If $x$ is a prime number greater than $3,$ what is the remainder when $x^2$ is divided by $8?$

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by M7MBA » Wed Sep 09, 2020 6:36 am

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If $x$ is a prime number greater than $3,$ what is the remainder when $x^2$ is divided by $8?$

A. 0
B. 1
C. 3
D. 4
E. 5

Answer: B

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Wed Sep 09, 2020 6:36 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: If $x$ is a prime number greater than $3,$ what is the remainder when $x^2$ is divided by $8?$

by deloitte247 » Sat Sep 12, 2020 11:51 pm

Prime numbers greater than 3 are 5, 7, 11, ...
$$So,\ if\ x=5,\ then\ \frac{x^2}{8}=\frac{5^2}{8}=\frac{25}{8}=3\ remainder1$$
$$So,\ if\ x=7,\ then\ \frac{x^2}{8}=\frac{7^2}{8}=\frac{49}{8}=6\ remainder1$$
$$So,\ if\ x=11,\ then\ \frac{x^2}{8}=\frac{11^2}{8}=\frac{121}{8}=15\ remainder1$$
In all cases, remainder = 1

Answer = option B

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