| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.25 |
| Score | 0% | 65% |
If \( \left|a + 3\right| \) + 6 = 3, which of these is a possible value for a?
| 5 | |
| -6 | |
| -17 | |
| -7 |
First, solve for \( \left|a + 3\right| \):
\( \left|a + 3\right| \) + 6 = 3
\( \left|a + 3\right| \) = 3 - 6
\( \left|a + 3\right| \) = -3
The value inside the absolute value brackets can be either positive or negative so (a + 3) must equal - 3 or --3 for \( \left|a + 3\right| \) to equal -3:
| a + 3 = -3 a = -3 - 3 a = -6 | a + 3 = 3 a = 3 - 3 a = 0 |
So, a = 0 or a = -6.
Which of the following is not an integer?
-1 |
|
0 |
|
1 |
|
\({1 \over 2}\) |
An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.
What is the greatest common factor of 72 and 44?
| 4 | |
| 16 | |
| 35 | |
| 21 |
The factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72] and the factors of 44 are [1, 2, 4, 11, 22, 44]. They share 3 factors [1, 2, 4] making 4 the greatest factor 72 and 44 have in common.
Cooks are needed to prepare for a large party. Each cook can bake either 3 large cakes or 17 small cakes per hour. The kitchen is available for 4 hours and 28 large cakes and 400 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?
| 6 | |
| 10 | |
| 9 | |
| 12 |
If a single cook can bake 3 large cakes per hour and the kitchen is available for 4 hours, a single cook can bake 3 x 4 = 12 large cakes during that time. 28 large cakes are needed for the party so \( \frac{28}{12} \) = 2\(\frac{1}{3}\) cooks are needed to bake the required number of large cakes.
If a single cook can bake 17 small cakes per hour and the kitchen is available for 4 hours, a single cook can bake 17 x 4 = 68 small cakes during that time. 400 small cakes are needed for the party so \( \frac{400}{68} \) = 5\(\frac{15}{17}\) cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 6 = 9 cooks.
In a class of 25 students, 15 are taking German and 13 are taking Spanish. Of the students studying German or Spanish, 8 are taking both courses. How many students are not enrolled in either course?
| 15 | |
| 17 | |
| 14 | |
| 5 |
The number of students taking German or Spanish is 15 + 13 = 28. Of that group of 28, 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 28 - 8 = 20 who are taking at least one language. 25 - 20 = 5 students who are not taking either language.