GMAT Math : Functions/Series

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Example Question #31 : Understanding Functions

The first two terms of an arithmetic sequence are

8, 24...

What is the tenth term of this sequence?

Possible Answers:

136

160

168

144

152

Correct answer:

152

Explanation:

The common difference of this arithmetic sequence is 24 - 8 = 16 , so the tenth term is

$8 + 16 (10-1) = 8 + 16 \times 9 = 152$

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Example Question #32 : Understanding Functions

The first two terms of a geometric sequence are

8, 20 ,...

What is the sum of the fourth and fifth terms?

Possible Answers:

175

124

100

$1,531 \frac{1}{4}$

$437 \frac{1}{2}$

Correct answer:

$437 \frac{1}{2}$

Explanation:

The common ratio of the sequence is $20 \div 8 = 2 \frac{1}{2 }$

The fourth and fifth terms can be found by repeated multiplication:

$20 \times 2 \frac{1}{2} = 50$

$50 \times 2 \frac{1}{2} = 125$ , the fourth term

$125 \times 2 \frac{1}{2} = 312 \frac{1}{2}$ , the fifth term

Add the fourth and fifth terms:

$125+ 312 \frac{1}{2} = 437 \frac{1}{2}$

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Example Question #33 : Understanding Functions

The first six terms of a sequence are:

15, 16, 20, 29, 45, 70,...

What is the next term?

Possible Answers:

119

106

110

Correct answer:

106

Explanation:

The numbers are generated by addition as follows:

$\begin{matrix} 15 + 1 = 16\\ 16+4=20\\ 20+9 = 29\\ 29+16 = 45\\ 45+25 =70\\ \end{matrix}$

Each entry is generated by adding the next perfect square to the previous entry. Therefore, the next entry will be generated as follows:

70 + 36 = 106

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Example Question #32 : Understanding Functions

The first six terms of a sequence are:

25, 27, 31, 37, 45, 55,...

What is the eight term?

Possible Answers:

Correct answer:

Explanation:

The terms are generated by adding an increment that increases by 2 with every term:

$\begin{matrix} 25+ 2 = 27\\ 27 + 4 = 31\\ 31+6=37\\ 37+8=45\\ 45+10=55\\ 55+12= 67\\ 67+14 = 81 \end{matrix}$

81 is the eighth term.

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Example Question #35 : Understanding Functions

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

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

Evaluate:

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

Possible Answers:

Correct answer:

Explanation:

$6 \Omega 6$ can be evaluated by using the second part of the definition, since both numbers are positive:

$6 \Omega 6 = 6 \times 6 = 36$

$\left ( -6 \right )\Omega \left ( -6 \right )$ can be evaluated by using the first part of the definition, since both numbers are negative:

$\left ( -6 \right )\Omega \left ( -6 \right ) = 0$

$6 \Omega 6 + \left ( -6 \right )\Omega \left ( -6 \right ) = 36 + 0 = 36$

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Example Question #36 : Understanding Functions

Define an operation $\triangleright$ on two real numbers as follows:

For all real numbers a,b ,

$a \triangleright b = \frac{a}{b}$ if and only if $b \neq 0$ , and $a \triangleright b = a ^{2}$ otherwise.

Evaluate:

$\left (5 \triangleright 2 \right )-\left ( 2 \triangleright 5 \right )$

Possible Answers:

- 2.1

2.1

Correct answer:

2.1

Explanation:

We can evaluate both $5 \triangleright 2 \right$ and $2 \triangleright 5$ using the first part of the definition, since the second number is nonzero in both cases.

$a \triangleright b = \frac{a}{b}$

$5\triangleright 2 = \frac{5}{2} = 2.5$

$2\triangleright 5 = \frac{2}{5} = 0.4$

$\left (5 \triangleright 2 \right )-\left ( 2 \triangleright 5 \right ) = 2.5 - 0.4 = 2.1$

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Example Question #37 : Understanding Functions

Define an operation $\bullet$ on the real numbers as follows:

$a \bullet b = a ^{2} (b- 10)$ for all real a,b .

Evaluate:

$10 \bullet 5$

Possible Answers:

500

Correct answer:

Explanation:

$a \bullet b = a ^{2} (b- 10)$

$10 \bullet 5 = 10 ^{2} (5- 10) = 100 \cdot (-5) = -500$

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Example Question #38 : Understanding Functions

Define f (x) = 5x + 9 .

What is $f ^{-1}$ ?

Possible Answers:

$f ^{-1} (x)=- \frac{1}{5}x - \frac{9}{5}$

$f ^{-1} (x)= \frac{1}{5}x - 9$

$f ^{-1} (x)=- \frac{1}{5}x + \frac{9}{5}$

$f ^{-1} (x)=-5x -9$

$f ^{-1} (x)= \frac{1}{5}x - \frac{9}{5}$

Correct answer:

$f ^{-1} (x)= \frac{1}{5}x - \frac{9}{5}$

Explanation:

Replace f(x) with .

y = 5x + 9

Now exchange and and solve for in the new expression:

x = 5y + 9

x - 9 = 5y + 9 - 9

x - 9 = 5y

$\left (x - 9 \right ) \div 5 = 5y \div 5$

$\frac{1}{5}x - \frac{9}{5} = y$

$f ^{-1} (x)= \frac{1}{5}x - \frac{9}{5}$

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Example Question #181 : Algebra

Define $f (x) = x ^{3}$

What is $f ^{-1}$ ?

Possible Answers:

$f ^{-1} (x) = - \sqrt[3]{x}$

$f (x) = - \frac{1}{x ^{3}}$

$f (x) = \frac{1}{x ^{3}}$

$f (x) = - x ^{3}$

$f ^{-1} (x) = \sqrt[3]{x}$

Correct answer:

$f ^{-1} (x) = \sqrt[3]{x}$

Explanation:

Replace f(x) with .

$y= x ^{3}$

Now exchange and and solve for in the new expression:

$x= y^{3}$

$\sqrt[3]{x}= \sqrt[3]{y^{3}}$

$\sqrt[3]{x}=y$

$f^{-1}(x)= \sqrt[3]{x}$

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Example Question #40 : Understanding Functions

Define an operation $\bigstar$ on two real numbers as follows:

$a \bigstar b = 100-ab$ for all real numbers a,b

Solve for :

$y \bigstar 7 = 44$

Possible Answers:

y=137

y = 49

y = 7

y=8

$y = 10 \frac{4}{7}$

Correct answer:

y=8

Explanation:

Substitute a=y,b=7 into the definition and solve:

$a \bigstar b = 100-ab$

$y \bigstar 7 = 44$

$100- y \cdot 7 = 44$

100- 7 y = 44

100- 7 y -100 = 44-100

- 7 y = -56

$- 7 y\div (-7) = -56 \div (-7)$

y=8

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GMAT Math : Functions/Series

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #31 : Understanding Functions

Example Question #32 : Understanding Functions

Example Question #33 : Understanding Functions

Example Question #32 : Understanding Functions

Example Question #35 : Understanding Functions

Example Question #36 : Understanding Functions

Example Question #37 : Understanding Functions

Example Question #38 : Understanding Functions

Example Question #181 : Algebra

Example Question #40 : Understanding Functions

All GMAT Math Resources

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