Answer: B

Solution:

Note that $1$ cm represents $72 \div 12 = 6$ kilometers. This means that $17$ cm represents $6 \cdot 17 = 102$ kilometers.

Thus, B is the correct answer.

Answer: B

Solution:

Note that there are $2$ non-zero digits that could be the thousands digit.

After choosing that, we need to arrange the other $3$ digits. There are $3$ spots for the other non-zero digit.

This gives us $2 \cdot 3 = 6$ possible numbers.

Thus, B is the correct answer.

Answer: A

Solution:

Note that $12$ meals feed $18$ people. This means that one meal feeds $\dfrac{18}{12} = \dfrac{3}{2}$ people.

This means that they need $12 \div \dfrac{3}{2} = 8$ meals for $12$ people.

Thus, A is the correct answer.

Answer: B

Solution:

If there are $3$ starters, then one person must not be starting. Choosing the person who doesn't start determines the starters.

There are $4$ choices for the person who doesn't start.

Thus, B is the correct answer.

Answer: D

Solution:

Note that after every game, one team gets eliminated. For there to be one team remaining, $15$ teams must have been eliminated.

This means that $15$ games had to have been played.

Thus, D is the correct answer.

Answer: C

Solution:

Sally made $20 \times .55 = 11$ of her first $20$ shots. Then we get that $$\dfrac{11 + x}{25} = .56,$$ which tells us that $$11 + x = 14$$ and $x = 3.$

Thus, C is the correct answer.

Answer: B

Solution:

The maximum heart rate for this athlete would be $220 - 26 = 194.$ Then the target heart rate would be $194 \times .8 \approx 155.$

Thus, B is the correct answer.

Answer: B

Solution:

Note that the tens digit can range from $1$ to $7,$ and this digit determines the units digit.

Therefore, there are $7$ numbers.

Thus, B is the correct answer.

Answer: D

Solution:

The sum of all $5$ numbers is $54 \cdot 5 = 270.$ The sum of the first $2$ numbers is $48 \cdot 2 = 96.$

The sum of the last $3$ numbers is $270 - 96 = 174.$ The average is therefore $174 \div 3 = 58.$

Thus, D is the correct answer.

Answer: E

Solution:

Aaron worked $75$ minutes on Monday, $50$ minutes on Tuesday, $145$ minutes on Wednesday, and $30$ minutes on Friday.

The total is $75+50+145+30=300$ minutes, or $5$ hours.

At $\$3$ per hour, he earned $5\cdot3=15$ dollars.

Thus, E is the correct answer.

Answer: C

Solution:

Note that the largest, smallest, and median numbers cannot be the first or last number.

This means that the first and last numbers are $4$ and $9$ in some order. The average is $$(4 + 9) \div 2$$$$= 13 \div 2$$$$= 6.5.$$

Thus, C is the correct answer.

Answer: B

Solution:

When not in use, her cell phone uses up $\frac{1}{24}$ of its battery per hour. When it is in use, it uses up $\frac{1}{3}$ of its battery per hour.

Niki's phone has been on for $9$ hours, with $8$ of those hours being idle and $1$ hour being used to talk on the phone.

This means that the phone has used up $\frac{2}{3}$ of its battery. In order to drain the remaining $\frac{1}{3}$ of the battery, the phone can last for $8$ more hours without being used.

Thus, B is the correct answer.

Answer: E

Solution:

If Bill were oldest, then statements I and II would both be true, so Bill is not oldest.

If Celine were oldest, then statements II and III would both be true, so Celine is not oldest.

Therefore Amy is oldest. Statements I and II are false, so statement III must be the single true statement. Thus Celine is not youngest, leaving Bill youngest.

The order is Amy, Celine, Bill.

Thus, E is the correct answer.

Answer: C

Solution:

Place the quadrilateral inside the surrounding $10\times10$ square, whose area is $100$.

The five outside pieces have areas $15$, $\frac12\cdot6\cdot7=21$, $\frac12\cdot1\cdot3=\frac32$, $\frac12\cdot4\cdot5=10$, and $\frac12\cdot6\cdot10=30$.

The outside area is $15+21+\frac32+10+30=77\frac12$, so the quadrilateral area is $100-77\frac12=22\frac12$.

Thus, C is the correct answer.

Answer: C

Solution:

The original figure has $13$ shaded tiles and $6$ unshaded tiles.

The new border is the next hexagonal ring around the figure, which has $18$ unshaded tiles.

The new figure has $6+18=24$ unshaded tiles and $13$ shaded tiles, so the difference is $24-13=11$.

Thus, C is the correct answer.

Answer: C

Solution:

The first pitcher contains $600 \cdot \dfrac{1}{3} = 200$ mL of orange juice. The second one has $600 \cdot \dfrac{2}{5} = 240$ mL.

The large container then has $200 + 240 = 440$ mL of orange juice. The total amount of mixture is $2 \cdot 600 = 1200$ mL.

Then the fraction of orange juice is $\dfrac{440}{1200} = \dfrac{11}{30}.$

Thus, C is the correct answer.

Answer: D

Solution:

First give each friend one pencil. Then $3$ pencils remain to distribute among the $3$ friends.

If one friend gets all $3$ remaining pencils, there are $3$ ways. If the remaining pencils split as $2$ and $1$, there are $3\cdot2=6$ ways. If each friend gets one more, there is $1$ way.

The total number of ways is $3+6+1=10$.

Thus, D is the correct answer.

Answer: A

Solution:

The only way to get Ben's score is with a $1$ and $3$ since he can't hit $2$ twice.

Cindy can achieve her score with $$1 + 6, 2 + 5, \text{ or } 3 + 4.$$ Ben already hit $1$ and $3,$ so Cindy must have hit $2$ and $5.$

Similarly, Dave must have hit $4$ and $7.$ Finally, since $7$ is already used, Alice is forced to have hit $6$ and $10$ with Ellen hitting $8$ and $9.$

Thus, A is the correct answer.

Answer: B

Solution:

Let $x$ be the number. Then $x - 2$ is divisible by $3, 4, 5,$ and $6.$

The least common multiple of these numbers is $60,$ which makes $x$ $62.$

Thus, B is the correct answer.

Answer: D

Solution:

Since $3/4$ of the chairs are occupied, the $6$ empty chairs are $1/4$ of all the chairs. Thus there are $24$ chairs.

The number of seated people is $3/4$ of $24$, which is $18$.

Those $18$ seated people are $2/3$ of all the people, so the total number of people is $18\div\frac23=27$.

Thus, D is the correct answer.

Answer: D

Solution:

For the product to be even, then at least one of the spinners must land on an even number.

We can use complementary counting and calculate the probability of both spinners landing on odds.

This happens with a probability of $$\dfrac{1}{2} \cdot \dfrac{2}{3} = \dfrac{1}{3}.$$

Then the probability of landing on at least one even is $$1 - \dfrac{1}{3} = \dfrac{2}{3}.$$

Thus, D is the correct answer.

Answer: B

Solution:

WLOG, let there be $5$ women in the room. Then there are $5 \cdot \dfrac{2}{5} = 2$ single women.

This means that there are $5 - 2 = 3$ married women, which is also the number of married men.

There are a total of $5 + 3 = 8$ people in the room. The fraction of married men is $\dfrac{3}{8}.$

Thus, B is the correct answer.

Answer: D

Solution:

Starting at $J$, Tess’s distance from home increases as she runs from $J$ to $K$.

From $K$ to $L$, her distance continues to increase, but with a different shape, reaching its maximum at the opposite corner $L$.

From $L$ to $M$ and then from $M$ back to $J$, her distance decreases back to $0$, again changing behavior at $M$.

Graph $D$ is the only graph with this increase, changed-rate increase, changed-rate decrease, and final decrease to $0$.

Thus, D is the correct answer.

Answer: C

Solution:

The rectangle has side lengths $10$ and $8$, so its area is $80$.

The four corner triangles have total area $2\cdot\frac12\cdot3\cdot4+2\cdot\frac12\cdot6\cdot5=12+30=42$. Thus parallelogram $EFGH$ has area $80-42=38$.

Segment $HE$ has length $5$ by the $3-4-5$ right triangle. Since the parallelogram area is $HE\cdot d$, we have $5d=38$, so $d=7.6$.

Thus, C is the correct answer.

Answer: D

Solution:

The two $4\times4$ squares have total area $32$, but their overlap is a $2\times2$ square with area $4$. Thus the area covered by the union of the two squares is $32-4=28$.

The circle’s diameter is the diagonal of that $2\times2$ overlap square, so the diameter is $2\sqrt2$ and the radius is $\sqrt2$.

The circle area is $\pi(\sqrt2)^2=2\pi$, so the shaded area is $28-2\pi$.

Thus, D is the correct answer.