Integers — Multiple Choice Questions

The addition of -30, -15, -10, 20 and 15 is :

1. -20

2. 25

3. -15

4. 15

Answer

Solving,

(-30) + (-15) + (-10) + 20 + 15

= -55 + 35

= -20

Hence, option 1 is the correct option.

Two integers a and b are such that a ÷ b = -2; then (a, b) is :

1. (-8, -4)

2. (-2, 4)

3. (6, -3)

4. (10, 5)

Answer

Checking each option for a ÷ b = -2 :

For (6, -3) : 6 ÷ (-3) = -2

Hence, option 3 is the correct option.

15 ÷ (-5) - (2 × -3) is equal to :

1. 9

2. -9

3. 3

4. -3

Answer

Solving,

15 ÷ (-5) - (2 × -3)

= -3 - (-6)

= -3 + 6

= 3

Hence, option 3 is the correct option.

7 - 8 ÷ (-2) + 3 × (-4) is equal to :

1. 1

2. -13

3. 13

4. -1

Answer

Solving,

7 - 8 ÷ (-2) + 3 × (-4)

= 7 - (-4) + (-12)

= 7 + 4 - 12

= -1

Hence, option 4 is the correct option.

-[8 - {11 + 30 ÷ (4 - $\overline{7 - 5}$)}] is equal to :

1. -18

2. 18

3. 16

4. -14

Answer

Solving,

-[8 - {11 + 30 ÷ (4 - $\overline{7 - 5})$}]

= -[8 - {11 + 30 ÷ (4 - 2)}]

= -[8 - {11 + 30 ÷ 2}]

= -[8 - {11 + 15}]

= -[8 - 26]

= -[-18]

= 18.

Hence, option 2 is the correct option.

The number that must be subtracted from -2 to get -15 is :

1. -17

2. 17

3. -13

4. 13

Answer

Let the number to be subtracted be x.

-2 - x = -15

-x = -15 + 2

-x = -13

x = 13

Hence, option 4 is the correct option.

$\Bigg\lbrace -2 \div \left(-\dfrac{1}{2}\right)\Bigg\rbrace \Bigg\lbrace -3 \div \left(-\dfrac{1}{3}\right)\Bigg\rbrace\Bigg\lbrace -4 \div \left(-\dfrac{1}{4}\right)\Bigg\rbrace$ is equal to :

1. (-4) × (-9) × (-16)

2. 4 × 9 × 16

3. $\left(-\dfrac{1}{4}\right)\left(-\dfrac{1}{9}\right)\left(-\dfrac{1}{16}\right)$

4. $\dfrac{1}{4\times9\times16}$

Answer

$-2 \div \left(-\dfrac{1}{2}\right) = -2 × (-2) = 4 \\[1em] -3 \div \left(-\dfrac{1}{3}\right) = -3 × (-3) = 9 \\[1em] -4 \div \left(-\dfrac{1}{4}\right) = -4 × (-4) = 16$

So, the expression = 4 × 9 × 16

Hence, option 2 is the correct option.

(-45) × 0 + (-45) ÷ 0 is equal to :

1. 1

2. 0

3. -90

4. none of these

Answer

The term (-45) ÷ 0 involves division by zero, which is not defined. Hence, the value of the expression is not defined.

Hence, option 4 is the correct option.

5 ÷ [5 + {5 - (5 - $\overline{5 - 5}$)}] is :

1. 0

2. 1

3. -1

4. 5

Answer

5 ÷ [5 + {5 - (5 - $\overline{5 - 5})$}]

= 5 ÷ [5 + {5 - (5 - 0)}]

= 5 ÷ [5 + {5 - 5}]

= 5 ÷ [5 + 0]

= 5 ÷ 5

= 1.

Hence, option 2 is the correct option.

$12 \div \dfrac{2}{9} \times 2\dfrac{1}{4}$ is :

1. $\dfrac{32}{9}$

2. $\dfrac{243}{2}$

3. 8

4. none of these

Answer

$12 \div \dfrac{2}{9} \times 2\dfrac{1}{4} \\[1em] = 12 \times \dfrac{9}{2} \times \dfrac{9}{4} \\[1em] = \dfrac{12 \times 9 \times 9}{2 \times 4} \\[1em] = \dfrac{972}{8} \\[1em] = \dfrac{243}{2}$

Hence, option 2 is the correct option.

(-3) × [5 + (-9)] is equal to :

1. -12

2. 12

3. 6

4. -6

Answer

Solving,

(-3) × [5 + (-9)]

= (-3) × (-4)

= 12

Hence, option 2 is the correct option.

Liquid at 15°C is cooled to temperature -5°C, the fall in temperature is :

1. 10°C

2. -10°C

3. 20°C

4. -20°C

Answer

Fall in temperature = 15°C - (-5°C) = 15°C + 5°C = 20°C

Hence, option 3 is the correct option.

The number 25 is decreased by 6 in every second. The number by which 25 will decrease in 6 seconds :

1. 5

2. -5

3. 30

4. 36

Answer

Decrease in 6 seconds = 6 × 6 = 36

Hence, option 4 is the correct option.

A = -9, B = -12 and C = 10; then A + B - C is equal to :

1. 31

2. -31

3. -11

4. 11

Answer

Solving,

A + B - C

= (-9) + (-12) - 10

= -21 - 10

= -31

Hence, option 2 is the correct option.