For a certain integer \(x,\) the units digit of \((x+2)^2\) is \(9.\) Which of the following could be the units digit of

[VJesus12]

For a certain integer \(x,\) the units digit of \((x+2)^2\) is \(9.\) Which of the following could be the units digit of \(|x+1|?\)

A. 0
B. 3
C. 4
D. 5
E. 7

Answer: C

Source: Veritas Prep

[swerve]

For a certain integer \(x,\) the units digit of \((x+2)^2\) is \(9.\) Which of the following could be the units digit of \(|x+1|?\)

A. 0
B. 3
C. 4
D. 5
E. 7

Answer: C

Source: Veritas Prep

Unit digit on squaring any number can be 9 if and only if unit number of which we are squaring, must be either \(3\) or \(7\)

And to have \(7\) or \(3\) at unit digit \(x\) can be \(1,5,-5,-9\)

When \(x = 1, |x + 1| = 2, \quad \Large{\color{red}\chi}\)

When \(x = 5, |x + 1| = 6, \quad \Large{\color{red}\chi}\)

When \(x = -5, |x + 1| = |-4| = 4, \quad \Large{\color{green}\checkmark}\)

When \(x = -9, |x + 1| = |-8| = 8, \quad \Large{\color{red}\chi}\)

Therefore, C