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 one lap in $25/10=2.5$ minutes. Now she swims one lap in $24/12=2$ minutes.

Therefore, she improved her lap time by $2.5-2=0.5=\dfrac{1}{2}$ minute.

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 minus the number of females surveyed: $200-96=104$.

Of those males, $26$ do not listen, so $104-26=78$ males listen. The desired percentage is $\dfrac{78}{104}\cdot 100\%=75\%$.

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:

The positive integer factor pairs $(w,l)$ with $wl=12$ are $(1,12),(2,6),(3,4),(4,3),(6,2),$ and $(12,1)$.

These points form a decreasing set of six points, and only graph A matches them.

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 $0.7\cdot 10=7$ questions right on the first test. Similarly, she got $0.8\cdot 20=16$ and $0.9\cdot 30=27$ problems right on her second and third tests.

Adding these up yields $50$ correct questions. Her score on the combined test would have been $100\cdot \dfrac{50}{60}=83\frac{1}{3}\%$, closest to $83\%$.

Thus, D is the correct answer.

Solution:

By the time Brian starts biking, Cassie has already traveled $\dfrac{1}{2}\cdot 12=6$ miles. This means that Cassie and Brian are then $62-6=56$ miles apart.

Together, they close the distance at $12+16=28$ miles per hour. This means that they meet $56\div 28=2$ hours after 9:00 AM.

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

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:

Spinner $Q$ always lands on an even number, so it does not change the parity of the total. Spinner $R$ always lands on an odd number.

For the full sum to be odd, the number from spinner $P$ must be even. Only one of the three equal sectors of spinner $P$ contains an even number.

Therefore the probability is $\dfrac{1}{3}$.

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

Thus, C is the correct answer.

Solution:

The base area of the aquarium is $100\cdot 40=4000 ext{ cm}^2$.

The submerged rock displaces $1000 ext{ cm}^3$ of water, so the water level rises by $1000\div 4000=0.25$ 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, put $b=1$ in the middle and $2,3$ in the outer cells. This yields a top number of $7$.

To maximize it, put $b=9$ in the middle and $7,8$ in the outer cells. This yields a top number 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:

The common sum must be odd. If the common sum were even, then the hidden numbers behind $44$ and $38$ would both have to be even primes, but there is only one even prime.

So the prime hidden behind the odd visible number $59$ must be $2$, making the common sum $59+2=61$.

The other two hidden primes are $61-44=17$ and $61-38=23$.

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

Thus, B is the correct answer.