Practice MCQ Questions and Answer on Simplification

41.

If 3.352 - (9.759 - x) - 19.64 = 7.052, then what is the value of x?

• (A) -6.181
• (B) 13.581
• (C) 33.099
• (D) 39.803

Show Answer

 3.352 - (9.759 - x) - 19.64 = 7.052 ⇒ 3.352 - 9.759 + x - 19.64 - 7.052 = 0 ⇒ x = 36.451 - 3352 ∴ x = 33.099

42.

What is the value of $$0.51\overline{345}$$  in vulgar fraction?

• (A) $$\frac{51294}{90990}$$
• (B) $$\frac{52194}{99000}$$
• (C) $$\frac{51294}{90000}$$
• (D) $$\frac{51294}{99900}$$

Show Answer

 $$\eqalign{ & 0.51\overline {345} \cr & = \frac{{51345 - 51}}{{99900}} \cr & = \frac{{51294}}{{99900}} \cr} $$

43.

$$4\frac{4}{5}÷6\frac{2}{5}=?$$

• (A) $$\frac{3}{4}$$
• (B) $$\frac{5}{7}$$
• (C) $$\frac{5}{8}$$
• (D) $$\frac{7}{11}$$

Show Answer

 $$\eqalign{ & {\text{Given expression}} \cr & \frac{{24}}{5} \div \frac{{32}}{5} \cr & = \frac{{24}}{5} \times \frac{5}{{32}} \cr & = \frac{3}{4} \cr} $$

44.

David gets on the elevator at the 11^th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?

• (A) 19th floor
• (B) 28th floor
• (C) 30th floor
• (D) 37th floor

Show Answer

 Suppose their paths cross after x minutes Then, 11 + 57x = 51 - 63x ⇒ 57x + 63x = 51 - 11 ⇒ 120x = 40 ⇒ x = $$\frac{1}{3}$$ Number of floors covered by David in $$\frac{1}{3}$$ min. $$\eqalign{ & = {\frac{1}{3} \times 57} \cr & = 19 \cr} $$ So, their paths cross at (11 + 19) i.e., 30th floor

45.

If a = -12, b = -6 and c = 18, then what is the value of $$\frac{2\text{abc}}{9}.$$

• (A) 554
• (B) 288
• (C) 272
• (D) 144

Show Answer

 $$\eqalign{ & \frac{{2{\text{abc}}}}{9} \cr & = \frac{{2 \times - 12 \times - 6 \times 18}}{9} \cr & = 288 \cr} $$

46.

$$\sqrt{\frac{0.25}{0.0009}}\times \sqrt{\frac{0.09}{0.36}}$$     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

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

47.

If $$a+\frac{1}{b}=1$$   and $$b+\frac{1}{c}=1\text{,}$$   then $$c+\frac{1}{a}$$   is equal to = ?

• (A) 0
• (B) $$\frac{1}{2}$$
• (C) 1
• (D) 2

Show Answer

 $$\eqalign{ & a + \frac{1}{b} = 1{\text{ }} \cr & \Rightarrow ab + 1 = b \cr & \Rightarrow ab - b = - 1 \cr & \Rightarrow b\left( {a - 1} \right) = - 1 \cr & \Rightarrow b = \frac{1}{{\left( {1 - a} \right)}} \cr & \cr & b + \frac{1}{c} = 1 \cr & \Rightarrow bc + 1 = c \cr & \Rightarrow bc - c = - 1 \cr & \Rightarrow c\left( {b - 1} \right) = - 1 \cr & \Rightarrow c = \frac{1}{{\left( {1 - b} \right)}} \cr & \cr & \therefore c + \frac{1}{a} = \frac{1}{{\left( {1 - b} \right)}} + \frac{1}{a} \cr & c + \frac{1}{a} = \frac{1}{{1 - \left( {\frac{1}{{1 - a}}} \right)}} + \frac{1}{a} \cr & c + \frac{1}{a} = \frac{1}{{\frac{{\left( {1 - a} \right) - 1}}{{\left( {1 - a} \right)}}}} + \frac{1}{a} \cr & c + \frac{1}{a} = \frac{{\left( {1 - a} \right)}}{{ - a}} + \frac{1}{a} \cr & c + \frac{1}{a} = \frac{{\left( {a - 1} \right)}}{a} + \frac{1}{a} \cr & c + \frac{1}{a} = \frac{{a - 1 + 1}}{a} \cr & c + \frac{1}{a} = \frac{a}{a} \cr & c + \frac{1}{a} = 1 \cr} $$

48.

If the sum of two numbers is 22 and the sum of their squares is 404, then the product of two numbers is = ?

• (A) 40
• (B) 44
• (C) 80
• (D) 88

Show Answer

 $$\eqalign{ & {\text{According to the question}} \cr & x + y = 22\,......(i) \cr & {x^2} + {y^2} = 404\,......(ii){\text{ }} \cr & \therefore {\left( {x + y} \right)^2} = {x^2} + {y^2} + 2xy \cr & \Rightarrow {\left( {22} \right)^2} = 404 + 2xy \cr & \Rightarrow 484 = 404 + 2xy \cr & \Rightarrow 2xy = 80 \cr & \Rightarrow xy = 40 \cr} $$

49.

If x + y + z = 0, then x³ + y³ + z³ + 3xyz is equal to = ?

• (A) 0
• (B) 6xyz
• (C) 12xyz
• (D) xyz

Show Answer

 As we know a3 + b3 + c3 + 3abc = (a2 + b2 + c2 - ab - bc - ca)(a + b + c) When, a + b + c = 0 Then a3 + b3 + c3 - 3abc = 0 When, x + y + z = 0 ⇒ x3 + y3 + z3 = 3xyz ⇒ x3 + y3 + z3 + 3xyz = 3xyz + 3xyz ⇒ x3 + y3 + z3 + 3xyz = 6xyz

50.

The simplified value of $$\sqrt{5+\sqrt{11+\sqrt{19+\sqrt{29+\sqrt{49}}}}}$$      = ?

• (A) 3
• (B) 2
• (C) 4
• (D) 6

Show Answer

 $$\eqalign{ & {\text{According to question,}} \cr & \,\,\,\, \sqrt {5 + \sqrt {11 + \sqrt {19 + \sqrt {29 + \sqrt {49} } } } } \cr & \Rightarrow \sqrt {5 + \sqrt {11 + \sqrt {19 + \sqrt {29 + 7} } } } \cr & \Rightarrow \sqrt {5 + \sqrt {11 + \sqrt {19 + \sqrt {36} } } } \cr & \Rightarrow \sqrt {5 + \sqrt {11 + \sqrt {19 + 6} } } \cr & \Rightarrow \sqrt {5 + \sqrt {11 + \sqrt {25} } } \cr & \Rightarrow \sqrt {5 + \sqrt {11 + 5} } \cr & \Rightarrow \sqrt {5 + \sqrt {16} } \cr & \Rightarrow \sqrt {5 + 4} \cr & \Rightarrow \sqrt 9 \cr & \Rightarrow 3 \cr} $$