CAT 1998 — QA Question 29
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
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 , 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.