CAT 2005QA Question 16

Number TheoryEasy
Passage / Data

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

Solution

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).

CAT 2005 QA Q16: The rightmost non-zero digit of the number 30 2720 is — Solution | TheCATExam