Solution:

Since all the values are already close to a whole number, we can just add the sums of the rounded numbers.

These prices round to $\$ 2,$ $\$ 5,$ and $\$ 10,$ which add to $\$ 17.$

Thus, D is the correct answer.

Solution:

Since the AMC $8$ only awards $1$ point for each correct question, Billy will get $13$ points.

Thus, C is the correct answer.

Solution:

Initially, Elisa swam $1$ lap in $$\dfrac{25}{10} = \dfrac{5}{2}$$ minutes. Now, she swims $1$ lap in $$\dfrac{24}{12} = 2$$ minutes.

Therefore, she improved her lap time by $\dfrac{5}{2} - 2 = \dfrac{1}{2}$ minutes.

Thus, A is the correct answer.

Solution:

If the spinner goes $2 \frac{1}{4}$ revolutions clockwise and $3 \frac{3}{4}$ revolutions counterclockwise, it goes $1 \frac{1}{2}$ revolutions counterclockwise.

This means that the spinner will be pointing east.

Thus, B is the correct answer.

Solution:

Note that we can fold all the triangles in to perfectly cover the smaller square. This means that area of the smaller square is half the area of the larger square.

This makes the area of the smaller square $60 \div 2 = 30.$

Thus, D is the correct answer.

Solution:

If we found the total perimeter of the two rectangles separately, we would have gotten $$2(2(2 + 4)) = 2 \cdot 2 \cdot 6 = 24.$$

In the letter T, we can see that their intersection removes a piece of length $2$ from each of the rectangles. Therefore, the perimeter of the T is $$24 - 2 \cdot 2 = 20.$$

Thus, C is the correct answer.

Solution:

Recall that $C = 2 \pi r$ and $A = \pi r^2.$ Using these formulas we get that the radius of $Y$ is $$8 \pi \div (2 \pi) = 4.$$ We also get that the radius of $Z$ is $$\sqrt{9 \pi \div \pi} = 3.$$ As $\pi$ is greater than $3$ and less than $4,$ the correct order is $Z,X,Y.$

Thus, the answer is B.

Solution:

The total number of males surveyed is the total number surveyed by the total number of women surveyed: $$200 - 96 = 104.$$ The percentage of males that listen to the station is $100 \%$ minus the percent that don't listen to the station: $$100 \% - 100 \cdot \dfrac{26}{104} \%$$$$= 100 \% - 25 \%$$$$= 75 \%.$$

Thus, E is the correct answer.

Solution:

Note that the numerator of every fraction cancels with the denominator of the following fraction. This leaves two numbers: $$\dfrac{2006}{2} = 1003.$$

Thus, C is the correct answer.

Solution:

We know that $wl = 12,$ so $w = \dfrac{12}{l}.$

This shows that $w$ and $l$ are inversely proportional, which can only be represented by a non-linear graph.

Thus, A is the correct answer.

Solution:

There is $1$ number whose digit sum is $1: 10.$

There are $4$ numbers whose digit sum is $4: 13, 22, 31,$ and $40.$

There are $9$ numbers whose digit sum is $9: 18, 27, 36, 45, 54,$ $63, 72, 81,$ and $90.$

There are $3$ numbers whose digit sum is $16: 79, 88,$ and $97.$

Therefore, there are $17$ numbers that satisfy the problem statement.

Thus, C is the correct answer.

Solution:

Antonette got $.7 \cdot 10 = 7$ questions write on the first test. Similarly, she got $.8 \cdot 20 = 16$ and $.9 \cdot 30 = 27$ problems right on her second and third tests respectively.

Adding these up yields a total of $50$ correct questions. Her score on the $60$-problem test would have been a $$100 \cdot \dfrac{50}{60} = 100 \cdot .8\overline{3} \approx 83 \%.$$

Thus, D is the correct answer.

Solution:

By the time Brian starts biking, Marquette has already traveled $\dfrac{1}{2} \cdot 12 = 6$ miles. This means that Brian and Marquette must then travel a total of $62 - 6 = 56$ miles.

Combined, the two bike at $12 + 16 = 28$ miles per hour. This means that they can travel $56$ miles in $56 \div 28 = 2$ hours.

This means that they meet at $11:00.$

Thus, D is the correct answer.

Solution:

Bob will take $760 \cdot 45$ seconds to read the book, and Chandra will take $760 \cdot 30$ seconds.

The difference between the time they spent reading is $$760 \cdot 45 - 760 \cdot 30$$$$= 760(45 - 30)$$$$= 760 \cdot 15$$$$= 11,400$$ seconds.

Thus, B is the correct answer.

Solution:

Let $x$ be the number of pages that Chandra will read. Then Bob will read $760 - x$ pages.

For them to read for the same amount of time, $$\begin{align*} 30x &= 45(760 - x) \\ 30x &= 45 \cdot 760 - 45x \\ 75x &= 45 \cdot 760 \\ 5x &= 3 \cdot 760 \\ x &= 3 \cdot 152 \\ x &= 456. \end{align*}$$

Thus, C is the correct answer.

Solution:

If all $3$ individuals read the same amount of time, then the number of pages Bob, Chandra, and Alice will read will be in the ratio $4:6:9$ respectively.

This means that they will read $160, 240,$ and $360$ pages respectively. Since they all read for the same amount of time, we can just calculate how long it takes for Bob to read his portion.

Bob will take $45 \cdot 160 = 7200$ seconds to read his portion.

Thus, E is the correct answer.

Solution:

Note that adding an even number to a number does not affects is parity. Therefore, whatever the second spinner lands on will not impact whether the sum is odd.

The only way for a number on $P$ and a number on $R$ to add to an odd number is if $P$ lands on $2.$ Otherwise, it would be the sum of two odd numbers, which is even.

$P$ lands on $2$ with a $\dfrac{1}{3}$ probability.

Thus, B is the correct answer.

Solution:

Since each face has the same black and white surface area, we can analyze what fraction of one side is white.

On one side, there are $9$ unit squares. $4$ of them are black. This means that $\dfrac{5}{9}$ of each face is white.

Thus, D is the correct answer.

Solution:

By the congruency condition, we know that $$AB = EC = 11.$$

Also from the isosceles condition, we know that $$BC = AB = 11.$$

Since $D$ is the midpoint of $\overline{BC},$ we know that $$BD = BC \div 2 = 5.5$$

Thus, D is the correct answer.

Solution:

In every match, there was exactly one winner. There are $6 \cdot 5 \div 2 = 15$ games and therefore $15$ wins.

There are already $$4 + 3 + 3 + 2 + 2 = 13$$ wins accounted for, so Monica won $15 - 13 = 2$ games.

Thus, C is the correct answer.

Solution:

The original volume of the water was $$100 \cdot 40 \cdot 37 = 168,000 \text{ cm}^3.$$

The volume after the rock was added is $$168,000 + 1,000 = 169,000 \text{ cm}^3.$$

This means the new height is $$169,000 \div 100 \div 40 = 37.25 \text{ cm}.$$

This means that water level rose by $.25$ cm.

Thus, A is the correct answer.

Solution:

If the lower cells contain $a,$ $b,$ and $c,$ the middle row will have $a + b$ and $b + c.$

This means that the top row will have $a + 2b + c.$ To minimize this, we can let $b = 1,$ $a = 2,$ and $c = 3.$ This yields a top element of $7.$

To maximize, this we can let $b = 9,$ $a = 8,$ and $c = 7.$ This yields a top element of $33.$ The desired difference is $33 - 7 = 26.$

Thus, D is the correct answer.

Solution:

The positive integers that leave a remainder of $4$ when divided by $6$ are $$4, 10, 16, 22, 28, 34, 40, \cdots.$$ The positive integers that leave a remainder of $3$ when divided by $5$ are $$3, 8, 13, 18, 23, 28, 33, \cdots.$$

From this, we can see that the smallest number of coins that work is $28.$ This leaves a remainder of $0$ when divided by $7.$

Thus, A is the correct answer.

Solution:

Note that $$CDCD = 101 \cdot CD.$$ This forces $ABA = 101.$ Then $A = 1,$ $B = 0,$ and $A + B = 1.$

Thus, A is the correct answer.

Solution:

Note that if we add an odd number to $59,$ we will get an even number. To make the other two sums even numbers, the primes on the back of $44$ and $38$ must both be even.

They also have to be different, however. Since there is only one even prime, the number on the back of $59$ must be an even prime, namely $2.$

This means that the sum of the front and back of all the cards is $59 + 2 = 61.$ This makes the other two primes $61 - 44 = 17$ and $61- 38 = 23.$

The average of the primes is therefore $$\dfrac{2 + 17 + 23}{3} = \dfrac{42}{3} = 14.$$

Thus, B is the correct answer.