Practice MCQ Questions and Answer on Simplification

91.

The value of $$\left[\frac{4}{7}\text{ of }2\frac{4}{5}\times 1\frac{2}{3}-\left(3\frac{1}{2}-2\frac{1}{6}\right)\right]÷\left(3\frac{1}{5}÷4\frac{1}{2}\text{ of }5\frac{1}{3}\right)\text{is:}$$

• (A) $$\text{7}\frac{1}{2}$$
• (B) $$1\frac{1}{3}$$
• (C) 10
• (D) 15

Show Answer

 $$\eqalign{ & \left[ {\frac{4}{7}{\text{ of }}2\frac{4}{5} \times 1\frac{2}{3} - \left( {3\frac{1}{2} - 2\frac{1}{6}} \right)} \right] \div \left[ {\left( {3\frac{1}{5} \div 4\frac{1}{2}{\text{ of }}5\frac{1}{3}} \right)} \right] \cr & = \left[ {\frac{4}{7}{\text{ of }}\frac{{14}}{5} \times \frac{5}{3} - \left( {\frac{7}{2} - \frac{{13}}{6}} \right)} \right] \div \left[ {\left( {\frac{{16}}{5} \div \frac{9}{2}{\text{ of }}\frac{{16}}{3}} \right)} \right] \cr & = \left[ {\frac{8}{3} - \left( {\frac{{21 - 13}}{6}} \right)} \right] \div \left[ {\left( {\frac{{16}}{5} \div 24} \right)} \right] \cr & = \left[ {\frac{8}{3} - \frac{8}{6}} \right] \div \left[ {\frac{{16}}{5} \times \frac{1}{{24}}} \right] \cr & = \frac{4}{3} \div \frac{2}{{15}} \cr & = \frac{4}{3} \times \frac{{15}}{2} \cr & = 10 \cr} $$

92.

$$\text{If }\frac{3a+4b}{3c+4d}\text{ = }\frac{3a-4b}{3c-4d}\text{ then}$$

• (A) ab = cd
• (B) ad = bc
• (C) ac = bd
• (D) a = b =c ≠ d

Show Answer

 $$\eqalign{ & {\text{According to question,}} \cr & \frac{{3a + 4b}}{{3a - 4b}}{\text{ = }}\frac{{3c + 4d}}{{3c - 4d}} \cr & \Rightarrow \frac{{3a}}{{4b}} = \frac{{3c}}{{4d}} \cr & \Rightarrow ad = bc \cr} $$

93.

If $$\text{45 - }\left[28-\left\{37-\left(15-\ast \right)\right\}\right]=58$$       then * equal to?

• (A) -29
• (B) -19
• (C) 19
• (D) 29

Show Answer

 $$\eqalign{ & {\text{Let,}} \cr & 45 - \left[ {28 - \left\{ {37 - \left( {15 - x} \right)} \right\}} \right] = 58 \cr & {\text{then,}} \cr & {\text{45}} - \left[ {28 - \left\{ {37 - 15 + x} \right\}} \right] = 58 \cr & \Rightarrow 45 - \left[ {28 - \left\{ {22 + x} \right\}} \right] = 58 \cr & \Rightarrow 45 - \left[ {28 - 22 - x} \right] = 58 \cr & \Rightarrow 45 - \left[ {6 - x} \right] = 58 \cr & \Rightarrow 45 - 6 + x = 58 \cr & \Rightarrow 39 + x = 58 \cr & \Rightarrow x = 58 - 39 \cr & \Rightarrow x = 19 \cr} $$

94.

The difference of two numbers is 1564. After dividing the larger number by the smaller, we get 6 as quotient and 19 as remainder. What is the smaller number?

• (A) 456
• (B) 287
• (C) 623
• (D) 309

Show Answer

 $$\eqalign{ & {\text{Let two numbers}} = a{\text{ and }}b \cr & a > b \cr & a - b = 1564{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {\text{i}} \right) \cr & 6b + 19 = a \cr & a - 6b = 19{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {{\text{ii}}} \right) \cr & {\text{From equation }}\left( {\text{i}} \right){\text{ and }}\left( {{\text{ii}}} \right) \cr & a - b = 1564 \cr & a - 6b = 19 \cr & - \,\,\,\,\, + \,\,\,\,\, - \cr & \overline {\,\,\,\,\,\,\,5b = 1545\,} \cr & b = 309 \cr & {\text{Smaller number}} = 309 \cr} $$

95.

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

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

96.

$$\text{If }\left(n^r-tn+\frac{1}{4}\right)$$     be a perfect square, then the values of t are = ?

• (A) ± 2
• (B) 1, 2
• (C) 2, 3
• (D) ± 1

Show Answer

 $$\eqalign{ & {\text{If }}\left( {{n^r} - tn + \frac{1}{4}} \right){\text{be a perfect square}} \cr & r = 2t = \pm 1 \cr & \left( {{\text{If }}t = 1} \right)\,\,{n^2} - n + \frac{1}{4} \cr & = {n^2} - 2 \times n \times \frac{1}{2} + \frac{1}{4} \cr & = {\left( {n - \frac{1}{2}} \right)^2} \cr & \left( {{\text{If }}t = - 1} \right)\,\,{n^2} + n + \frac{1}{4} \cr & = {n^2} + 2 \times n \times \frac{1}{2} + \frac{1}{4} \cr & = {\left( {n + \frac{1}{2}} \right)^2} \cr} $$

97.

If $$\sqrt{\text{4096}}$$  = 64, then the value of $$\sqrt{\text{40}\text{.96}}$$   $$+$$ $$\sqrt{\text{0}\text{.4096}}$$   $$+$$ $$\sqrt{\text{0}\text{.004096}}$$    $$+$$ $$\sqrt{\text{0}\text{.00004096}}$$     up to two place of decimals is = ?

• (A) 7.09
• (B) 7.10
• (C) 7.11
• (D) 7.12

Show Answer

 $$\eqalign{ & {\text{According to question,}} \cr & \sqrt {40.96} {\text{ + }}\sqrt {0.4096} {\text{ + }}\sqrt {0.004096} {\text{ + }}\sqrt {0.00004096} \cr & \Rightarrow \sqrt {\frac{{4096}}{{100}}} + \sqrt {\frac{{4096}}{{10000}}} + \sqrt {\frac{{4096}}{{1000000}}} + \sqrt {\frac{{4096}}{{100000000}}} \cr & \Rightarrow \frac{{64}}{{10}} + \frac{{64}}{{100}} + \frac{{64}}{{1000}} + \frac{{64}}{{10000}} \cr & \Rightarrow 6.4 + 0.64 + 0.064 + 0.0064 \cr & \Rightarrow 7.11 \cr} $$

98.

What will come at place of x, (x 10) for $$\frac{\left(132÷12\times x-3\times 3\right)}{\left(5^2-6\times 4+x^2\right)}=1?$$

• (A) 2
• (B) 4
• (C) 3
• (D) 1

Show Answer

 $$\eqalign{ & \frac{{132 \div 12 \times x - 3 \times 3}}{{{5^2} - 6 \times 4 + {x^2}}} = 1 \cr & 11 \times x - 9 = 25 - 24 + {x^2} \cr & 11x - 9 = 1 + {x^2} \cr & {x^2} + 1 + 9 - 11x = 0 \cr & {x^2} - 11x + 10 = 0 \cr & {x^2} - 10x - x + 10 = 0 \cr & x\left( {x - 10} \right) - 1\left( {x - 10} \right) = 0 \cr & \left( {x - 10} \right)\left( {x - 1} \right) = 0 \cr & x = 10,\,1 \cr & {\text{For the condition}}\left( {x 10} \right) \cr & x = 1 \cr} $$

99.

Solve 4376 + 3209 - 1784 + 97 = 3125 + ?

• (A) 2713
• (B) 2743
• (C) 2773
• (D) 2793

Show Answer

 4376 + 3209 - 1784 + 97 = 3125 + x ⇒ 7682 - 1784 = 3125 + x or, x = 7682 - 1784 - 3125 ⇒ x = 2773 Hence, the number is 2773

100.

The value of $$7\frac{1}{2}\times \left(3\frac{1}{5}÷4\frac{1}{2}\text{ of }5\frac{1}{3}\right)+\left[11-\left(\frac{5}{8}+3-1\frac{1}{4}\right)\right]÷5\frac{3}{4}-5÷5\times 5\text{of }5÷25\text{is:}$$

• (A) $$\frac{1}{2}$$
• (B) $$\frac{1}{10}$$
• (C) $$\frac{3}{10}$$
• (D) $$1\frac{1}{2}$$

Show Answer

 7 1 2 × 3 1 5 ÷4 1 2  of 5 1 3 + 11− 5 8 +3−1 1 4 ÷5 3 4 −5÷5×5 of 5÷25 = 15 2 16 5 ÷ 9 2  of  16 3 + 11− 5 8 +3− 3 4 ÷ 23 4 −5÷5× 5 of 5 ⎵ ÷25 = 15 2 16 5 ÷24 + 11− 5 8 + 24−10 8 ÷ 23 4 −5÷5 = 15 2 2 15 + 88−19 8 ÷ 23 4 −1 =1+ 69 8 × 4 23 −1 = 3 2 =1 1 2