Practice MCQ Questions and Answer on Simplification

31.

The value of 18% of 15% of $$\frac{{25}}{9}$$ of 3800 is:

• (A) 285
• (B) 582
• (C) 583
• (D) 385

Show Answer

 $$\eqalign{ & 3800 \times \frac{{25}}{9} \times 15\% \times 18\% \cr & = 3800 \times \frac{{25}}{9} \times \frac{3}{{20}} \times \frac{{18}}{{100}} \cr & = 19 \times 15 \cr & = 285 \cr} $$

32.

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

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

33.

If 4x = p(x + 3) + q(x - 1) is an identity, then the values of p and q are?

• (A) 1, -3
• (B) 1, 3
• (C) 1, 1
• (D) 3, 1

Show Answer

 $$\eqalign{ & {\text{4}}x = p\left( {x + 3} \right) + q\left( {x - 1} \right) \cr & \Rightarrow 4x = px + 3p + qx - q \cr & \Rightarrow 4x = \left( {p + q} \right)x + \left( {3p - q} \right) \cr & \Rightarrow p + q = 4\,and\,3p - q = 0 \cr & \Rightarrow p + q = 4\,and\,p = \frac{q}{3} \cr & \Rightarrow \frac{q}{3} + q = 4 \cr & \Rightarrow \frac{{4q}}{3} = 4 \cr & \Rightarrow q = 3 \cr & p + q = 4\,\,\,and \cr & \Rightarrow p = 1 \cr & \Rightarrow q = 3 \cr} $$

34.

Which of the following statement is correct?
I. The value of 100² - 99² + 98² - 97² + 96² - 95² + 94² - 93² + . . . . + 2² - 1² is 5050.
II. If 8x + $$\frac{8}{{\text{x}}}$$ = -16 and x 0, then the value of x¹⁹⁷ + x^-197 is 2.

• (A) Only I
• (B) Only II
• (C) Both I and II
• (D) Neither I nor II

Show Answer

 I.  100 2 − 99 2 ⎵ + 98 2 − 97 2 + . . . .+ 2 2 − 1 2 $$\eqalign{ & = \left( {100 + 99} \right)\left( {100 - 99} \right) + \left( {98 + 97} \right)\left( {98 - 97} \right) + \left( {96 + 95} \right)\left( {96 - 95} \right) + \,.\,.\,.\,.\, + \left( {2 + 1} \right)\left( {2 - 1} \right) \cr & \Rightarrow \frac{{n\left( {n + 1} \right)}}{2} = {\text{ sum of }}n{\text{ terms}} \cr & = \frac{{100 \times 101}}{2} \cr & = 5050 \cr & {\text{Statement I is true}} \cr & {\text{II}}{\text{. }}8x + \frac{8}{x} = - 16 \cr & {\text{Put }}x = - 1 \cr & {\text{Then }}{x^{197}} + {x^{ - 197}} \cr & = {\left( { - 1} \right)^{197}} + {\left( { - 1} \right)^{ - 197}} \cr & = - 1 - 1 \cr & = - 2 \cr & {\text{Statement II is incorrect}} \cr} $$

35.

$${{{{(469 + 174)}^2} - {{(469 - 174)}^2}} \over {(469 \times 174)}} = ?$$

• (A) 1
• (B) 4
• (C) 295
• (D) 643

Show Answer

 $$\eqalign{ & \frac{{{{\left( {469 + 174} \right)}^2} - {{\left( {469 - 174} \right)}^2}}}{{\left( {469 \times 174} \right)}} = ? \cr & {\text{We}}\,{\text{ know that}}, \cr & 4ab = {\left( {a + b} \right)^2} - {\left( {a - b} \right)^2} \cr & \therefore \frac{{{{\left( {469 + 174} \right)}^2} - {{\left( {469 - 174} \right)}^2}}}{{\left( {469 \times 174} \right)}} \cr & = \frac{{4 \times 469 \times 174}}{{469 \times 174}} \cr & = 4 \cr} $$

36.

The value of $$\left( {2.\overline 4 \times 2.\overline 6 \times 3 \times 0.1\overline 6 } \right) \times \left[ {0.\overline {27} \times \left( {0.8\overline 3 \div 0.1\overline 6 } \right)} \right]{\text{is:}}$$

• (A) 1.11
• (B) $$1.\overline 1 $$
• (C) $$1.\overline {36} $$
• (D) 0.814

Show Answer

 $$\eqalign{ & \left( {2.\overline 4 \times 2.\overline 6 \times 3 \times 0.1\overline 6 } \right) \times \left[ {0.\overline {27} \times \left( {0.8\overline 3 \div 0.1\overline 6 } \right)} \right] \cr & = \left( {\frac{{22}}{9} \times \frac{6}{9} \times 3 \times \frac{{15}}{{90}}} \right) \times \left[ {\frac{{27}}{{99}} \times \left( {\frac{{75}}{{90}} \div \frac{{15}}{{90}}} \right)} \right] \cr & = \frac{{22}}{{27}} \times \left[ {\frac{{27}}{{99}} \times \left( {\frac{{75}}{{90}} \times \frac{{90}}{{15}}} \right)} \right] \cr & = \frac{{22}}{{27}} \times \frac{{27}}{{99}} \times 5 \cr & = \frac{{10}}{9} \cr & = 1.\overline 1 \cr} $$

37.

The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is:

• (A) Rs. 3500
• (B) Rs. 3750
• (C) Rs. 3840
• (D) Rs. 3900

Show Answer

 $$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{cost}}\,{\text{of}}\,{\text{a}}\,{\text{chair}}\,{\text{and}}\,{\text{that}}\,{\text{of}}\,\,{\text{table}} \cr & \,{\text{be}}\,Rs.\,x\,{\text{and}}\,Rs.\,y\,{\text{respectively}}. \cr & {\text{Then}},\,10x = 4y\,\,\,or\,\,\,y = \frac{5}{2}x \cr & \therefore 15x + 2y = 4000 \cr & \Rightarrow 15x + 2 \times \frac{5}{2}x = 4000 \cr & \Rightarrow 20x = 4000 \cr & \therefore x = 200 \cr & {\text{So}},\,y = {\frac{5}{2} \times 200} = 500 \cr & {\text{Hence,}}\,{\text{the}}\,{\text{cost}}\,{\text{of}}\,{\text{12}}\,{\text{chairs}}\,{\text{and}}\,{\text{3}}\,{\text{tables}} \cr & = 12x + 3y \cr & = Rs.\,\left( {2400 + 1500} \right) \cr & = Rs.\,3900 \cr} $$

38.

Find the sum : $$\frac{1}{2} + $$ $$\frac{1}{6} + $$ $$\frac{1}{{12}} + $$ $$\frac{1}{{20}} + $$ $$\frac{1}{{30}} + $$ $$\frac{1}{{42}} + $$ $$\frac{1}{{56}} + $$ $$\frac{1}{{72}} + $$ $$\frac{1}{{90}} + $$ $$\frac{1}{{110}} + $$ $$\frac{1}{{132}}$$ $$ = ?$$

• (A) $$\frac{7}{8}$$
• (B) $$\frac{{11}}{{12}}$$
• (C) $$\frac{{11}}{{12}}$$
• (D) $$\frac{{17}}{{18}}$$

Show Answer

 Given expression,  $${\text{ = }}\left( {1 - \frac{1}{2}} \right)$$   $$ + $$ $$\left( {\frac{1}{2} - \frac{1}{3}} \right)$$   $$ + $$ $$\left( {\frac{1}{3} - \frac{1}{4}} \right)$$   $$ + $$ $$\left( {\frac{1}{4} - \frac{1}{5}} \right)$$   $$ + $$ . . . . . $$ + $$ $$\left( {\frac{1}{{11}} - \frac{1}{{12}}} \right)$$ $$\eqalign{ & = \left( {1 - \frac{1}{{12}}} \right) \cr & = \frac{{11}}{{12}} \cr} $$

39.

Which of the following is the smallest fraction?

• (A) $$\frac{{12}}{{15}}$$
• (B) $$\frac{{11}}{{16}}$$
• (C) $$\frac{4}{7}$$
• (D) $$\frac{7}{{12}}$$

Show Answer

 A. $$\frac{{12}}{{15}}$$ = 0.8 B. $$\frac{{11}}{{16}}$$ = 0.6875 C. $$\frac{4}{7}$$ = 0.5714 D. $$\frac{7}{{12}}$$ = 0.5833 Smallest fraction = $$\frac{4}{7}$$ Answer

40.

$$1\frac{3}{4} - 1\frac{1}{5} + 1\frac{5}{8} = ?$$

• (A) $$2\frac{7}{{40}}$$
• (B) $$3\frac{7}{{40}}$$
• (C) $$9\frac{5}{8}$$
• (D) $$10\frac{7}{8}$$

Show Answer

 $$\eqalign{ & {\text{Given expression,}} \cr & \frac{7}{4} - \frac{6}{5} + \frac{{13}}{8} \cr & = \frac{{70 - 48 + 65}}{{40}} \cr & = \frac{{87}}{{40}} \cr & = 2\frac{7}{{40}} \cr} $$