Tip #46 to Get a Top SAT Math Score

This is something that you learned for maybe two classes, three years ago in Algebra I. But, for some reason, it's on the SAT. Weird, but here's the good news: it's super easy. In fact, it's an "easy" topic for us because as long as you know what's on this page, it's cake; the reason it's rated "medium" or "hard" is because most students don't know it.

"Directly proportional" means "x times some number gives you y." This table shows a "directly proportional" relationship because 4 multiplied by each x yields each y value.

The equation for the relationship in the table is y = 4x, and the equation for directly proportional in general is y = kx.  Also since they are directly proportional, we can set up a proportion between any two  (x,y) values in the table.  For example: . 

Sometimes the SAT also calls this "varies directly", as in "y varies directly with x".  This is exactly the same as "directly proportional."

That's it, that's all the SAT does with directly proportional.

Let's look at this question:

Solution: "y is directly proportional to x³" means y/x³.  So we set up a proportion between the two sets of (x,y) values and solve for the unknown x.

    =         When you see a proportion, cross multiply.

64x³ = (8)(216)    simplify (8)(216)

64x³ = 1728         divide both sides by 64

x³ = 27                  take cube root of both sides

x = 3

Correct answer: 3

Example Problems

Medium

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

2.  If y is directly proportional to x² , and y=18 when x=3, what is x when y =50?

3. If y varies directly with x in the table above, what is the value of y when x = 7.5?

A. 30

B. 32.5

C. 35

D. 37.5

E. 40

Hard

4. If y varies directly with x ^-1 in the table above, what is the value of y when x = 5?

A. 0.5

B. 0.4

C. 0.3

D. 0.2

E. 0.1

Answers

1. B For "yto be directly proportional to x," each ymust equal a constant (a number) multiplied by each x. Choice B is correct since each xmultiplied by 5 yields each y.
2. 5 "yis directly proportional to x² " means So we set up a proportion between the two sets of (x, y) values, cross-multiply, and solve for the unknown x. Remember Skill 20: when you see a proportion, cross-multiply.





3. D Each yin the table is found by multiplying each xvalue by 5. So simply multiply 7.5 × 5 = 37.5.
4. B "yvaries directly with x^–1 " means exactly the same as "yis directly proportional to x^–1," so set up a proportion between a pair of numbers in the table and (5, y). Then crossmultiply and solve for y.

Go to: Tip #47