Question

On dividing a number by 35, we get 29 as remainder. If the same number is divided by 7, then the remainder is

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

When divisors are multiples, reduce the remainder using the smaller divisor.

Answer 1

The Correct Option is A

To solve this problem, we need to understand how remainders work in division. Given that when a number \( x \) is divided by 35, the remainder is 29, we can express this situation as:

\(x = 35k + 29\), where \( k \) is an integer.

We need to find the remainder when the same number \( x \) is divided by 7.

Let's substitute the expression for \( x \) and simplify it modulo 7:

\(x = 35k + 29\)

Now, reduce each term modulo 7.

• \(35 \equiv 0 \pmod{7}\)
• \(29 \equiv 1 \pmod{7}\)

Thus, we can write:

\(x = 35k + 29 \equiv 0 \cdot k + 1 \equiv 1 \pmod{7}\)

Hence, the remainder when the number \( x \) is divided by 7 is 1.

Conclusion: The remainder when the number is divided by 7 is 1.