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

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

by VJesus12 » Thu Jan 13, 2022 5:12 am

00:00

A

B

C

D

E

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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

Source: Veritas Prep

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### Re: For a certain integer $$x,$$ the units digit of $$(x+2)^2$$ is $$9.$$ Which of the following could be the units digi

by swerve » Fri Jan 14, 2022 5:38 am
VJesus12 wrote:
Thu Jan 13, 2022 5:12 am
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

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

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