Solution:

Grouping the numerator in pairs gives $(10-9) + (8-7) + (6-5) + (4-3) + (2-1) = 5.$

Grouping the denominator as $(1-2) + (3-4) + (5-6) + (7-8) + 9$ gives four pairs of $-1$ plus $9$, which is $5.$

So the expression is $\dfrac{5}{5} = 1.$

Thus, the correct answer is B .

Solution:

Note $\dfrac54 = 1\dfrac14.$ Now check each choice: $\dfrac{10}{8} = \dfrac54,$ $1\dfrac14 = \dfrac54,$ $1\dfrac{3}{12} = 1\dfrac14 = \dfrac54,$ and $1\dfrac{10}{40} = 1\dfrac14 = \dfrac54.$

But $1\dfrac15 = \dfrac65 \neq \dfrac54.$

Thus, the correct answer is D .

Solution:

The largest difference uses the largest number, $12$, minus the smallest number, $-16.$

This gives $12 - (-16) = 28.$

Thus, the correct answer is D .

Solution:

The non-single hits number $1 + 1 + 5 = 7,$ so the singles number $35 - 7 = 28.$

The fraction of singles is $\dfrac{28}{35} = \dfrac45 = 80\%.$

Thus, the correct answer is E .

Solution:

The rectangle has area $6,$ and the removed circle has area $\pi\left(\dfrac12\right)^2 = \dfrac{\pi}{4} \approx 0.79.$

So the shaded region has area $6 - 0.79 \approx 5.2,$ whose closest whole number is $5.$

Thus, the correct answer is E .

Solution:

The first triple gives $1 + 3 - 4 = 0,$ and the second gives $2 + 5 - 6 = 1.$

Their sum is $0 + 1 = 1.$

Thus, the correct answer is D .

Solution:

A digit-sum of $26$ with three digits requires the digits $9, 9, 8.$ The $3$-digit numbers using them are $899, 989,$ and $998.$

Of these, only $998$ is even, so there is exactly $1$ such number.

Thus, the correct answer is A .

Solution:

The pencils cost $1500 \times \$0.10 = \$150.$ To make a $100 profit, the revenue must be $\$150 + \$100 = \$250.$

At $0.25 each, he must sell $\dfrac{\$250}{\$0.25} = 1000$ pencils.

Thus, the correct answer is C .

Solution:

If there are $M$ males, then there are $2M$ females, and together $M + 2M = 480.$

So $3M = 480,$ giving $M = 160.$

Thus, the correct answer is B .

Solution:

The large triangle has area $\dfrac12 \times 8 \times 8 = 32,$ so each of the $16$ congruent small triangles has area $\dfrac{32}{16} = 2.$

Ten of the small triangles are shaded, so the shaded area is $10 \times 2 = 20.$

Thus, the correct answer is B .

Solution:

The total number surveyed is $50 + 60 + 40 + 60 + 40 = 250.$

The percent preferring blue is $\dfrac{60}{250} = 24\%.$

Thus, the correct answer is B .

Solution:

During the $30{,}000$ miles, $4$ tires are always in use, so the total tire-mileage is $4 \times 30{,}000 = 120{,}000$ tire-miles.

Split equally among $5$ tires, each tire is used $\dfrac{120{,}000}{5} = 24{,}000$ miles.

Thus, the correct answer is C .

Solution:

The five scores sum to $5 \times 90 = 450.$ The median is the third score, $91.$ Since $94$ is the mode, it must appear at least twice, and both copies lie above the median, so the two highest scores are $94, 94.$

The three highest scores are $91, 94, 94,$ summing to $279.$ So the two lowest sum to $450 - 279 = 171.$

Thus, the correct answer is B .

Solution:

The $4$ gallons account for the change from $\dfrac13$ full to $\dfrac12$ full, which is $\dfrac12 - \dfrac13 = \dfrac16$ of the capacity.

If $\dfrac16$ of the capacity is $4$ gallons, the full capacity is $4 \times 6 = 24$ gallons.

Thus, the correct answer is D .

Solution:

The sequence is the $9$-letter block $ABCDEDCBA$ repeated again and again.

Since $1992 = 9 \times 221 + 3,$ the $1992$nd letter is the $3$rd letter of a block, which is $C.$

Thus, the correct answer is C .

Solution:

The given cylinder has volume $\pi \times 10^2 \times 5 = 500\pi,$ so a cylinder of twice the volume has volume $1000\pi.$

The choices have volumes $\pi \times 20^2 \times 5 = 2000\pi$ (A), $\pi \times 10^2 \times 10 = 1000\pi$ (B), $\pi \times 5^2 \times 20 = 500\pi$ (C), and $\pi \times 20^2 \times 10 = 4000\pi$ (D). Only (B) equals $1000\pi.$

Thus, the correct answer is B .

Solution:

By the triangle inequality, $6.5 + s$ must exceed the longest side $10,$ so $s \gt 3.5.$

The smallest whole number greater than $3.5$ is $4,$ and it does form a valid triangle.

Thus, the correct answer is B .

Solution:

The car covered $80 + 100 = 180$ miles in total, over $1.5 + 0.5 + 2 = 4$ hours (the traffic stop still counts as time).

The average speed is $\dfrac{180}{4} = 45$ miles per hour.

Thus, the correct answer is A .

Solution:

From the $5$th exit to the $26$th exit there are $26 - 5 = 21$ gaps between consecutive exits, each at least $5$ miles.

To maximize one gap, make the other $20$ gaps exactly $5$ miles, using $20 \times 5 = 100$ miles. The remaining gap is $118 - 100 = 18$ miles.

Thus, the correct answer is C .

Solution:

Each of the five patterns has $6$ squares. Folding patterns (A), (B), (C), and (E) wraps the squares neatly onto the six faces of a cube.

For pattern (D), any attempt to fold forces two of the squares to land on the same face, so they overlap and no cube can be formed.

Thus, the correct answer is D .

Solution:

Reading the graph gives (drums, bugles): January $(7, 9),$ February $(5, 3),$ March $(9, 6),$ April $(9, 12),$ and May $(8, 10).$

The percent excess of the larger over the smaller is $\tfrac{2}{7} \approx 29\%$ in January, $\tfrac{2}{3} \approx 67\%$ in February, $\tfrac{3}{6} = 50\%$ in March, $\tfrac{3}{9} \approx 33\%$ in April, and $\tfrac{2}{8} = 25\%$ in May. The greatest is February, where $5$ exceeds $3$ by about $67\%.$

Thus, the correct answer is B .

Solution:

A tile that shares exactly one side adds $2$ to the perimeter (four new edges minus two hidden), while a tile sharing two sides adds $0.$

With two added tiles the perimeter can change by $0,$ $2,$ or $4,$ giving new perimeters of $14,$ $16,$ or $18.$ Of the choices, only $18$ is possible.

Thus, the correct answer is C .

Solution:

There are $36$ equally likely outcomes. Counting the ordered pairs whose product exceeds $10$: with a first die of $2$ there is $1$ (namely $2 \times 6$); of $3$, there are $3$; of $4$, there are $4$; of $5$, there are $4$; of $6$, there are $5.$

That is $1 + 3 + 4 + 4 + 5 = 17$ favorable outcomes, so the probability is $\dfrac{17}{36}.$

Thus, the correct answer is B .

Solution:

Because adjacent circles are tangent, the square through the centers has side $2 \times 3 = 6$ and area $36.$

Inside the square, each circle contributes a quarter-circle, and the four quarters make one full circle of area $9\pi \approx 28.3.$ The shaded region is $36 - 9\pi \approx 7.7.$

Thus, the correct answer is A .

Solution:

After the $n$th pouring, the fraction remaining is $\dfrac12 \times \dfrac23 \times \dfrac34 \times \cdots \times \dfrac{n}{n+1},$ which telescopes to $\dfrac{1}{n+1}.$

Setting $\dfrac{1}{n+1} = \dfrac{1}{10}$ gives $n = 9.$

Thus, the correct answer is D .