Question:
The product of two numbers \(x,8\) when divided by \(10\) leaves the remainder \(6\). Then what is the least positive integer \(x\)?
The product of two numbers \(x,8\) when divided by \(10\) leaves the remainder \(6\). Then what is the least positive integer \(x\)?
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For small-number remainder questions, direct substitution is often the fastest method.
Updated On: Jul 15, 2026
- \(7\)
- \(2\)
- \(5\)
- \(12\)
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The Correct Option is B
Solution and Explanation
Concept:
Translate the statement into modular arithmetic.
Step 1: Form the congruence.
Given: \[ 8x \equiv 6 \pmod{10} \]
Step 2: Simplify.
Check smallest positive integers. For: \[ x=1 \] \[ 8(1)=8 \] Remainder when divided by \(10\): \[ 8 \] Not correct. For: \[ x=2 \] \[ 8(2)=16 \] Remainder when divided by \(10\): \[ 6 \] Correct.
Step 3: Find least positive integer.
The least value is: \[ \boxed{2} \]
Step 1: Form the congruence.
Given: \[ 8x \equiv 6 \pmod{10} \]
Step 2: Simplify.
Check smallest positive integers. For: \[ x=1 \] \[ 8(1)=8 \] Remainder when divided by \(10\): \[ 8 \] Not correct. For: \[ x=2 \] \[ 8(2)=16 \] Remainder when divided by \(10\): \[ 6 \] Correct.
Step 3: Find least positive integer.
The least value is: \[ \boxed{2} \]
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