View source for 2017 AMC 10B Problems

{{AMC10 Problems|year=2017|ab=B}}
==Problem 1==
Mary thought of a positive two-digit number. She multiplied it by <math>3</math> and added <math>11</math>. Then she switched the digits of the result, obtaining a number between <math>71</math> and <math>75</math>, inclusive. What was Mary's number? 

<math>\textbf{(A)}\ 11\qquad\textbf{(B)}\ 12\qquad\textbf{(C)}\ 13\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 15</math>

[[2017 AMC 10B Problems/Problem 1|Solution]]

==Problem 2==
Sofia ran <math>5</math> laps around the <math>400</math>-meter track at her school. For each lap, she ran the first <math>100</math> meters at an average speed of <math>4</math> meters per second and the remaining <math>300</math> meters at an average speed of <math>5</math> meters per second. How much time did Sofia take running the <math>5</math> laps?

<math>\textbf{(A)}\ 5</math> minutes and <math>35</math> seconds <math>\qquad\textbf{(B)}\ 6</math> minutes and <math>40</math> seconds <math>\qquad\textbf{(C)}\ 7</math> minutes and <math>5</math> seconds <math>\qquad\textbf{(D)}\ 7</math> minutes and <math>25</math> seconds <math>\qquad\textbf{(E)}\ 8</math> minutes and <math>10</math> seconds

[[2017 AMC 10B Problems/Problem 2|Solution]]

==Problem 3==
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[[2017 AMC 10B Problems/Problem 3|Solution]]

==Problem 4==
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[[2017 AMC 10B Problems/Problem 4|Solution]]

==Problem 5==
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[[2017 AMC 10B Problems/Problem 5|Solution]]

==Problem 6==
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==Problem 7==
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==Problem 8==
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==Problem 9==
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[[2017 AMC 10B Problems/Problem 9|Solution]]

==Problem 10==
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[[2017 AMC 10B Problems/Problem 10|Solution]]

==Problem 11==
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[[2017 AMC 10B Problems/Problem 11|Solution]]

==Problem 12==
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[[2017 AMC 10B Problems/Problem 12|Solution]]

==Problem 13==
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[[2017 AMC 10B Problems/Problem 13|Solution]]

==Problem 14==
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[[2017 AMC 10B Problems/Problem 14|Solution]]

==Problem 15==
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[[2017 AMC 10B Problems/Problem 15|Solution]]

==Problem 16==
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[[2017 AMC 10B Problems/Problem 16|Solution]]

==Problem 17==
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[[2017 AMC 10B Problems/Problem 17|Solution]]

==Problem 18==
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[[2017 AMC 10B Problems/Problem 18|Solution]]

==Problem 19==
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[[2017 AMC 10B Problems/Problem 19|Solution]]

==Problem 20==
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[[2017 AMC 10B Problems/Problem 20|Solution]]

==Problem 21==
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[[2017 AMC 10B Problems/Problem 21|Solution]]

==Problem 22==
The diameter <math>AB</math> of a circle of radius <math>2</math> is extended to a point <math>D</math> outside the circle so that <math>BD=3</math>. Point <math>E</math> is chosen so that <math>ED=5</math> and line <math>ED</math> is perpendicular to line <math>AD</math>. Segment <math>AE</math> intersects the circle at a point <math>C</math> between <math>A</math> and <math>E</math>. What is the area of <math>\triangle 
ABC</math>?

<math>\textbf{(A)}\ \frac{120}{37}\qquad\textbf{(B)}\ \frac{140}{39}\qquad\textbf{(C)}\ \frac{145}{39}\qquad\textbf{(D)}\ \frac{140}{37}\qquad\textbf{(E)}\ \frac{120}{31}</math>

[[2017 AMC 10B Problems/Problem 22|Solution]]

==Problem 23==
Let <math>N=123456789101112\dots4344</math> be the <math>79</math>-digit number that is formed by writing the integers from <math>1</math> to <math>44</math> in order, one after the other. What is the remainder when <math>N</math> is divided by <math>45</math>?

<math>\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 18\qquad\textbf{(E)}\ 44</math>

[[2017 AMC 10B Problems/Problem 23|Solution]]

==Problem 24==
The vertices of an equilateral triangle lie on the hyperbola <math>xy=1</math>, and a vertex of this hyperbola is the centroid of the triangle. What is the square of the area of the triangle?

<math>\textbf{(A)}\ 48\qquad\textbf{(B)}\ 60\qquad\textbf{(C)}\ 108\qquad\textbf{(D)}\ 120\qquad\textbf{(E)}\ 169</math>

[[2017 AMC 10B Problems/Problem 24|Solution]]

==Problem 25==
Last year Isabella took <math>7</math> math tests and received <math>7</math> different scores, each an integer between <math>91</math> and <math>100</math>, inclusive. After each test she noticed that the average of her test scores was an integer. Her score on the seventh test was <math>95</math>. What was her score on the sixth test?

<math>\textbf{(A)}\ 92\qquad\textbf{(B)}\ 94\qquad\textbf{(C)}\ 96\qquad\textbf{(D)}\ 98\qquad\textbf{(E)}\ 100</math>

[[2017 AMC 10B Problems/Problem 25|Solution]]