| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.31 |
| Score | 0% | 66% |
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 40% off." If Bob buys two shirts, each with a regular price of $48, how much money will he save?
| $4.80 | |
| $12.00 | |
| $21.60 | |
| $19.20 |
By buying two shirts, Bob will save $48 x \( \frac{40}{100} \) = \( \frac{$48 x 40}{100} \) = \( \frac{$1920}{100} \) = $19.20 on the second shirt.
In a class of 19 students, 8 are taking German and 12 are taking Spanish. Of the students studying German or Spanish, 6 are taking both courses. How many students are not enrolled in either course?
| 5 | |
| 13 | |
| 14 | |
| 19 |
The number of students taking German or Spanish is 8 + 12 = 20. Of that group of 20, 6 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 20 - 6 = 14 who are taking at least one language. 19 - 14 = 5 students who are not taking either language.
Simplify \( \frac{24}{64} \).
| \( \frac{7}{11} \) | |
| \( \frac{3}{7} \) | |
| \( \frac{3}{8} \) | |
| \( \frac{7}{18} \) |
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:
\( \frac{24}{64} \) = \( \frac{\frac{24}{8}}{\frac{64}{8}} \) = \( \frac{3}{8} \)
What is the least common multiple of 2 and 6?
| 6 | |
| 7 | |
| 5 | |
| 3 |
The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 have in common.
If a rectangle is twice as long as it is wide and has a perimeter of 42 meters, what is the area of the rectangle?
| 98 m2 | |
| 8 m2 | |
| 18 m2 | |
| 128 m2 |
The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 42 meters so the equation becomes: 2w + 2h = 42.
Putting these two equations together and solving for width (w):
2w + 2h = 42
w + h = \( \frac{42}{2} \)
w + h = 21
w = 21 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 21 - 2w
3w = 21
w = \( \frac{21}{3} \)
w = 7
Since h = 2w that makes h = (2 x 7) = 14 and the area = h x w = 7 x 14 = 98 m2