Question

A number when divided by 7 leaves a remainder of 4. What is the remainder when it is divided by 5?

• A. 2
• B. 3
• C. 4
• D. 5

Hint:

For remainder problems, express the number in terms of the divisor and compute modulo the new divisor.

Answer 1

The Correct Option is B

The problem states that a number when divided by 7 leaves a remainder of 4, which implies the number can be expressed in the form of \(n = 7k + 4\), where \(k\) is an integer.

We need to find the remainder when this number is divided by 5.

Substitute the expression for \(n\) into the division by 5:

\[n = 7k + 4\]

\[(7k + 4) \div 5\]

We simplify \[7k\] considering its division by 5:

7 can be expressed in terms of modulo 5:

\[7 \equiv 2 \pmod{5}\]

Thus:

\[7k \equiv 2k \pmod{5}\]

Therefore,

\[7k + 4 \equiv 2k + 4 \pmod{5}\]

We need a value for \(k\) to test, as the modulo behavior of \((7k + 4)\) holds over \(\mathbb{Z}\). Let's use the minimal non-trivial cycle:

Values of \(k\)	\(7k + 4\)	Remainder when divided by 5
0	4	4
1	11	1
2	18	3
3	25	0
4	32	2

To match the problem statement, where the number divided by 7 gives remainder 4, the correct \(n\) initial value \(7k+4 = 11, 18, 25,...\). We determine:

Thus, choosing \(k=2\) gives \((7*2+4)\), producing a remainder of \[3\] when divided by 5.

The remainder is \[3\].

Hence, the correct answer is option: 3.