Waste less time on Facebook — follow Brilliant.
×

Numbers and Operations

Factors, Divisibility, Remainders

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

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) \(\ \ 11 \)

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

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

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) \(\ \ 6\)

×

Problem Loading...

Note Loading...

Set Loading...