Question Bank / Math / Ratios, Rates, and Proportions
Ratios, rates, proportional relationships, and units SAT question
Math · Problem-Solving and Data Analysis · Hard · Answer it here, explanation included.
| Species of tree | Growth factor |
|---|---|
| Red maple | 4.5 |
| River birch | 3.5 |
| Cottonwood | 2.0 |
| Black walnut | 4.5 |
| White birch | 5.0 |
| American elm | 4.0 |
| Pin oak | 3.0 |
| Shagbark hickory | 7.5 |
One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for that species. The table above gives the growth factors for eight species of trees. If a white birch tree and a pin oak tree each now have a diameter of 1 foot, which of the following will be closest to the difference, in inches, of their diameters 10 years from now? (1 foot = 12 inches)
ExplanationShow
Choice C is correct. According to the given information, multiplying a tree species’ growth factor by the tree’s diameter is a method to approximate the age of the tree. A white birch with a diameter of 12 inches (or 1 foot) has a given growth factor of 5 and is approximately 60 years old. A pin oak with a diameter of 12 inches (or 1 foot) has a given growth factor of 3 and is approximately 36 years old. The diameters of the two trees 10 years from now can be found by dividing each tree’s age in 10 years, 70 years, and 46 years, by its respective growth factor. This yields 14 inches and 
inches. The difference between and 14 is 
, or approximately 1.3 inches.
Alternate approach: Since a white birch has a growth factor of 5, the age increases at a rate of 5 years per inch or, equivalently, the diameter increases at a rate of 
of an inch per year. Likewise, the pin oak has a growth factor of 3, so its diameter increases at a rate of 
of an inch per year. Thus, the pin oak grows 
of an inch per year more than the white birch. In 10 years it will grow 
of an inch more, which is approximately 1.3 inches.
Choices A, B, and D are incorrect and a result of incorrectly calculating the diameters of the two trees in 10 years.
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