Question

If \(-75=9a+b\) where \(0 ≤ b <9\),\( a, b\) are unique integers, then \(b =\)

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The Correct Option is D

We are given the equation: \[ -75 = 9a + b \] where \(0 \leq b < 9\), and \(a\) and \(b\) are integers.
Rearrange the equation to express \(b\): \[ b = -75 - 9a \] Now, we will substitute different integer values for \(a\) such that \(0 \leq b < 9\). 1. If \(a = -9\): \[ b = -75 - 9(-9) = -75 + 81 = 6 \] Thus, when \(a = -9\), \(b = 6\), which satisfies \(0 \leq b < 9\).

The correct option is (D): \(6\)