Solution:

The scale is divided into fourths between $10$ and $11,$ so the interior tick marks fall at $10.25,$ $10.5,$ and $10.75.$

The arrow points just past the $10.25$ mark, so the reading is between $10.25$ and $10.5.$ Of the choices, only $10.3$ lies in that range.

Thus, the correct answer is D .

Solution:

Write the decimals as fractions: $8 \times \dfrac14 \times 2 \times \dfrac18.$

Grouping, $\left(8 \times \dfrac18\right)\left(\dfrac14 \times 2\right) = 1 \times \dfrac12 = \dfrac12.$

Thus, the correct answer is C .

Solution:

Each fraction equals $\dfrac{1}{10} = .1,$ since $\dfrac{2}{20} = \dfrac{3}{30} = \dfrac{1}{10}.$

So the sum is $.1 + .1 + .1 = .3.$

Thus, the correct answer is D .

Solution:

In each horizontal row the squares alternate dark, light, dark, and so on, beginning and ending with a dark square. So every row has exactly one more dark square than light square.

The figure has $8$ rows, so the dark squares exceed the light squares by $8.$

Thus, the correct answer is B .

Solution:

Reading the protractor, ray $BA$ is at about $20^\circ$ and ray $BD$ is at about $160^\circ.$

Because $\angle CBD$ is a right angle, ray $BC$ is at $160^\circ - 90^\circ = 70^\circ.$

Therefore $\angle ABC = 70^\circ - 20^\circ = 50^\circ.$

Thus, the correct answer is C .

Solution:

The numerator is $(.2)^3 = .008$ and the denominator is $(.02)^2 = .0004.$

So the value is $\dfrac{.008}{.0004} = \dfrac{80}{4} = 20.$

Thus, the correct answer is E .

Solution:

Round each factor: $2.46 \approx 2.5,$ $8.163 \approx 8,$ and $5.17 + 4.829 \approx 10.$

The product is about $2.5 \times 8 \times 10 = 200.$

Thus, the correct answer is B .

Solution:

The factors $0.075$ and $2.56$ have $3$ and $2$ decimal places, for a total of $5.$

Placing the decimal point $5$ digits from the right of $19200$ gives $0.19200 = .192.$

Thus, the correct answer is B .

Solution:

Read each triangle's side lengths from the grid. A horizontal or vertical side is counted directly, and a slanted side spanning $a$ units across and $b$ units up has length $\sqrt{a^2 + b^2}.$

Top-left triangle: its two slanted sides each span $1$ across and $2$ up, so each has length $\sqrt{5},$ with a base of length $2.$ Two equal sides, so it is isosceles.

Top-middle triangle: it has a vertical side of length $2$ and a horizontal side of length $2$ (its third side is the slant $2\sqrt{2}$). Two equal sides, so it is isosceles.

Top-right triangle: its sides are $2,$ $\sqrt{5},$ and $\sqrt{13},$ which are all different, so it is not isosceles.

Bottom-left (wide, flat) triangle: its two slanted sides each span $3$ across and $1$ up, so each has length $\sqrt{10}.$ Two equal sides, so it is isosceles.

Bottom-right triangle: two of its sides each span $2$ and $1$ (giving length $\sqrt{5}$), while the third is $\sqrt{10}.$ Two equal sides, so it is isosceles.

Four of the five triangles are isosceles.

Thus, the correct answer is D .

Solution:

Days of the week repeat every $7$ days. Since $60 = 8 \times 7 + 4,$ the day $60$ days later is $4$ days after Thursday.

Counting forward from Thursday: Friday, Saturday, Sunday, Monday. So it is a Monday.

Thus, the correct answer is A .

Solution:

Since $12^2 = 144$ and $13^2 = 169,$ and $144 \lt 164 \lt 169,$ the value $\sqrt{164}$ lies between $12$ and $13.$

Thus, the correct answer is E .

Solution:

Each person's share is $\dfrac{20 \text{ billion}}{250 \text{ million}} = \dfrac{2 \times 10^{10}}{2.5 \times 10^{8}}.$

This equals $.8 \times 10^{2} = 80.$

Thus, the correct answer is C .

Solution:

The bushes surround the circular edge, so their number is about the circumference $2\pi r = 2\pi(12).$

Using $\pi \approx 3.14,$ this is about $2 \times 3.14 \times 12 \approx 75$ feet, so roughly $75$ bushes are needed.

Thus, the correct answer is D .

Solution:

The factor pairs of $36$ are $1 \times 36,$ $2 \times 18,$ $3 \times 12,$ $4 \times 9,$ and $6 \times 6.$

The sum is largest for the most spread-out pair, $1 + 36 = 37.$

Thus, the correct answer is E .

Solution:

Adding, $\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{3}{6} + \dfrac{2}{6} = \dfrac{5}{6}.$

The reciprocal of $\dfrac{5}{6}$ is $\dfrac{6}{5}.$

Thus, the correct answer is C .

Solution:

A placement of $6$ X's works: leave the three squares along one main diagonal empty and fill the other six. Then each row and each column is missing one square, the used diagonal has an empty square, and the other diagonal passes through the empty center, so no line of three is complete.

Seven X's is impossible: only two squares would be empty, and two empty squares can lie in at most two of the three rows, forcing the remaining row to be completely filled with three X's.

So the greatest number is $6.$

Thus, the correct answer is E .

Solution:

The horizontal rectangle has area $10 \times 2 = 20,$ and the vertical rectangle has area $3 \times 8 = 24.$ Their overlap, a $3 \times 2$ rectangle, has area $6.$

Adding the two rectangles counts the overlap twice, so the shaded area is $20 + 24 - 6 = 38.$

Thus, the correct answer is B .

Solution:

The total weight is $6 \times 150 + 4 \times 120 = 900 + 480 = 1380$ pounds.

The average of the $10$ children is $\dfrac{1380}{10} = 138$ pounds.

Thus, the correct answer is C .

Solution:

The sequence starts at $1$ with common difference $4.$ The $100$th term is reached by adding $4$ to the first term $99$ times.

So the $100$th term is $1 + 99 \times 4 = 1 + 396 = 397.$

Thus, the correct answer is A .

Solution:

Let $n$ be the full capacity. Then $\dfrac{45}{n} = \dfrac{36}{100}.$

Solving, $n = \dfrac{45 \times 100}{36} = 125$ cups.

Thus, the correct answer is C .

Solution:

The five numbers have sum $28 + n$ and mean $\dfrac{28 + n}{5}.$ The median is the middle value when sorted, which is $6,$ $n,$ or $9$ depending on the size of $n.$

If the median is $6$: $\dfrac{28 + n}{5} = 6$ gives $n = 2,$ which is indeed less than $6.$ If the median is $n$: $\dfrac{28 + n}{5} = n$ gives $n = 7,$ which is between $6$ and $9.$ If the median is $9$: $\dfrac{28 + n}{5} = 9$ gives $n = 17,$ which is indeed greater than $9.$

Each case yields a valid value, so $n$ can be $2,$ $7,$ or $17$ — three possible values.

Thus, the correct answer is C .

Solution:

Increasing by $25\%$ multiplies the price by $1.25,$ and then taking $20\%$ off multiplies by $0.80.$

The overall factor is $1.25 \times 0.80 = 1.00,$ so the sale price equals the original price.

Thus, the correct answer is E .

Solution:

Consider disks in dozens, since $12$ is a multiple of both $4$ and $3.$ A dozen disks costs $3 \times \$5 = \$15$ to buy and sells for $4 \times \$5 = \$20,$ for a profit of $5 per dozen.

To make $100 profit she needs $\dfrac{100}{5} = 20$ dozen, which is $20 \times 12 = 240$ disks.

Thus, the correct answer is D .

Solution:

Each roll of the square over one edge of the hexagon turns it $150^\circ$ clockwise. (At the pivot corner the square turns through $360^\circ$ minus the square's own $90^\circ$ corner minus the hexagon's $120^\circ$ interior angle, which leaves $150^\circ.$)

From the top of the hexagon to the bottom is $3$ rolls, for a total of $3 \times 150^\circ = 450^\circ.$ That is one complete revolution ($360^\circ$) plus an extra $90^\circ$ clockwise.

The triangle starts pointing straight up, so after the extra quarter turn clockwise it points to the right.

Thus, the correct answer is A .

Solution:

For a single-digit hour $h$ (from $1$ to $9$), the display $h\!:\!m_1 m_2$ reads the same backwards when $m_2 = h.$ The tens digit $m_1$ can be $0, 1, 2, 3, 4,$ or $5,$ giving $6$ palindromes per hour, so $9 \times 6 = 54.$

For the two-digit hours $10, 11, 12,$ the display $h_1 h_2\!:\!m_1 m_2$ is a palindrome when $m_1 = h_2$ and $m_2 = h_1,$ giving exactly 10:01, 11:11, and 12:21 — one each, for $3$ more.

The total is $54 + 3 = 57.$

Thus, the correct answer is A .