Difference between revisions of "G285 2021 MC10B"

Revision as of 20:19, 12 May 2021

Problem 1

Find $\left \lceil {\frac{3!+4!+5!+6!}{2+3+4+5+6}} \right \rceil$

$\textbf{(A)}\ 42\qquad\textbf{(B)}\ 43\qquad\textbf{(C)}\ 44\qquad\textbf{(D)}\ 45\qquad\textbf{(E)}\ 46$

Solution

Problem 2

If $deg(Q(x))=3$ , and $deg(K(x))=2$ , and $Q(x)=(x-2)K(x)$ , what is $deg(Q(x)-2K(x))$ ?

$\textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}\ 3\qquad\textbf{(E)}\ 4$

Solution

Problem 3

A convex hexagon of length $s$ is inscribed in a circle of radius $r$ , where $r \neq s$ . If $\frac{s}{2r}=\frac{21}{29}$ , and $rs=58$ , find the area of the hexagon.

$\textbf{(A)}\ 42\qquad\textbf{(B)}\ 60\qquad\textbf{(C)}\ 84\qquad\textbf{(D)}\ 90\qquad\textbf{(E)}\ 120$

Solution

Problem 4

Find the smallest $n$ such that: $n \equiv 3 \pmod{9}$ $2n \equiv 7 \pmod{13}$ $5n \equiv 14 \pmod{17}$

$\textbf{(A)}\ 1560\qquad\textbf{(B)}\ 1713\qquad\textbf{(C)}\ 2211\qquad\textbf{(D)}\ 3273\qquad\textbf{(E)}\ 3702$

Solution

@@ Line 24: / Line 24: @@
 Find the smallest <math>n</math> such that: <cmath>n \equiv 3 \pmod{9}</cmath><cmath>2n \equiv 7 \pmod{13}</cmath><cmath>5n \equiv 14 \pmod{17}</cmath>
+<math>\textbf{(A)}\ 1560\qquad\textbf{(B)}\ 1713\qquad\textbf{(C)}\ 2211\qquad\textbf{(D)}\ 3273\qquad\textbf{(E)}\ 3702</math>
 [[G285 MC10B Problems/Problem 4|Solution]]
 ==Problem 5==

Page

Toolbox

Search

Difference between revisions of "G285 2021 MC10B"

Revision as of 20:19, 12 May 2021

Contents

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5