| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.99 |
| Score | 0% | 60% |
What is the greatest common factor of 56 and 76?
| 4 | |
| 23 | |
| 55 | |
| 5 |
The factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 the greatest factor 56 and 76 have in common.
In a class of 25 students, 10 are taking German and 7 are taking Spanish. Of the students studying German or Spanish, 4 are taking both courses. How many students are not enrolled in either course?
| 23 | |
| 12 | |
| 16 | |
| 17 |
The number of students taking German or Spanish is 10 + 7 = 17. Of that group of 17, 4 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 17 - 4 = 13 who are taking at least one language. 25 - 13 = 12 students who are not taking either language.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 30% off." If Alex buys two shirts, each with a regular price of $28, how much will he pay for both shirts?
| $47.60 | |
| $35.00 | |
| $39.20 | |
| $32.20 |
By buying two shirts, Alex will save $28 x \( \frac{30}{100} \) = \( \frac{$28 x 30}{100} \) = \( \frac{$840}{100} \) = $8.40 on the second shirt.
So, his total cost will be
$28.00 + ($28.00 - $8.40)
$28.00 + $19.60
$47.60
If a rectangle is twice as long as it is wide and has a perimeter of 24 meters, what is the area of the rectangle?
| 8 m2 | |
| 32 m2 | |
| 128 m2 | |
| 18 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 24 meters so the equation becomes: 2w + 2h = 24.
Putting these two equations together and solving for width (w):
2w + 2h = 24
w + h = \( \frac{24}{2} \)
w + h = 12
w = 12 - h
From the question we know that h = 2w so substituting 2w for h gives us:
w = 12 - 2w
3w = 12
w = \( \frac{12}{3} \)
w = 4
Since h = 2w that makes h = (2 x 4) = 8 and the area = h x w = 4 x 8 = 32 m2
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 3 to 2 and the ratio of baseball to basketball cards is 3 to 1, what is the ratio of football to basketball cards?
| 9:2 | |
| 3:1 | |
| 5:2 | |
| 1:1 |
The ratio of football cards to baseball cards is 3:2 and the ratio of baseball cards to basketball cards is 3:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 9:6 and the ratio of baseball cards to basketball cards as 6:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 9:6, 6:2 which reduces to 9:2.