Tip #47 to Get a Top SAT Math Score

"Inversely proportional" means some number divided by x equals y. This table shows an inverse proportion:

The equation for the relationship in the table is , and the equation for inversely proportional, in general, is . This also means that xy = k. In the SAT this is also called "inverse variation" or "varies inversely," as in "y varies inversely with x." Either way, it's the same.

Let's look at this question:

Solution: "y is inversely proportional to x" means . Plug the first pair of values into this equation to find the value of k: 12 = . So k = 48. Now, using k = 48, plug the second pair of values (x, 8) into the equation: 8 = . Cross-multiply 8x = 48, so x = 6. You could also use xy = k, so (12)(4) = 48, and (x)(8) must also equal 48, so x = 6.

Correct answer: D

Example Problems

Medium

1. Which of the following expresses a relationship where y is inversely proportional to x?





2. The table above gives values of a relation for selected values of x. Which of the following defines y in terms of x?
   1. y = 1.5x
   2. y = x^–1
   3. y =
   4. y =
   5. y =

Hard

3. If y is inversely proportional to x², and y = 16 when x = 2, what is x when y = ?
   1. 8
   2. 4
   3. 
   4. 16
   5. 32
4. If y varies inversely with x and y = 10 when x = 3, what is the value of x when y = 8?
   1. 1.75
   2. 2.75
   3. 3.75
   4. 4.75
   5. 5.75

Answers

1. C "yis inversely proportional to x" implies That and therefore yx = k. In other words, xtimes yshould equal the same constant for each (x, y) pair in the table. Choice C is correct since xtimes yfor each pair of values equals 108.
2. E Just choose an (x, y) pair from the table and try it in each answer choice. The one that works is the right answer. If two work, just try another (x, y) pair as a tie breaker.
3. A "yis inversely proportional to x2" means Plug the first pair of values into this equation to find the value of k. So k = 64. Now, using k = 64, plug the second pair of values into the equation. Cross-multiply x2 = 128, so x =
4. C "yis inversely proportional to x" means Plug the first pair of values into this equation to find the value of k. So k= 30. Now, using k = 30, plug the second pair of values (x,8) into the equation. Cross-multiply 8x = 30, so x = 3.75.

Go to: Tip #48