Practice MCQ Questions and Answer on Simplification

1.

Which of the following values of x and y satisfy the following equations i and ii?
i. 3x + y = 19
ii. x - y = 9

• (A) -7, -2
• (B) -7, 2
• (C) 7, -2
• (D) 7, 2

Show Answer

 $$\eqalign{ & {\text{3}}x + y = 19\,.....(i) \cr & x - y = 9\,.....(ii) \cr & {\text{Adding (i) and (ii),}} \cr & {\text{we get }} \cr & {\text{4}}x = 28 \cr & x = 7 \cr & {\text{Putting }}x\,{\text{ = 7}}\,{\text{in (i),}} \cr & {\text{we get }} \cr & 3x + y = 19 \cr & 21 + y = 19 \cr & y = 19 - 21 = - 2 \cr & {\text{Answer is 7, }} - {\text{2}} \cr} $$

2.

The value of $$\frac{3}{1^2\times 2^2}+$$   $$\frac{5}{2^2\times 3^2}+$$   $$\frac{7}{3^2\times 4^2}+$$   $$\frac{9}{4^2\times 5^2}+$$   $$\frac{11}{5^2\times 6^2}+$$   $$\frac{13}{6^2\times 7^2}+$$   $$\frac{15}{7^2\times 8^2}+$$   $$\frac{17}{8^2\times 9^2}+$$   $$\frac{19}{9^2\times {10}^2}$$   is = ?

• (A) $$\frac{1}{100}$$
• (B) $$\frac{99}{100}$$
• (C) 1
• (D) $$\frac{101}{100}$$

Show Answer

 $$\eqalign{ & {\text{Given expression,}} \cr & \left( {\frac{1}{{{1^2}}} - \frac{1}{{{2^2}}}} \right) + \left( {\frac{1}{{{2^2}}} - \frac{1}{{{3^2}}}} \right) + \left( {\frac{1}{{{3^2}}} - \frac{1}{{{4^2}}}} \right) + \left( {\frac{1}{{{4^2}}} - \frac{1}{{{5^2}}}} \right) . . . . + \left( {\frac{1}{{{9^2}}} - \frac{1}{{{{10}^2}}}} \right) \cr & = \left( {\frac{1}{{{1^2}}} - \frac{1}{{{2^2}}}} \right) \cr & = \left( {1 - \frac{1}{{100}}} \right) \cr & = \frac{{99}}{{100}} \cr} $$

3.

Evaluated : $$\frac{9\left|3-5\right|-5\left|4\right|÷10}{-3\left(5\right)-2\times 4÷2}$$

• (A) $$\frac{9}{10}$$
• (B) $$-\frac{8}{17}$$
• (C) $$-\frac{16}{19}$$
• (D) $$\frac{4}{7}$$

Show Answer

 $$\eqalign{ & {\text{According to question}} \cr & \frac{{9|3 - 5| - 5|4| \div 10}}{{ - 3\left( 5 \right) - 2 \times 4 \div 2}} \cr & \Rightarrow \frac{{9 \times 2 - 20 \div 10}}{{ - 15 - 2 \times 2}} \cr & \Rightarrow \frac{{18 - 2}}{{ - 15 - 4}} \cr & \Rightarrow - \frac{{16}}{{19}} \cr} $$

4.

The value of x in the equation $$\frac{113\times 4-x\times 2}{13\times 9-5\times 7}\text{ = 5}$$     is?

• (A) 21
• (B) 27
• (C) 35
• (D) 42

Show Answer

 $$\eqalign{ & \frac{{113 \times 4 - x \times 2}}{{13 \times 9 - 5 \times 7}} = 5 \cr & \Rightarrow \frac{{452 - 2x}}{{117 - 35}} = 5 \cr & \Rightarrow \frac{{452 - 2x}}{{82}} = 5 \cr & \Rightarrow 452 - 2x = 410 \cr & \Rightarrow 2x = 452 - 410 = 42 \cr & \Rightarrow x = 21 \cr} $$

5.

What is the maximum number of half - pint bottles of cream that can be filled with a 4-gallon can of cream? (2pt. = 1qt. and 4qt. = 1gal.)

• (A) 16
• (B) 24
• (C) 30
• (D) 64

Show Answer

 $$\eqalign{ & {\text{4 gal}} \cr & {\text{ = (4}} \times {\text{4)qt}} \cr & {\text{ = 16 qt}} \cr & {\text{ = }}\left( {16 \times 2} \right){\text{pt}} \cr & {\text{ = 32 pt}} \cr & \therefore {\text{Number of botteles}} \cr & {\text{ = }}\frac{{32}}{{\frac{1}{2}}} \cr & {\text{ = 64}} \cr} $$

6.

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

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

Show Answer

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

7.

If x is a positive number, then which of the following fractions has the greatest value ?

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

Show Answer

 Clearly, $$\frac{{x + 1}}{x}$$ is the only fraction in which the numerator is greater then the denominator. So, it is greatest fraction.

8.

$$4848÷24\times 11-222=?$$

• (A) 200
• (B) 2444
• (C) 2000
• (D) $$115\frac{3}{8}$$

Show Answer

 $$\eqalign{ & \frac{{4848}}{{24}} \times 11 - 222 \cr & = 202 \times 11 - 222 \cr & = 2222 - 222 \cr & = 2000 \cr} $$

9.

The value of 1 + 3 + 5 + 7 + . . . . . . (2n - 1) is:

• (A) (2n - 1) × (2n - 1)
• (B) $$\frac{n}{2}$$
• (C) n × n
• (D) $$\frac{n\left(n+1\right)}{2}$$

Show Answer

 1 + 3 + 5 + 7 + . . . . . . (2n - 1) We know that such of N odd number = n2 = n × n

10.

$$\frac{{\left(3\frac{2}{3}\right)}^2-{\left(2\frac{1}{2}\right)}^2}{{\left(4\frac{3}{4}\right)}^2-{\left(3\frac{1}{3}\right)}^2}$$   $$÷$$ $$\frac{3\frac{2}{3}-2\frac{1}{2}}{4\frac{3}{4}-3\frac{1}{3}}$$   = ?

• (A) $$\frac{37}{97}$$
• (B) $$\frac{74}{97}$$
• (C) $$1\frac{23}{74}$$
• (D) None of these

Show Answer

 $$\eqalign{ & {\text{If }}a = 3\frac{2}{3}, \cr & b = 2\frac{1}{2}, \cr & c = 4\frac{3}{4}, \cr & d = 3\frac{1}{3}, \cr & {\text{then}} \cr & {\text{Given expression ,}} \cr & \,\,\,\,\frac{{\left( {{a^2} - {b^2}} \right)}}{{\left( {{c^2} - {d^2}} \right)}} \div \frac{{\left( {a - b} \right)}}{{\left( {c - d} \right)}} \cr & = \frac{{\left( {{a^2} - {b^2}} \right)}}{{\left( {{c^2} - {d^2}} \right)}} \times \frac{{\left( {c - d} \right)}}{{\left( {a - b} \right)}} \cr & = \frac{{\left( {a + b} \right)}}{{\left( {c + d} \right)}} \cr & = \frac{{3\frac{2}{3} + 2\frac{1}{2}}}{{4\frac{3}{4} + 3\frac{1}{3}}} \cr & = \frac{{\frac{{11}}{3} + \frac{5}{2}}}{{\frac{{19}}{4} + \frac{{10}}{3}}} \cr & = \frac{{37}}{6} \times \frac{{12}}{{97}} \cr & = \frac{{74}}{{97}} \cr} $$