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Suppose \(m\) and \(n\) are integers such that \(m\) is divisible by \(8\) and \(n\) is divisible by \(5\). Which of the following integers must be divisible by \(40?\)

\(\begin{array}{r r l}
&\mbox{I.} & mn \\

&\mbox{II.} & 5m - 8n \\

&\mbox{III.} & 8m - 5n \\

\end{array}\)

(A) I only

(B) I and II only

(C) I and III only

(D) II and III only

(E) I, II, and III

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If \(n\) is a positive integer, what is the remainder when \(4n + 11\) is divided by \(4?\)

(A) \(\ \ 0\)

(B) \(\ \ 1\)

(C) \(\ \ 3\)

(D) \(\ \ 4\)

(E) \(\ \ 11 \)

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Suppose \(m\) and \(n\) are both positive integers strictly greater than 1. If \(m\) divides both \(n+9\) and \(n+22\), which of the following is a possible value of \(m\)?

(A) \(\ \ 1\)

(B) \(\ \ 9\)

(C) \(\ \ 13\)

(D) \(\ \ 22\)

(E) \(\ \ \)None of the above

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How many positive integers \(k\) are there such that dividing \(48\) by \(k\) leaves a remainder of \(4\)?

(A) \(\ \) One

(B) \(\ \) Two

(C) \(\ \) Three

(D) \(\ \) Four

(E) \(\ \) Five

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Let \(n\) be a positive integer such that the remainder of \(3n + 6\) upon division by \(4\) is \(1.\) Which of the following is a possible value for \(n\)?

(A) \(\ \ 0\)

(B) \(\ \ 2\)

(C) \(\ \ 4\)

(D) \(\ \ 5\)

(E) \(\ \ 6\)

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