| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.24 |
| Score | 0% | 65% |
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?
| 32\(\frac{1}{2}\)% | |
| 37\(\frac{1}{2}\)% | |
| 22\(\frac{1}{2}\)% | |
| 30% |
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\(\frac{1}{2}\)%
How many hours does it take a car to travel 240 miles at an average speed of 60 miles per hour?
| 4 hours | |
| 5 hours | |
| 3 hours | |
| 8 hours |
Average speed in miles per hour is the number of miles traveled divided by the number of hours:
speed = \( \frac{\text{distance}}{\text{time}} \)Solving for time:
time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{240mi}{60mph} \)
4 hours
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 25% off." If Ezra buys two shirts, each with a regular price of $21, how much money will he save?
| $2.10 | |
| $1.05 | |
| $4.20 | |
| $5.25 |
By buying two shirts, Ezra will save $21 x \( \frac{25}{100} \) = \( \frac{$21 x 25}{100} \) = \( \frac{$525}{100} \) = $5.25 on the second shirt.
A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 7 parts per hour. Yesterday the machine was shut down for 5 hours for maintenance.
How many error-free parts did the machine produce yesterday?
| 142.5 | |
| 125 | |
| 169.2 | |
| 117.2 |
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 7 = \( \frac{6 \times 7}{100} \) = \( \frac{42}{100} \) = 0.42 errors per hour
So, in an average hour, the machine will produce 7 - 0.42 = 6.58 error free parts.
The machine ran for 24 - 5 = 19 hours yesterday so you would expect that 19 x 6.58 = 125 error free parts were produced yesterday.
What is the next number in this sequence: 1, 4, 10, 19, 31, __________ ?
| 46 | |
| 38 | |
| 40 | |
| 45 |
The equation for this sequence is:
an = an-1 + 3(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 + 3(6 - 1)
a6 = 31 + 3(5)
a6 = 46