Functions/Series

Practice Questions

GMAT Quantitative Reasoning › Functions/Series

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1

There is water tank already $\frac{4}{7}$ full. If Jose adds 5 gallons of water to the water tank, the tank will be $\frac{13}{14}$ full. How many gallons of water would the water tank hold if it were full?

2

If $f(x)=x^{2}$ , find $\frac{f(x+h)-f(x)}{h}$ .

3

Define an operation $\Omega$ on the set of real numbers as follows:

For all real numbers , $a \Omega b = 0$ if and only if and , and $a \Omega b = a b$ otherwise.

Evaluate:

$6 \Omega 6 + \left ( -6 \right )\Omega \left ( -6 \right )$

4

For any values , , define the operation $\Gamma$ as follows:

$a; \Gamma; b = 2ab - a - b$

Which of the following expressions is equal to $2x; \Gamma; 2y$ ?

5

Define an operation $\odot$ as follows:

For any real numbers ,

$a \odot b = (a-1) (b-1)$

Evaluate $\left (5 \odot 5 \right )\odot 5$ .

6

A sequence is formed the same way the Fibonacci sequence is formed. Its third and fourth terms are 16 and 30, respectively. What is its first term?

7

$\left \lfloor N \right \rfloor$ is defined to be the greatest integer less than or equal to .

Define $f (x) = \left \lfloor x ^{2} \right \rfloor - \left \lfloor 4 x \right \rfloor + 8$ .

Evaluate $f \left ( \frac{3}{5} \right )$ .

8

Piecewise

Let be the piecewise-defined function graphed above. Define function $g(x) = x^{2} - 11$ .

Evaluate $\left (g \circ f^{-1} \right ) (4)$ .

9

Define the operation $\Theta$ as follows:

$a ; \Theta ; b = ab + 100$

Solve for : $4; \Theta ; x = 72$

10

$\left \lfloor x \right \rfloor$ is defined as the greatest integer less than or equal to .

Solve for : $\left \lfloor 3y - 1 \right \rfloor = 7$

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