Consider the following statements. A : Remainder when 346 is divided by 33 is 1. B : Remainder when 348 is divided by 35 is 34. C : Remainder when 345 is divided by 35 is 1. Which of the following statement(s) is/are TRUE?

Consider the following statements. A : Remainder when 346 is divided by 33 is 1. B : Remainder when 348 is divided by 35 is 34. C : Remainder when 345 is divided by 35 is 1. Which of the following statement(s) is/are TRUE? Correct Answer Only A

GIVEN:

Three statements.

CALCULATION:

We know that:

For all-natural values of ‘a’ and ‘n’ :

When aⁿ is divided by (a – 1), then remainder will always be 1.

When aⁿ is divided by (a + 1), then remainder-

• When ‘n’ is even, then remainder will always be 1.
• When ‘n’ is odd, the remainder will always be ‘a’.

A:

Remainder when 34⁶ is divided by (34 – 1) = 1

B:

Remainder when 34⁸ is divided by (34 + 1) = 1

C:

Remainder when 34⁵ is divided by (34 + 1) = 34

Hence, only A is TRUE.