CAT 2005 — QA Question 16
Answer the next 2 questions based on the information given below.
Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.
The rightmost non-zero digit of the number 302720 is
Answer & solution
1
- B
3
- C
7
- D
9
302720 = 32720 × 102720
The rightmost non-zero digit of 302720 will be the digit in the unit’s place of 32720.
3’s power cycle is 3, 9, 7, 1 and cyclicity is 4.
i.e. if we get a remainder of 1, 2, 3, or 0 when 2720 is divided by 4, then the digit in the units place will be 3, 9, 7, or 1 respectively.
2720 = 680 × 4, i.e. the remainder is 0
∴ The digit in the unit’s place of 32720 is 1.
∴ The rightmost non-zero digit of 302720 is 1.
Hence, option (a).