Answer: D

Solution:

A line and a circle can intersect at no more than two points, and two distinct lines can intersect at no more than one point.

Arrange the two lines so each meets the circle twice and the two lines meet at a different point. This gives $$2+2+1=5.$$

Thus, D is the correct answer.

Answer: A

Solution:

Since the total $\$17$ is odd, the number of $\$5$ bills must be odd.

One $\$5$ bill leaves $\$12$, which is six $\$2$ bills. Three $\$5$ bills leave $\$2$, which is one $\$2$ bill. Five $\$5$ bills is too much.

Therefore, there are $2$ combinations.

Thus, A is the correct answer.

Answer: C

Solution:

To get the smallest possible average, we want to use the smallest $4$ positive even integers.

This can be achieved as follows: $$\dfrac{2 + 4 + 6 + 8}{4} = \dfrac{20}{4}$$$$= 5.$$

Thus, C is the correct answer.

Answer: B

Solution:

We don't want to increase the thousands digit, so we can keep that as $2.$

This means that we have to increase the tens and hundreds digits to $1,$ to yield the next palindrome of $2112.$ The product of its digits is $4.$

Thus, B is the correct answer.

Answer: C

Solution:

The days of the week cycle every $7$ days. After $700$ days, the day of the week will still be Saturday.

After $6$ more days, the day of the week will be Friday.

Thus, C is the correct answer.

Answer: A

Solution:

Before the birdbath overflows, it gains $20-18=2$ milliliters of water per minute, so its volume increases steadily.

Once the birdbath is full, the incoming extra water overflows, so the volume remains constant. Only graph A shows an increasing line followed by a horizontal line.

Thus, A is the correct answer.

Answer: E

Solution:

There are a total of $$6 + 8 + 4 + 2 + 5 = 25$$ students in the class. The percent that chose $E$ is $$100 \cdot \dfrac{5}{25} = \dfrac{100}{5} = 20 \%.$$

Thus, E is the correct answer.

Answer: D

Solution:

Note that France and Spain are the European countries. The number of ‘$80$s stamps from these countries respectively is $15$ and $9$ for a total of $$15 + 9 = 24$$ stamps.

Thus, D is the correct answer.

Answer: B

Solution:

Brazil and Peru are the South American countries.

Brazil has $4+7=11$ stamps before the ‘$70$s, costing $11\cdot6=66$ cents. Peru has $6+4=10$ such stamps, costing $10\cdot4=40$ cents.

The total cost is $66+40=106$ cents, or $\$1.06$.

Thus, B is the correct answer.

Answer: E

Solution:

The ‘$70$s stamps cost $$12\cdot6+12\cdot6+6\cdot4+13\cdot5=72+72+24+65=233$$ cents.

There are $12+12+6+13=43$ stamps, so the average cost is $233\div43$, a little more than $5$ cents and closest to $5.5$ cents.

Thus, E is the correct answer.

Answer: C

Solution:

The sixth and seventh squares have side lengths $6$ and $7$ tile lengths.

They use $6^2=36$ and $7^2=49$ tiles, respectively, so the seventh square requires $49-36=13$ more tiles.

Thus, C is the correct answer.

Answer: B

Solution:

The total probability is $1.$ We need to subtract the probability of the spinner landing on $B$ and $A$ to get $C,$ which is $$1 - \dfrac{1}{3} - \dfrac{1}{2} = \dfrac{1}{6}.$$

Thus, B is the correct answer.

Answer: E

Solution:

The larger box will have approximately $$125 \cdot 2 \cdot 2 \cdot 2 = 1000$$ jellybeans.

Thus, E is the correct answer.

Answer: B

Solution:

Let the original price be $x$. After the $30\%$ discount, the price is $0.70x$.

Taking another $20\%$ off that sale price leaves $0.80\cdot0.70x=0.56x$.

The customer pays $56\%$ of the original price, so the total discount is $44\%$.

Thus, B is the correct answer.

Answer: E

Solution:

The number of boxes enclosed by each polygon can be obtained by dividing the polygon into unit squares and right triangles with sidelength $1$ and adding up their values.

The unit squares count as $1$ and the triangles count as $.5.$

$A$ has a total area of $5,$ $B$ has $5,$ $C$ has $5,$ $D$ has $4.5,$ and $E$ has $5.5.$

Thus, E is the correct answer.

Answer: E

Solution:

For a right isosceles triangle built on a side of length $s$, the two legs have length $s$, so its area is $s^2/2$.

$$W=\frac{3\cdot4}{2}=6,\quad X=\frac{3^2}{2}=4.5,\quad Y=\frac{4^2}{2}=8,\quad Z=\frac{5^2}{2}=12.5.$$

These values satisfy $X+Y=Z$, and the other listed equations do not.

Thus, E is the correct answer.

Answer: C

Solution:

Let $x$ be the number of correct answers. Then she answered $10 - x$ questions incorrectly.

This gives her a total score of $$5x - 2(10 - x) = 7x - 20.$$

We know that this equals $29,$ and solving yields $$7x - 20 = 29$$$$x = 7.$$

Thus, C is the correct answer.

Answer: E

Solution:

Gage has skated a total of $$5 \cdot 75 + 3 \cdot 90 = 645 \text{ min.}$$

For an average of $85$ minutes over $9$ days, Gage must have skated a total of $$85 \cdot 9 = 765 \text{ min.}$$

This means that Gage must skate $$765 - 645 = 120 \text{ min.}$$ on the last day. Note that $120$ minutes is the same as $2$ hours.

Thus, E is the correct answer.

Answer: D

Solution:

Note that the $0$ digit can either be the tens or the units digit. This gives us $2$ options for this.

There are $9$ options for each of the other digits for a total of $$2 \cdot 9 \cdot 9 = 162$$ numbers.

Thus, D is the correct answer.

Answer: D

Solution:

Since $XY=XZ$ and $XC$ bisects $YZ$, altitude $XC$ splits $\triangle XYZ$ into two congruent triangles. The left half $\triangle XYC$ has area $4$.

In $\triangle XYC$, point $A$ is the midpoint of $XY$. The horizontal segment through $A$ meets $XC$ halfway up, so the small top triangle is similar to $\triangle XYC$ with scale factor $1/2$. Its area is therefore $1/4$ of $4$, or $1$.

The shaded region is the rest of the left half, so its area is $4-1=3$.

Thus, D is the correct answer.

Answer: E

Solution:

There are $2^4=16$ equally likely outcomes for four coin tosses.

At least as many heads as tails means getting $2$, $3$, or $4$ heads. The number of such outcomes is $$\binom{4}{2}+\binom{4}{3}+\binom{4}{4}=6+4+1=11.$$

Thus the probability is $\dfrac{11}{16}$.

Thus, E is the correct answer.

Answer: C

Solution:

We can count the number of unexposed sides to find how many sides contribute to the surface area.

Three cubes have $1$ side unexposed, two cubes have $2$ sides unexposed, and one cube has $3$ sides unexposed.

This gives us a total of $$3 \cdot 1 + 2 \cdot 2 + 1 \cdot 3 = 10$$ unexposed sides, which gives us $$6 \cdot 6 - 10 = 36 - 10$$$$= 26$$ exposed sides.

Each exposed side contributes $1^2 = 1$ to the surface area, for a total surface area of $1 \cdot 26 = 26.$

Thus, C is the correct answer.

Answer: B

Solution:

Notice that there are repeating $3 \times 3$ regions with the same pattern (they might be rotated differently).

In this region, there are three unit squares, and two triangles that combine to form another unit square.

This makes the area of the darker region $4$ and the whole region $9.$ The desired fraction is then $\dfrac{4}{9}.$

Thus, B is the correct answer.

Answer: B

Solution:

Use $6$ pears and $6$ oranges, which is an equal number of each fruit.

Since $3$ pears make $8$ ounces, $6$ pears make $16$ ounces. Since $2$ oranges make $8$ ounces, $6$ oranges make $24$ ounces.

The blend has $16+24=40$ ounces total, of which $16$ ounces is pear juice. The pear-juice percent is $16/40=40\%$.

Thus, B is the correct answer.

Answer: B

Solution:

WLOG, assume that everyone gave Ott $\$1.$ This means that Moe had $\$5,$ Loki had $\$4,$ and Nick had $\$3$ originally.

Ott now has $\$3,$ and the total amount of money is $$\$5 + \$4 + \$3 = \$12.$$

This means that Ott has $$\dfrac{3}{12} = \dfrac{1}{4}$$ of the group's money.

Thus, B is the correct answer.