The chart below provides information on how bonuses of certain amounts were distributed among the employees of a business:
| Bonus paid to an employee (dollars) | Number of employees |
|---|---|
| 50 | 7 |
| 100 | 37 |
| 150 | 4 |
| 200 | 2 |
a) What was the average bonus per employee?
b) If the median bonus is m dollars, the average bonus a dollars, and the mode bonus is p dollars, which of the must be true?
A. $m < a < p$.
B. $m < a = p$.
C. $m = p < a$.
D. $m < p < a$.
**Editorial note for this self-study exercise:** Answer both parts in one entry: mean in dollars;option letter, with no spaces, for example 90;A. Enter an integer for the mean and one letter A–D for part (b).
Town A and Town B are 435km apart. At 9 : 15 a.m, a car left Town A and traveled toward Town B at a constant speed of 80km/h. At the same time, a lorry left B and traveled toward Town A at a constant speed. When they met, the car traveled a distance of 240km. Find the speed of the lorry.
**Editorial note for this self-study exercise:** Both vehicles use the same route, travel without stopping, and meet between A and B. Enter the lorry speed in km/h, without units.
**Editorial note for this self-study exercise:** Enter the figure symbol or its shape and fill, for example “filled circle”; both shape and shading matter.
The cost of a T-shirt and a skirt was $\$85$. Janet bought 6 such T-shirts, 2 such skirts and a hat for $\$430$. If the cost of 1 T-shirt and 1 hat was $\$125$, find the cost of 1 skirt.
**Editorial note for this self-study exercise:** Enter the cost of one skirt in dollars, without the currency symbol.
The number 64 has the property that it is divisible by its units (ones) digit. How many whole numbers between 10 and 50 have the same property?
A. 15
B. 16
C. 17
D. 18
E. None of the above
**Editorial note for this self-study exercise:** Enter the number of qualifying integers, not an option letter. A zero units digit cannot be used as a divisor.
1/12 of Bob’s marbles and 0.75 of Dan’s marbles are equal to 34. If both of them have 88 marbles altogether, how many marbles does each boy have?
**Editorial note for this self-study exercise:** As in the source equation, the two portions ADD to 34: Bob’s total divided by 12 plus 0.75 times Dan’s total. Enter Bob’s count;Dan’s count as two integers separated by a semicolon, with no spaces.
$\overline{AB}$ is a 2-digit number. The digit B is 3 more than A. When $\overline{AB}$ is divided by sum of its digits the quotient is 4 and remainder is 3. Find the 2-digit number.
**Editorial note for this self-study exercise:** A is the tens digit and B is the units digit. The overbar denotes a numeral, not multiplication. Enter the two-digit number.
The figure below is made up of a quadrant ABG, a rectangle BCEG and an isosceles triangle CDE. Find the total area of the shaded part.
**Editorial note for this self-study exercise:** Use the geometry marked in the figure: A, B, C, D are collinear in that order; G, F, E are collinear; the quadrant has centre B; CE=CD=21 cm; AD=64 cm. Give the exact shaded area as aπ+b square centimetres. Enter a;b using reduced fractions and no spaces, for example 3/2;5/4. Do not replace π by a decimal or 22/7.
A seven-digit number, $2\,006\,\square\square\square$, is divisible by 3, by 4 and by 25. Find the possible values of the missing digits.
**Editorial note for this self-study exercise:** Enter all possible three-digit endings in increasing order, separated by semicolons, with no spaces in the answer; give the missing blocks, not the full seven-digit numbers.
Ages of the First 12 United States Presidents at the Beginning of Their Terms in Office
President | Age (Years) | President | Ages (Years)
--- | --- | --- | ---
Washington | 57 | Jackson | 62
Adams | 62 | Van Buren | 55
Jefferson | 58 | Harrison | 68
Madison | 58 | Tyler | 51
Monroe | 59 | Polk | 50
Rooney | 58 | Taylor | 65
The table above lists the ages of the first 12 United States presidents when they began their first term in office. According to the table, what was the mean age, in years, of these presidents at the beginning of their terms? (Round your answer to the nearest tenth.)
**Editorial note for this self-study exercise:** Calculate from the twelve printed ages, including the source’s “Rooney” entry, without silently repairing the data. Round to the nearest tenth and enter years without units. This is a table-arithmetic exercise, not a verified historical dataset.
A television set has a 30-inch screen size, i.e. the length of the diagonal of the screen is 30 inches. The aspect ratio of the screen is 4 : 3. Find the height of the screen. Leave your answer to the nearest whole number if necessary. (Note: The aspect ratio of the screen refers to the ratio of the width of the screen to its height.)
A. 13 inches
B. 18 inches
C. 21 inches
D. 24 inches
E. None of the above
**Editorial note for this self-study exercise:** The screen is rectangular. Enter its height in inches without units, not an option letter.
In the diagram below, ABCD is a square, ∠CDE = 72° and ∠CED = 54°. Find the angle ∠EAD.
**Editorial note for this self-study exercise:** E lies inside square ABCD, as shown. Enter ∠EAD in degrees, without the degree sign. Do not infer extra incidence relations from the not-to-scale drawing.
Team A takes 10 days to complete a project. Team B takes 30 days to complete the same project. The two teams now work together on the same project. Meanwhile, Team A rest for 2 days and Team B rest for 8 days. None of the team rests in the same day. How many days are needed to complete the same project?
**Editorial note for this self-study exercise:** Assume constant daily work rates, and that all the stated non-overlapping rest days occur before the project is completed.
Gina’s 6-digit postal code has the following interesting properties:
- It is the same number if your read it from right to left.
- It is a multiple of 9.
- If you remove the first and last digits, the only prime factor of the remaining 4-digit number is 11.
Find the first 3 digits of Gina’s postal code.
**Editorial note for this self-study exercise:** A six-digit code has a nonzero first digit. Enter only the first three digits. The supplied solution contains arithmetic errors identified below.
