Question:
Six times a number when divided by \(8\) leaves remainder \(4\). How many such numbers are there between \(0\) and \(8\)?
Six times a number when divided by \(8\) leaves remainder \(4\). How many such numbers are there between \(0\) and \(8\)?
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For remainder problems, convert into modular equations and test within the given range.
Updated On: Jul 15, 2026
- \(1\)
- \(2\)
- \(3\)
- \(4\)
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The Correct Option is B
Solution and Explanation
Concept:
Translate the condition into congruence.
Step 1: Form the equation.
Given: \[ 6x \equiv 4 \pmod 8 \] Divide by \(2\): \[ 3x \equiv 2 \pmod 4 \]
Step 2: Find values between \(0\) and \(8\).
Check integers: For \(x=2\), \[ 6(2)=12 \] When divided by \(8\), remainder is: \[ 4 \] For \(x=6\), \[ 6(6)=36 \] When divided by \(8\), remainder is: \[ 4 \]
Step 3: Count them.
The numbers are: \[ 2,\;6 \] Total: \[ 2 \] Thus, the required answer is: \[ \boxed{2} \]
Step 1: Form the equation.
Given: \[ 6x \equiv 4 \pmod 8 \] Divide by \(2\): \[ 3x \equiv 2 \pmod 4 \]
Step 2: Find values between \(0\) and \(8\).
Check integers: For \(x=2\), \[ 6(2)=12 \] When divided by \(8\), remainder is: \[ 4 \] For \(x=6\), \[ 6(6)=36 \] When divided by \(8\), remainder is: \[ 4 \]
Step 3: Count them.
The numbers are: \[ 2,\;6 \] Total: \[ 2 \] Thus, the required answer is: \[ \boxed{2} \]
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