CAT 1998QA Question 29

Number TheoryEasy
Passage / Data

Answer the next 2 questions based on the following information.

A company purchases components A and B from Germany and USA respectively. A and B form 30% and 50% of the total production cost. Current gain is 20%. Due to change in the international scenario, cost of the German mark increased by 30% and that of USA dollar increased by 22%. Due to market conditions, the selling price cannot be increased beyond 10%.

What is the digit in the unit’s place of 251?

Answer & solution

  • A

    2

  • 8

  • C

    1

  • D

    4

Solution

Since 2 has a cyclicity of 4,
i.e. 21 = 2, 22 = 4, 23 = 8, 24 = 16, 25 = 32, 26 = 64 ..., the last digits (2, 4, 8, 6) are in four cycles.
∴ On dividing 514, we get the remainder as 3.

∴ The last digits has tobe 23 = 8

Shortcut:
Since cyclicity of the power of 2 is 4, so 251 can be written in 24(12) + 3 or unit digit will be 23 = 8.

CAT 1998 QA Q29: What is the digit in the unit’s place of 2 51 ? — Solution | TheCATExam