McGraw-Hill Education GRE 2019

A company estimates the number of potential customers, P, in a day by

using the following formula: P =^8 zc 43 , where c = the number of customers the

company had the previous day and z = the number of competitors for that

month. If the company had 10 customers yesterday and has 2 competitors

this month, how many customers will the company have today?

SOLUTION: Substitute the given values into the formula. Substitute 10 for c and

2 for z: 8(10) 243 = 8,000 16 = 500.

Formulas with Unknown Amounts

Sometimes, formula questions will not give you values for the variables. Instead,

they will ask you to determine how changes in certain variables affect the output of

the formula. In these cases, you should always plug in numbers! For example:

The formula for the volume of a sphere is^43 πr^3. If the radius of a sphere is

doubled, the volume of the resulting sphere will be how many times the

volume of the original sphere?

A 2

B 4

C 8

D 16

E 32

SOLUTION: Let the original radius = 2. The original volume is thus (^43 )π(2^3 ) =

(^43 )π(8). After the radius doubles, the new volume is (^43 )π(4^3 ) = (^43 )π(6 4).

(^) ( 4
3 )π(64)
(^43 ) π(8)
= 8. The correct answer is C.
Functions
You can think of a function as a recipe. Recipes specify certain steps you need to
take to achieve a desired dish; in the same way, functions specify certain operations
you need to perform to achieve a given outcome. Because of their strange notation,
functions tend to intimidate a lot of people, but it is important to remember that
fundamentally functions are just substitution!
A simple function question would be the following:
If, for all numbers, x, f(x) is defined by f(x) = 3x + 5, then f(7) =
It is important to note that “f(x)” does not mean f × x. f is the name of the
function, and the term in the parentheses represents the input of the function.
Using the recipe analogy, this formula tells you that to get the value (also known
as “output”) of the function, f, you must multiply what is inside of the parentheses
by 3 and then add 5. So in the preceding example, to get the value of f(7), you must
multiply 7 by 3 and then add 5. 3(7) + 5 = 26.
292 PART 4 ■ MATH REVIEW
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