| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.19 |
| Score | 0% | 64% |
Simplify \( \frac{24}{64} \).
| \( \frac{1}{2} \) | |
| \( \frac{7}{15} \) | |
| \( \frac{3}{8} \) | |
| \( \frac{4}{17} \) |
To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{24}{64} \) = \( \frac{\frac{24}{8}}{\frac{64}{8}} \) = \( \frac{3}{8} \)
The total water usage for a city is 30,000 gallons each day. Of that total, 33% is for personal use and 62% is for industrial use. How many more gallons of water each day is consumed for industrial use over personal use?
| 8,700 | |
| 6,300 | |
| 7,700 | |
| 3,400 |
62% of the water consumption is industrial use and 33% is personal use so (62% - 33%) = 29% more water is used for industrial purposes. 30,000 gallons are consumed daily so industry consumes \( \frac{29}{100} \) x 30,000 gallons = 8,700 gallons.
If the ratio of home fans to visiting fans in a crowd is 3:1 and all 42,000 seats in a stadium are filled, how many home fans are in attendance?
| 24,667 | |
| 31,500 | |
| 33,333 | |
| 30,000 |
A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:
42,000 fans x \( \frac{3}{4} \) = \( \frac{126000}{4} \) = 31,500 fans.
What is the next number in this sequence: 1, 5, 13, 25, 41, __________ ?
| 57 | |
| 61 | |
| 54 | |
| 58 |
The equation for this sequence is:
an = an-1 + 4(n - 1)
where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:
a6 = a5 + 4(6 - 1)
a6 = 41 + 4(5)
a6 = 61
In a class of 30 students, 15 are taking German and 10 are taking Spanish. Of the students studying German or Spanish, 8 are taking both courses. How many students are not enrolled in either course?
| 16 | |
| 13 | |
| 15 | |
| 22 |
The number of students taking German or Spanish is 15 + 10 = 25. Of that group of 25, 8 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 25 - 8 = 17 who are taking at least one language. 30 - 17 = 13 students who are not taking either language.