$\eqalign{ & {\text{According to question,}} \cr & \sqrt {32} {\text{ }} - \sqrt {128} {\text{ + }}\sqrt {50} \cr & \Rightarrow \sqrt {16 \times 2} - \sqrt {64 \times 2} + \sqrt {25 \times 2} \cr & \Rightarrow 4\sqrt 2 - 8\sqrt 2 + 5\sqrt 2 \cr & \Rightarrow \sqrt 2 \cr & \Rightarrow 1.414 \cr} $$

9.

If $$\frac{a}{b+c}\text{ = }\frac{b}{c+a}$$   = $$\frac{c}{a+b}\text{ = k,}$$    then find the value of k is

• (A) -$$\frac{1}{2}$$
• (B) 1
• (C) -1
• (D) $$\frac{1}{2}$$

Show Answer

 $$\eqalign{ & \frac{a}{{b + c}} = k \cr & \Rightarrow a = k\left( {b + c} \right)\,....(i) \cr & \frac{b}{{c + a}} = k \cr & \Rightarrow b = k\left( {c + a} \right)\,....(ii) \cr & \frac{c}{{a + b}} = k \cr & \Rightarrow c = k\left( {a + b} \right)\,....(iii) \cr & {\text{Adding (i), (ii) and (iii) we get,}} \cr & a + b + c \cr & = k\left( {2a + 2b + 2c} \right) \cr & \Rightarrow k = \frac{{a + b + c}}{{2(a + b + c)}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{2} \cr} $$

10.

$$\text{If }x=\frac{1}{2+\frac{1}{2}}\text{ then }\frac{1}{x}=?$$

• (A) $$\frac{2}{5}$$
• (B) $$\frac{5}{2}$$
• (C) $$\frac{3}{5}$$
• (D) $$\frac{1}{2}$$

Show Answer

 $$\eqalign{ & x = \frac{1}{{2 + \frac{1}{2}}} = \frac{2}{5} \cr & \Rightarrow \frac{1}{x} = \frac{5}{2} \cr} $$