Question

Let x = 23729 × 78900 + 57492 The unit's digit in x is:
1. 1
2. 8
3. 6
4. 9

Answer 1

Correct Answer - Option 4 : 9

Given:

x = 23729 × 78900 + 57492 

Concept used:

According to cyclicity of 2, 3, and 7, unit digit of

Cyclicity of 2:

⇒ 21 = 2

⇒ 22 = 4

⇒ 23 = 8

⇒ 24 = 6

Cyclicity of 3:

⇒ 31 = 3

⇒ 32 = 9

⇒ 33 = 7

⇒ 34 = 1

Cyclicity of 7:

⇒ 71 = 7

⇒ 72 = 9

⇒ 73 = 3

⇒ 74 = 1

Calculation:

x = 23729 × 78900 + 57492 

x = 23729 × 2900 × 13⁹⁰⁰ × 3900 + 57492

Unit digit of 23729 is same as the unit digit of 3729

⇒ 23729 = 3(728 + 1)

⇒ 34 × 182 + 1

Hence unit digit of 34 × 182 + 1 is 3.

Now,

Unit digit of 2900 is 

⇒ 2900

⇒ 34 × 225 + 0

⇒ 24 × 225 + 4

Hence unit digit of 24 × 225 + 4 is 6.

Unit digit of 13900 × 3900 is same as the unit digit of 3900

⇒ 13900 × 3900 = 3900 × 3900

⇒ 34 × 225 + 0

⇒ 34 × 225 + 4

Hence unit digit of 34 × 225 + 4 is 1.

Unit digit of 57492  is same as the unit digit of 7492 

⇒ 57492 =7492 

⇒ 74 × 123 + 0

⇒ 74 × 123 + 4

Hence unit digit of ⇒ 74 × 123 + 4 is 1.

x = 23729 × 78900 + 57492 

x = 3 × 6 + 1

x = 19

∴ unit digit is 9.