2013年AMC 10B 真题及答案

2013年AMC 10B 真题：

Problem 1

What is $\frac{2+4+6}{1+3+5} - \frac{1+3+5}{2+4+6}$?

$\textbf{(A)}\ -1 \qquad\textbf{(B)}\ \frac{5}{36} \qquad\textbf{(C)}\ \frac{7}{12} \qquad\textbf{(D)}\ \frac{49}{20} \qquad\textbf{(E)}\ \frac{43}{3}$

Problem 2

Mr. Green measures his rectangular garden by walking two of the sides and finding that it is $15$ steps by $20$ steps. Each of Mr. Green's steps is $2$ feet long. Mr. Green expects a half a pound of potatoes per square foot from his garden. How many pounds of potatoes does Mr. Green expect from his garden?

$\textbf{(A)}\ 600 \qquad\textbf{(B)}\ 800 \qquad\textbf{(C)}\ 1000 \qquad\textbf{(D)}\ 1200 \qquad\textbf{(E)}\ 1400$

Problem 3

On a particular January day, the high temperature in Lincoln, Nebraska, was $16$ degrees higher than the low temperature, and the average of the high and the low temperatures was $3\,^\circ$. In degrees, what was the low temperature in Lincoln that day?

$\textbf{(A)}\ -13\qquad\textbf{(B)}\ -8\qquad\textbf{(C)}\ -5\qquad\textbf{(D)}\ -3\qquad\textbf{(E)}\ 11$

Problem 4

When counting from $3$ to $201$, $53$ is the $51^\mathrm{st}$ number counted. When counting backwards from $201$ to $3$, $53$ is the $n^\mathrm{th}$ number counted. What is $n$?

$\textbf{(A)}\ 146\qquad\textbf{(B)}\ 147\qquad\textbf{(C)}\ 148\qquad\textbf{(D)}\ 149\qquad\textbf{(E)}\ 150$

Problem 5

Positive integers $a$ and $b$ are each less than $6$. What is the smallest possible value for $2 \cdot a - a \cdot b$?

$\textbf{(A)}\ -20\qquad\textbf{{(B)}}\ -15\qquad\textbf{{(C)}}\ -10\qquad\textbf{{(D)}}\ 0\qquad\textbf{{(E)}}\ 2$

Problem 6

The average age of 33 fifth-graders is 11. The average age of 55 of their parents is 33. What is the average age of all of these parents and fifth-graders?

$\textbf{(A)}\ 22\qquad\textbf{(B)}\ 23.25\qquad\textbf{(C)}\ 24.75\qquad\textbf{(D)}\ 26.25\qquad\textbf{(E)}\ 28$

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