Answer: A

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In order for Danica to arrange her model cars in rows of exactly six, the number of model cars she has must be a multiple of six. The smallest multiple of $6$ greater than $23$ is $24,$ so she must buy $1$ more car to attain this amount.

Thus, A is the correct answer.

Answer: D

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During the sale, the price for half a pound is $\$3,$ and therefore, the price for a full pound is $2 \cdot \$3 = \$6.$

The sale price is $50\%$ off the regular price, and so the regular price is twice the sale price. Therefore, the regular price for a full pound of fish is $2 \cdot \$6 = \$12.$

Thus, D is the correct answer.

Answer: E

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Within the parentheses, pair consecutive terms: $$(-1+2)+(-3+4)+\cdots+(-999+1000).$$

Each pair has sum $1$, and there are $500$ pairs, so the value inside the parentheses is $500$. Multiplying by $4$ gives $2000$.

Thus, E is the correct answer.

Answer: C

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Since Judi's portion was fully covered by everyone's contributions, the portion of the bill she was responsible for was equal to $$7 \cdot \$2.50 = \$17.50.$$

As everyone paid the same amount, we can conclude that the total bill is $$8 \cdot \$17.50 = \$140.$$

Thus, C is the correct answer.

Answer: E

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The median weight is the middle value, which we can find as: $$\cancel{ 5 },\cancel{ 5 },\underline{6},\cancel{8},\cancel{106}$$ Therefore, the median is $6$ pounds.

The average (mean) can be calculated to be: $$\begin{align*} &\dfrac{106 + 5 + 5 + 6 + 8}{5} \\&= \dfrac{130}{5}\\ &= 26. \end{align*}$$ This is greater than the median, specifically, the mean is $20$ pounds greater than the median.

Thus, E is the correct answer.

Answer: C

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The product of the numbers in the second row is $600,$ so the missing number in the middle right box is $600 \div 30 = 20.$

Now we know that the product of $5$ and the missing number in the first row is $20.$ Therefore, the missing number is $20 \div 5 = 4.$

Thus, C is the correct answer.

Answer: C

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Converting $2$ minutes and $45$ seconds into seconds, we get $2 \cdot 60 + 45 = 165$ seconds. Since $6$ cars passed in $10$ seconds, at the same rate the number of cars $x$ passing in $165$ seconds satisfies $$\dfrac{6}{10}=\dfrac{x}{165}.$$

Solving gives $$x=\dfrac{165\cdot6}{10}=99.$$ The closest answer choice is $100$.

Thus, C is the correct answer.

Answer: C

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The outcomes with at least two consecutive heads are $HHT$, $THH$, and $HHH$. There are $2^3=8$ equally likely outcomes from three fair coin tosses, so the probability is $\dfrac{3}{8}$.

Thus, C is the correct answer.

Answer: C

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On the $n$th jump, the Hulk jumps $2^{n-1}$ meters. We need the smallest $n$ for which $2^{n-1}>1000$.

Since $2^9=512$ and $2^{10}=1024$, the first jump longer than $1000$ meters has $n-1=10$, so $n=11$.

Thus, C is the correct answer.

Answer: C

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Prime-factorize the two numbers: $$180=2^2\cdot3^2\cdot5,\qquad 594=2\cdot3^3\cdot11.$$

The greatest common factor uses the smaller powers, so it is $2\cdot3^2=18$. The least common multiple uses the larger powers, so it is $$2^2\cdot3^3\cdot5\cdot11=5940.$$ Therefore the desired ratio is $\dfrac{5940}{18}=330$.

Thus, C is the correct answer.

Answer: D

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Grandfather spent $\frac{2}{5}$ hours jogging on Monday. He spent $\frac{2}{3}$ hours walking on Wednesday and $\frac{2}{4}=\frac{1}{2}$ hours on Friday. Converting these times to minutes, we get $$\dfrac{2}{5} \cdot 60 = 24~\mathrm{minutes}$$ $$\dfrac{2}{3} \cdot 60 = 40~\mathrm{ minutes}$$ $$\dfrac{1}{2} \cdot 60 = 30~\mathrm{ minutes}$$ for Monday, Wednesday, and Friday respectively. Therefore, Grandfather totaled $94$ minutes of exercise throughout the week.

If he walked at a pace of $4$ miles per hour each day, he would have spent $\frac{2}{4}=\frac{1}{2}$ hours each day walking. This equals $\frac{2}{4} \cdot 60 = 30$ minutes every day. If he did this for $3$ days, he would have totaled $3 \cdot 30 = 90$ minutes of exercise.

Therefore, Grandfather would have walked for $94 - 90 = 4$ less minutes.

Thus, D is the correct answer.

Answer: B

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Javier saved $0.40 \cdot 50 = 20$ dollars on the second pair. He also saved $50 / 2 = 25$ dollars on the third pair. This shows that he saved a total of $45$ dollars.

As $$45 / 150 = 3 / 10 = .30,$$ we can conclude that Javier saved $30 \%$ compared to the regular price.

Thus, B is the correct answer.

Answer: A

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If the last two digits of the score are $10a+b$, then reversing those digits gives $10b+a$. The difference is $$(10a+b)-(10b+a)=9(a-b),$$ so the incorrect sum must differ from the correct sum by a multiple of $9$.

Among the answer choices, only $45$ is divisible by $9$.

Thus, A is the correct answer.

Answer: C

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There are $2\cdot4=8$ equally likely ways for Abe and Bea to choose their jelly beans. The colors match if they both choose green, which can happen in $1$ way, or if they both choose red, which can happen in $1\cdot2=2$ ways.

Thus $3$ of the $8$ outcomes match, for probability $\dfrac{3}{8}$.

Thus, C is the correct answer.

Answer: B

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Subtract the known number from each equation: $$3^p=90-81=9,\qquad 2^r=76-44=32,\qquad 6^s=1421-125=1296.$$

Therefore $p=2$, $r=5$, and $s=4$. Their product is $2\cdot5\cdot4=40$.

Thus, B is the correct answer.

Answer: E

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The number of $8^\text{th}$-graders must be a multiple of $5$ and $8,$ which means that it is at least $40.$ Using this number, we get that the number of $6^\text{th}$-graders is $40 \cdot \dfrac{3}{5} = 24.$ Similarly, the number of $7^\text{th}$-graders is $40 \cdot \dfrac{5}{8} = 25.$

The total number of students is therefore $40 + 24 + 25 = 89.$

Thus, E is the correct answer.

Answer: B

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Let the six consecutive integers be $x,x+1,x+2,x+3,x+4,x+5$. Their sum is $$6x+15=2013.$$

Thus $6x=1998$, so $x=333$. The largest integer is $x+5=338$.

Thus, B is the correct answer.

Answer: B

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The rectangular prism determined by the outside faces has volume $12\cdot10\cdot5=600$ cubic feet. The empty inside is smaller by $2$ feet in length, $2$ feet in width, and $1$ foot in height, so its dimensions are $10\times8\times4$.

The empty volume is $10\cdot8\cdot4=320$ cubic feet, so the fort contains $600-320=280$ one-foot cubical blocks.

Thus, B is the correct answer.

Answer: D

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Since Cassie deduced she didn't get the lowest score, she must have got a higher score than Hannah. Similarly, Bridget's statement reveals that she must have got a lower score than Hannah.

Therefore, the ranking from highest to lowest is Cassie, Hannah, and then Bridget.

Thus, D is the correct answer.

Answer: C

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Using the Pythagorean theorem, we get that the radius of the semicircle is $\sqrt{2}.$ This means that the area of the semicircle is $$\dfrac{1}{2} \cdot \pi \cdot \sqrt{2}^2 = \pi.$$ Thus, C is the correct answer.

Answer: E

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To reach the southwest corner of the park as quickly as possible, Samantha must go $2$ blocks east and $1$ block north, which can be arranged in $3$ ways. After the diagonal path through the park, she must go $2$ blocks east and $2$ blocks north to reach school, which can be arranged in $\binom{4}{2}=6$ ways.

The choices before and after the park are independent, so the total number of shortest routes is $3\cdot6=18$.

Thus, E is the correct answer.

Answer: E

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A $60$-by-$32$ grid has $61$ vertical grid lines, each made of $32$ toothpicks, and $33$ horizontal grid lines, each made of $60$ toothpicks.

Therefore the total number of toothpicks is $$61\cdot32+33\cdot60=1952+1980=3932.$$

Thus, E is the correct answer.

Answer: B

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The semicircle on $\overline{AB}$ has area $8\pi$, so its full circle would have area $16\pi$. Its radius is therefore $4$, and $AB=8$.

A semicircle of radius $r$ has arc length $\pi r$. Since the arc on $\overline{AC}$ has length $8.5\pi$, its radius is $8.5$, so $AC=17$.

Using the Pythagorean theorem in right triangle $ABC$, $$BC=\sqrt{17^2-8^2}=\sqrt{225}=15.$$ The radius of the semicircle on $\overline{BC}$ is $15/2=7.5$.

Thus, B is the correct answer.

Answer: C

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Let each square have side length $1$, so the total area of the three squares is $3$. It is easier to subtract the unshaded region to the left of diagonal $AJ$ from this total.

Using the solution diagram, rectangle $EDKF$ has area $1\cdot\dfrac12=\dfrac12$, and triangle $AKJ$ has area $$\dfrac12\cdot\dfrac32\cdot2=\dfrac32.$$ Thus the unshaded area is $\dfrac12+\dfrac32=2$, so the shaded pentagon has area $3-2=1$.

The requested ratio is $\dfrac{1}{3}$.

Thus, C is the correct answer.

Answer: A

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The ball has radius $2$. As the ball rolls, its center follows semicircular arcs parallel to the track. On the first and third arcs the center path is inside the track arcs, so those radii are $100-2=98$ and $80-2=78$. On the middle arc the center path is outside the track arc, so that radius is $60+2=62$.

The total distance traveled by the center is the sum of the three semicircle lengths: $$(98+62+78)\pi=238\pi.$$

Thus, A is the correct answer.