| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.99 |
| Score | 0% | 60% |
Which of these numbers is a factor of 36?
| 1 | |
| 14 | |
| 10 | |
| 27 |
The factors of a number are all positive integers that divide evenly into the number. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
If the ratio of home fans to visiting fans in a crowd is 5:1 and all 41,000 seats in a stadium are filled, how many home fans are in attendance?
| 25,833 | |
| 34,167 | |
| 24,750 | |
| 33,333 |
A ratio of 5:1 means that there are 5 home fans for every one visiting fan. So, of every 6 fans, 5 are home fans and \( \frac{5}{6} \) of every fan in the stadium is a home fan:
41,000 fans x \( \frac{5}{6} \) = \( \frac{205000}{6} \) = 34,167 fans.
Solve for \( \frac{5!}{6!} \)
| \( \frac{1}{504} \) | |
| \( \frac{1}{4} \) | |
| 1680 | |
| \( \frac{1}{6} \) |
A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:
\( \frac{5!}{6!} \)
\( \frac{5 \times 4 \times 3 \times 2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6} \)
\( \frac{1}{6} \)
In a class of 29 students, 11 are taking German and 15 are taking Spanish. Of the students studying German or Spanish, 2 are taking both courses. How many students are not enrolled in either course?
| 17 | |
| 5 | |
| 21 | |
| 16 |
The number of students taking German or Spanish is 11 + 15 = 26. Of that group of 26, 2 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 26 - 2 = 24 who are taking at least one language. 29 - 24 = 5 students who are not taking either language.
A circular logo is enlarged to fit the lid of a jar. The new diameter is 45% larger than the original. By what percentage has the area of the logo increased?
| 27\(\frac{1}{2}\)% | |
| 22\(\frac{1}{2}\)% | |
| 37\(\frac{1}{2}\)% | |
| 15% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 45% the radius (and, consequently, the total area) increases by \( \frac{45\text{%}}{2} \) = 22\(\frac{1}{2}\)%