Playing with Numbers — Multiple Choice Questions

Generalised form of three-digit number xyz is

1. x + y + z

2. 100x + 10y + z

3. 100z + 10y + x

4. 100y + 10x + z

Answer

In a 3-digit number xyz, hundred's digit is x, ten's digit is y and unit's digit is z.

∴ xyz = 100 × x + 10 × y + z = 100x + 10y + z

Hence, option 2 is the correct option.

The usual form of 100a + b + 10c is

1. abc

2. cab

3. bac

4. acb

Answer

100a + b + 10c = 100a + 10c + b

Here, hundred's digit is a, ten's digit is c and unit's digit is b.

∴ Usual form = acb

Hence, option 4 is the correct option.

When the sum of a 2-digit number ab and number obtained by reversing the digits is divided by (a + b), then quotient is

1. a - b

2. 9

3. 11

4. None of these

Answer

ab + ba = (10a + b) + (10b + a) = 11a + 11b = 11(a + b)

On dividing by (a + b), we get

Quotient = 11(a + b)/(a + b) = 11

Hence, option 3 is the correct option.

When the sum of a 3-digit number abc and numbers obtained by changing the order of the digits cyclically is divided by 111, then quotient is

1. 37

2. a - b + c

3. a + b + c

4. 3

Answer

abc + bca + cab = (100a + 10b + c) + (100b + 10c + a) + (100c + 10a + b) = 111a + 111b + 111c = 111(a + b + c)

On dividing by 111, we get

Quotient = 111(a + b + c)/111 = (a + b + c)

Hence, option 3 is the correct option.

If A + A + A = B1, where A and B are different digits, then

1. A = 1, B = 5

2. A = 5, B = 2

3. A = 5, B = 1

4. A = 7, B = 2

Answer

A + A + A = B1

⇒ 3A is a 2-digit number whose ones digit is 1.

Now, 3 × 7 = 21

⇒ A = 7 and B1 = 21

⇒ B = 2

Hence, option 4 is the correct option.

Which of the following numbers is not divisible by 2?

1. 437218

2. 437821

3. 437812

4. 437182

Answer

According to the divisibility of 2, if the unit's digit of the number is 0, 2, 4, 6 or 8 then the number is divisible by 2.

The unit's digit of 437821 is 1, which is an odd number.

∴ 437821 is not divisible by 2.

Hence, option 2 is the correct option.

Which of the following numbers is not divisible by 10?

1. 32570

2. 32750

3. 32500

4. 32075

Answer

According to the divisibility of 10, if the unit's digit of the number is 0 then the number is divisible by 10.

The unit's digit of 32075 is 5.

∴ 32075 is not divisible by 10.

Hence, option 4 is the correct option.

Which of the following numbers is divisible by 4?

1. 98764

2. 98746

3. 98674

4. 98647

Answer

According to the divisibility of 4, if the number formed by its last two (ten's and unit's) digits is divisible by 4 then the number is divisible by 4.

Number formed by last two digits of 98764 = 64 = 4 × 16, which is divisible by 4.

Number formed by last two digits of 98746 = 46, number formed by last two digits of 98674 = 74 and number formed by last two digits of 98647 = 47, which are not divisible by 4.

∴ 98764 is divisible by 4.

Hence, option 1 is the correct option.

Which of the following numbers is divisible by 8?

1. 32466

2. 32476

3. 32486

4. 32456

Answer

According to the divisibility of 8, if the number formed by its last three (hundred's, ten's and unit's) digits is divisible by 8 then the number is divisible by 8.

Number formed by last three digits of 32456 = 456 = 8 × 57, which is divisible by 8.

Number formed by last three digits of 32466, 32476 and 32486 are 466, 476 and 486 respectively, which are not divisible by 8.

∴ 32456 is divisible by 8.

Hence, option 4 is the correct option.

Which of the following numbers is divisible by 11?

1. 725824

2. 752824

3. 725842

4. 725482

Answer

According to the divisibility of 11, if the difference of the sum of digits at the odd places (starting from unit's place) and the sum of the digits at even places is either 0 or divisible by 11, then the number is divisible by 11.

For 725824,

Sum of digits at odd places = 4 + 8 + 2 = 14

Sum of digits at even places = 2 + 5 + 7 = 14

Their difference = 14 - 14 = 0

∴ 725824 is divisible by 11.

Hence, option 1 is the correct option.

Which of the following numbers is not divisible by 9?

1. 24354

2. 24453

3. 24534

4. 24564

Answer

According to the divisibility of 9, if the sum of the digits of the number is divisible by 9 then the number is divisible by 9.

Sum of digits of 24354 = 2 + 4 + 3 + 5 + 4 = 18, which is divisible by 9.

Sum of digits of 24453 = 2 + 4 + 4 + 5 + 3 = 18, which is divisible by 9.

Sum of digits of 24534 = 2 + 4 + 5 + 3 + 4 = 18, which is divisible by 9.

Sum of digits of 24564 = 2 + 4 + 5 + 6 + 4 = 21, which is not divisible by 9.

∴ 24564 is not divisible by 9.

Hence, option 4 is the correct option.

If 467x8 is divisible by 3, then value of x

1. 1

2. 2

3. 3

4. 4

Answer

According to the divisibility of 3, if the sum of the digits of the number is divisible by 3 then the number is divisible by 3.

∵ 467x8 is divisible by 3

⇒ 4 + 6 + 7 + x + 8 is divisible by 3

⇒ 25 + x is divisible by 3

⇒ 25 + x = 27, 30, 33, ...............

⇒ x = 2, 5, 8, ...............

Out of the given options, x = 2.

Hence, option 2 is the correct option.

If 36x52y8 is divisible by 9, then x + y is

1. 2

2. 3

3. 4

4. 5

Answer

According to the divisibility of 9, if the sum of the digits of the number is divisible by 9 then the number is divisible by 9.

∵ 36x52y8 is divisible by 9

⇒ 3 + 6 + x + 5 + 2 + y + 8 is divisible by 9

⇒ 24 + x + y is divisible by 9

⇒ 24 + x + y = 27, 36, ...............

⇒ x + y = 3, 12, ...............

Out of the given options, x + y = 3.

Hence, option 2 is the correct option.