Operations on Whole Numbers — Multiple Choice Questions

The smallest whole number is :

1. 1

2. 2

3. 10

4. none of these

Answer

The smallest whole number is 0.

Hence, option 4 is the correct option.

The least number of 4 digit which is exactly divisible by 7 is :

1. 1,015

2. 1,008

3. 1,001

4. 1,022

Answer

The smallest 4-digit number = 1000.

$\begin{array}{l} \phantom{x^2 }{142} \\ 7\overline{\smash{\big)}1000} \\ \phantom{x}\phantom{}\underline{-7} \\ \phantom{{x^2))}} 30 \\ \phantom{{x} )}\underline{-28} \\ \phantom{{x^2 } + } 20 \\ \phantom{{x} ))}\underline{-14} \\ \phantom{{x^2 +)}} 6 \\ \end{array}$

Quotient = 142

Remainder = 6

“To get the next multiple of 7, we add (7 − remainder) to 1000.”

Next multiple = 1000 + (7 − 6)

= 1000 + 1

= 1001.

Therefore, the least 4-digit number exactly divisible by 7 is 1,001.

Hence, option 3 is the correct option.

The largest number of 4 digits exactly divisible by 13 is

1. 9,996

2. 9,997

3. 9,995

4. 9,984

Answer

The largest 4-digit number = 9,999.

To find the largest 4-digit number exactly divisible by 13, we divide 9,999 by 13 and subtract the remainder to get the largest multiple.

$\begin{array}{l} \phantom{x^2}{769} \\ 13\overline{\smash{\big)}9999} \\ \phantom{x}\phantom{)}\underline{-91} \\ \phantom{{x^2 } +} 89 \\ \phantom{{x))} }\underline{-78} \\ \phantom{{x^2 } + 2} 119 \\ \phantom{{x} +)}\underline{-117} \\ \phantom{{x^2 + 3)}} 2 \\ \end{array}$

The remainder when 9,999 is divided by 13 is 2.

Therefore, 9,999 − 2 = 9,997.

Hence, option 2 is the correct option.

What least number should be subtracted from 10,003 to get a number exactly divisible by 11?

1. 7

2. 6

3. 5

4. 4

Answer

Given number = 10,003.

To make 10003 exactly divisible by 11, we divide 10,003 by 11 and subtract the remainder from 10,003.

$\begin{array}{l} \phantom{x^2 +}{\quad 909} \\ 11\overline{\smash{\big)}\quad 10003} \\ \phantom{x^ + )}\phantom{)}\underline{-99} \\ \phantom{{x^2 } + 2a} 10 \\ \phantom{{x} +1a}\underline{-00} \\ \phantom{{x^2 } + 2xa } 103 \\ \phantom{{x} +1xa}\underline{-99} \\ \phantom{{x^2 + 3x +)}} 4 \\ \end{array}$

The remainder when 10003 is divided by 11 is 4.

Least number to be subtracted = remainder = 4.

Hence, option 4 is the correct option.

What least number should be added to 6,000 to get a number exactly divisible by 19?

1. 9

2. 8

3. 4

4. 6

Answer

Given number = 6,000.

$\begin{array}{l} \phantom{x^21}{\quad 315} \\ 19\overline{\smash{\big)}\quad 6000} \\ \phantom{x^ + )}\phantom{)}\underline{-57} \\ \phantom{{x^2 } + 2a} 30 \\ \phantom{{x} +1a}\underline{-19} \\ \phantom{{x^2 } + 2xa } 110 \\ \phantom{{x} +1xa}\underline{-95} \\ \phantom{{x^2 + 3x +)}} 15 \\ \end{array}$

The remainder when 6000 is divided by 19 is 15.

Least number to be added to make the number divisible = 19 − 15 = 4.

Hence, option 3 is the correct option.

What whole number is nearest to 457 which is divisible by 11?

1. 462

2. 460

3. 451

4. 450

Answer

Given number = 457.

To find the nearest number divisible by 11 :

$\begin{array}{l} \phantom{x^21}{\quad 41} \\ 11\overline{\smash{\big)}\quad 457} \\ \phantom{x^ + )}\phantom{)}\underline{-44} \\ \phantom{{x^2 } + 2a} 17 \\ \phantom{{x} +1a}\underline{-11} \\ \phantom{{x^2 } + 2xa } 6\ \end{array}$

The multiple of 11 just below 457 is 11 x 41 = 451.

The multiple of 11 just above 457 is 11 x 42 = 462.

Distance from 457 to 451: ∣457 − 451∣ = 6.

Distance from 457 to 462: ∣457 − 462∣ = 5.

The smaller distance is 5, which corresponds to the number 462.

Therefore, the whole number nearest to 457 that is divisible by 11 is 462.

Hence, option 1 is the correct option.

How many whole numbers are there between 1,036 and 1,263?

1. 227

2. 228

3. 226

4. 225

Answer

Number of whole numbers = (1263 − 1036) − 1

= 227−1

= 226

Hence, option 3 is the correct option.

A number when divided by 43 gives 12 as quotient and 24 as remainder. The number is

1. 547

2. 545

3. 543

4. 540

Answer

Given:

Divisor = 43

Quotient = 12

Remainder = 24

By formula,

Dividend = Divisor x Quotient + Remainder

Substitute the values into the formula:

Dividend = 43 x 12 + 24

= 516 + 24

= 540.

Hence, option 4 is the correct option.

In a division sum, the dividend is 398, quotient is 15 and the remainder is 8. What is the divisor?

1. 31

2. 26

3. 17

4. 23

Answer

Given:

Dividend = 398

Quotient = 15

Remainder = 8

By formula; Dividend = Divisor x Quotient + Remainder

Substitute the values into the formula:

⇒ 398 = Divisor x 15 + 8

⇒ Divisor x 15 = 398 - 8

⇒ Divisor x 15 = 390

⇒ Divisor = $\dfrac{390}{15}$

⇒ Divisor = 26

Hence, option 2 is the correct option.

8 x 273 x 125 = ?

1. 27,300

2. 2,70,300

3. 2,73,000

4. 27,30,000

Answer

Given :

⇒ 8 x 273 x 125

⇒ 273 x (8 x 125)

⇒ 273 x 1,000

⇒ 2,73,000

Hence, option 3 is the correct option.

4 x 346 x 25 = ?

1. 28,400

2. 32,500

3. 33,800

4. 34,600

Answer

Given :

⇒ 4 x 346 x 25

⇒ 346 x (4 x 25)

⇒ 346 x 100

⇒ 34,600

Hence, option 4 is the correct option.

13,729 x 93 + 13,729 x 7 = ?

1. 23,62,900

2. 13,72,900

3. 6,86,450

4. 4,57,620

Answer

Given, 13,729 x 93 + 13,729 x 7

Using the Distributive law of multiplication over addition : a x b + a x c = a x (b + c)

⇒ 13,729 x (93 + 7)

⇒ 13,729 x 100

⇒ 13,72,900

Hence, option 2 is the correct option.

2,563 x 187 - 2,563 x 87 = ?

1. 2,56,300

2. 1,28,150

3. 3,84,450

4. none of these

Answer

Given,

2,563 x 187 - 2,563 x 87

Using the Distributive law of multiplication over subtraction: a x b - a x c = a x (b - c)

⇒ 2,563 x (187 - 87)

⇒ 2,563 x 100

⇒ 2,56,300

Hence, option 1 is the correct option.

546 x 98 = ?

1. 52,518

2. 53,508

3. 54,108

4. 52,708

Answer

Given,

⇒ 546 x 98

⇒ 546 x (100 - 2)

⇒ 546 x 100 - 546 x 2

⇒ 54,600 - 1,092

⇒ 53,508

Hence, option 2 is the correct option.

8,456 - ? = 3,580

1. 2,698

2. 4,586

3. 4,876

4. 5,016

Answer

Given,

8,456 - ? = 3,580

Let missing number be x.

⇒ 8,456 - x = 3,580

⇒ x = 8,456 - 3,580 = 4,876.

Hence, option 3 is the correct option.