The unit’s digit of (1373)³⁶ – (1442)²⁰ is:

Question

Question

This question was previously asked in

RRB ALP Electrician 22 Jan 2019 Official Paper (Shift 1)

Answer 1

Concept:

To find the unit digit, consider the unit digit of the given number and find its cyclicity from the power.

Example: 2⁵

∵ 2 as a unit digit repeats after every 4 power, 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32

⇒ Cyclicity of 2 = 4

Unit digit of 2⁵ = 2¹ = 2

Similarly, cyclicity of 3 = 4

Calculation:

Unit digit of (1373)³⁶ – (1442)²⁰

⇒ Unit digit of (3)³⁶ – (2)²⁰

⇒ Unit digit of {(3)^{9 × 4} – (2)^{5 × 4}}

⇒ Unit digit of {(3)⁴ – (2)⁴}

⇒ Unit digit of {81 – 16}

⇒ Unit digit of 65

⇒ 5