| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.95 |
| Score | 0% | 59% |
A circular logo is enlarged to fit the lid of a jar. The new diameter is 50% larger than the original. By what percentage has the area of the logo increased?
| 25% | |
| 30% | |
| 37\(\frac{1}{2}\)% | |
| 15% |
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 50% the radius (and, consequently, the total area) increases by \( \frac{50\text{%}}{2} \) = 25%
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 5 to 2 and the ratio of baseball to basketball cards is 5 to 1, what is the ratio of football to basketball cards?
| 5:2 | |
| 1:6 | |
| 1:1 | |
| 25:2 |
The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. 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 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.
13 members of a bridal party need transported to a wedding reception but there are only 2 4-passenger taxis available to take them. How many will need to find other transportation?
| 9 | |
| 4 | |
| 5 | |
| 2 |
There are 2 4-passenger taxis available so that's 2 x 4 = 8 total seats. There are 13 people needing transportation leaving 13 - 8 = 5 who will have to find other transportation.
A tiger in a zoo has consumed 63 pounds of food in 9 days. If the tiger continues to eat at the same rate, in how many more days will its total food consumtion be 84 pounds?
| 4 | |
| 3 | |
| 1 | |
| 11 |
If the tiger has consumed 63 pounds of food in 9 days that's \( \frac{63}{9} \) = 7 pounds of food per day. The tiger needs to consume 84 - 63 = 21 more pounds of food to reach 84 pounds total. At 7 pounds of food per day that's \( \frac{21}{7} \) = 3 more days.
What is \( \frac{9}{2} \) + \( \frac{4}{6} \)?
| \( \frac{5}{11} \) | |
| \( \frac{7}{12} \) | |
| 5\(\frac{1}{6}\) | |
| \( \frac{1}{4} \) |
To add these fractions, first find the lowest common multiple of their denominators. 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 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{9 x 3}{2 x 3} \) + \( \frac{4 x 1}{6 x 1} \)
\( \frac{27}{6} \) + \( \frac{4}{6} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{27 + 4}{6} \) = \( \frac{31}{6} \) = 5\(\frac{1}{6}\)