GMAT Functions Questions With Solutions PDF, Download Now

GMAT Functions Questions 2025

GMAT Functions questions are an important part of the GMAT Quant section. These questions check how well you understand how functions work, like plugging values into a formula, combining two functions, finding the original input from an output, or solving for a variable.

You might see function questions on their own or as part of longer word problems. The good news is, they are easy to solve once you know the basic rules and how to apply them. You don’t need advanced math, just a clear understanding and careful calculation.

In this blog, you’ll find a simple functions formula PDF, a set of practice questions with answers, and a few extra problems to try on your own. You’ll also take a GMAT mock test to understand your current level.

Important Concepts for GMAT Functions Questions

You only need a few easy ideas to solve function questions. These help you understand how to evaluate, combine, or reverse a function.

You can download the full formula PDF from the link above. Here’s a quick look at the main ones:

ConceptFormula / Explanation
Function Notationf(x) means apply the rule of the function to the number x
Plug In a ValueReplace x with a number: f(3) means plug in 3
Function Compositionf(g(x)) means do g(x) first, then plug into f(x)
Inverse Functionf⁻¹(x) gives the original input when you know the output
Solving a FunctionSet f(x) = value, then solve for x
Domain of a FunctionA set of input values that the function can accept
Function as a RuleThink of a function as a “machine” that takes an input, does something, and gives an output

These ideas are useful for solving questions about values, formulas, graphs, and patterns in GMAT function problems.

Top 5 Common Mistakes to Avoid in GMAT Functions Questions

  • Doing the steps in the wrong order: For questions like f(g(x)), always solve the inside part first (g), then the outside part (f).

  • Misreading the function: – f(x + 1) is not the same as f(x) + 1. Read carefully and follow the exact instructions.

  • Ignoring the domain: Some values may not be allowed (like dividing by zero). Always check the input.

  • Guessing the inverse: Don’t try to “undo” a function in your head. Use algebra to find the inverse correctly.

  • Thinking it’s harder than it is: Function questions often look scary, but are just simple substitutions. Stay calm and follow the steps.

List of GMAT Functions Questions

Here’s a short set of GMAT-style functions questions to help you practice. They include all common types of plug-in, composition, inverse, and solving for a variable. Practice these often to get faster and more confident before your GMAT test.

Question 1

If for all real numbers 'x', f(x+1) + f(x-1) = f(x), then what is the value of f(50) + f(47)?

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Question 2

Let $$f(x)$$ be a function satisfying $$f(x)f(y) = f(xy)$$ for all real x, y. If $$f(2) = 4$$, then what is the value of $$f(\frac{1}{2})$$?

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Question 3

Let f(x) = max (2x + 1, 3 - 4x), where x is any real number. Then the minimum possible value of f(x) is:

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Question 4

Find the sum $$\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}} +....+ \sqrt{1+\frac{1}{2007^2}+\frac{1}{2008^2}}$$

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Question 5

Let f(x) = max(2x+3,6-x). Then what is the minimum value of f(x)?

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Question 6

A function $$f(x)$$ is defined as $$f(x, y, z) = xyz - (x + y + z)$$. If it is known that x, y and z are integers such that their absolute values are not equal and $$-12 \leq x, y, z \leq 12$$. Find the maximum value of the function.

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Question 7

Let S be the set of all pairs (i, j) where 1 <= i < j <= n, and n >= 4 (i and j are natural numbers). Any two distinct members of S are called “friends” if they have one constituent of the pairs in common and “enemies” otherwise.

For example, if n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1,2) and (2, 3) are also friends, but (1,4) and (2, 3) are enemies.

For general n, consider any two members of S that are friends. How many other members of S will be common friends of both these members?

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Question 8

Let $$a_1= p$$ and $$b_1 = q$$, where p and q are positive quantities.

Define $$a_n = pb_{n-1} , b_n = qb_{n-1}$$ , for even n > 1. and $$a_n = pa_{n-1} , b_n = qa_{n-1}$$ , for odd n > 1.

Which of the following best describes $$a_n + b_n$$ for even n?

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Question 9

Let $$f(x) = ax^2 + bx + c$$, where a, b and c are certain constants and $$a \neq 0$$?

It is known that $$f(5) = - 3f(2)$$ and that 3 is a root of $$f(x) = 0$$.

What is the other root of f(x) = 0?

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Question 10

Let $$f(x) = ax^2 + bx + c$$, where a, b and c are certain constants and $$a \neq 0$$?

It is known that f(5) = - 3f(2). and that 3 is a root of f(x) = 0.

What is the value of a + b + c?

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Question 11

Let S be the set of all pairs (i, j) where 1 <= i < j <= n, and n >= 4 (i and j are natural numbers). Any two distinct members of S are called “friends” if they have one constituent of the pairs in common and “enemies” otherwise.

For example, if n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1,2) and (2, 3) are also friends, but (1,4) and (2, 3) are enemies.

For general n, how many enemies will each member of S have?

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Question 12

Consider the formula, $$S = \frac {a*w}{t + p*w}$$ where a,w,t and p are all positive integers. If 'w' is increased and 'a' , 't' and 'p' are kept constant, then S:

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