GMAT Math : Arithmetic

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Example Questions

Example Question #1982 : Problem Solving Questions

Each of $\bigcirc, \square, \bigtriangleup$ $\displaystyle \bigcirc, \square, \bigtriangleup$ stands for a real number; if one appears more than once in a choice, it stands for the same number each time.

Which of the following diagrams demonstrates the transitive property?

Possible Answers:

$\bigcirc = \bigcirc$ $\displaystyle \bigcirc = \bigcirc$

$\bigcirc \times (\square + \bigtriangleup) = \bigcirc \times \square + \bigcirc \times \bigtriangleup$ $\displaystyle \bigcirc \times (\square + \bigtriangleup) = \bigcirc \times \square + \bigcirc \times \bigtriangleup$

$\bigcirc + \bigtriangleup = \bigtriangleup + \bigcirc$ $\displaystyle \bigcirc + \bigtriangleup = \bigtriangleup + \bigcirc$

If $\bigcirc = \bigtriangleup$ $\displaystyle \bigcirc = \bigtriangleup$ then $\bigtriangleup = \bigcirc$ $\displaystyle \bigtriangleup = \bigcirc$

If $\bigcirc = \bigtriangleup$ $\displaystyle \bigcirc = \bigtriangleup$ and $\bigtriangleup = \square$ $\displaystyle \bigtriangleup = \square$, then $\bigcirc = \square$ $\displaystyle \bigcirc = \square$

Correct answer:

Explanation:

According to the transitive property of equality, if two numbers are equal to the same third number, they are equal to each other. This is demonstrated by this diagram:

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Example Question #1983 : Problem Solving Questions

Which of the following diagrams demonstrates the symmetric property?

Possible Answers:

$\bigcirc +0 = \bigcirc$ $\displaystyle \bigcirc +0 = \bigcirc$

If $\bigcirc = \bigtriangleup$ $\displaystyle \bigcirc = \bigtriangleup$ then $\bigtriangleup = \bigcirc$ $\displaystyle \bigtriangleup = \bigcirc$

$\bigcirc + \bigtriangleup = \bigtriangleup + \bigcirc$ $\displaystyle \bigcirc + \bigtriangleup = \bigtriangleup + \bigcirc$

Correct answer:

If $\bigcirc = \bigtriangleup$ $\displaystyle \bigcirc = \bigtriangleup$ then $\bigtriangleup = \bigcirc$ $\displaystyle \bigtriangleup = \bigcirc$

Explanation:

According to the symmetric property of equality, if one number is equal to another, the second is equal to the first. This is demonstrated by the diagram

If $\bigcirc = \bigtriangleup$ $\displaystyle \bigcirc = \bigtriangleup$ then $\bigtriangleup = \bigcirc$ $\displaystyle \bigtriangleup = \bigcirc$

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Example Question #1984 : Problem Solving Questions

Which of the following diagrams demonstrates an identity property?

Possible Answers:

If $\bigcirc = \bigtriangleup$ $\displaystyle \bigcirc = \bigtriangleup$ then $\bigtriangleup = \bigcirc$ $\displaystyle \bigtriangleup = \bigcirc$

$\bigcirc = \bigcirc$ $\displaystyle \bigcirc = \bigcirc$

$\bigcirc +0 = \bigcirc$ $\displaystyle \bigcirc +0 = \bigcirc$

$\bigcirc + \bigtriangleup = \bigtriangleup + \bigcirc$ $\displaystyle \bigcirc + \bigtriangleup = \bigtriangleup + \bigcirc$

Correct answer:

$\bigcirc +0 = \bigcirc$ $\displaystyle \bigcirc +0 = \bigcirc$

Explanation:

0 is called the additive identity, since it can be added to any number to yield, as a sum, the latter number. This property is demonstrated in the diagram

$\bigcirc +0 = \bigcirc$ $\displaystyle \bigcirc +0 = \bigcirc$

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Example Question #30 : Real Numbers

$\displaystyle A$ is the additive inverse of $\displaystyle C$.

Which of the following is equivalent to

ABC $\displaystyle ABC$

for all values of the variables?

Possible Answers:

$\displaystyle 1$

$-A^{2}B$ $\displaystyle -A^{2}B$

$A^{2}B$ $\displaystyle A^{2}B$

$\displaystyle B$

$\displaystyle 0$

Correct answer:

$-A^{2}B$ $\displaystyle -A^{2}B$

Explanation:

If $\displaystyle A$ is the additive inverse of $\displaystyle C$, then

C+A = 0 $\displaystyle C+A = 0$, or, equivalently,

C = -A $\displaystyle C = -A$

Substituting,

$ABC = AB (-A) = A \cdot (-A) \cdot B = -A^{2}B$ $\displaystyle ABC = AB (-A) = A \cdot (-A) \cdot B = -A^{2}B$.

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Example Question #431 : Arithmetic

$\displaystyle A$ is the additive inverse of $\displaystyle C$.

Which of the following is equivalent to

$\displaystyle A+ (B + C)$

for all values of the variables?

Possible Answers:

B + 1 $\displaystyle B + 1$

$A+ \frac{1}{A} + B$ $\displaystyle A+ \frac{1}{A} + B$

$\displaystyle 0$

$\displaystyle B$

2 A+ B $\displaystyle 2 A+ B$

Correct answer:

$\displaystyle B$

Explanation:

If $\displaystyle A$ is the additive inverse of $\displaystyle C$, then

C+A = 0 $\displaystyle C+A = 0$.

It follows by way of the commutative and associative properties that

$\displaystyle A+ (B + C)$

$\displaystyle = (B + C) + A$

$\displaystyle = B + (C + A)$

= B + 0 $\displaystyle = B + 0$

= B $\displaystyle = B$

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Example Question #31 : Understanding Real Numbers

$\displaystyle A$ is the additive inverse of $\displaystyle C$. Which of the following expressions is equivalent to

$\displaystyle A (B + C)$

for all values of the variables?

Possible Answers:

$AB - A^{2}$ $\displaystyle AB - A^{2}$

$\displaystyle B$

$AB + A^{2}$ $\displaystyle AB + A^{2}$

AB + 1 $\displaystyle AB + 1$

AB - 1 $\displaystyle AB - 1$

Correct answer:

$AB - A^{2}$ $\displaystyle AB - A^{2}$

Explanation:

If $\displaystyle A$ is the additive inverse of $\displaystyle C$, then

C+A = 0 $\displaystyle C+A = 0$, or, equivalently,

C = -A $\displaystyle C = -A$

By way of the distributive property and substitution,

$\displaystyle A (B + C)$

$\displaystyle = A B + A C$

$\displaystyle = A B + A (-A)$

$= A B- A ^{2}$ $\displaystyle = A B- A ^{2}$

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Example Question #1982 : Problem Solving Questions

$\displaystyle B$ is the multiplicative inverse of $\displaystyle C$. Which of the following expressions is equivalent to

$\displaystyle A (B + C)$

for all values of the variables?

Possible Answers:

$\displaystyle A$

$AB + \frac{A}{B}$ $\displaystyle AB + \frac{A}{B}$

$\displaystyle 1$

$\displaystyle 0$

$\displaystyle AB$

Correct answer:

$AB + \frac{A}{B}$ $\displaystyle AB + \frac{A}{B}$

Explanation:

If $\displaystyle B$ is the multiplicative inverse of $\displaystyle C$, then

BC = 1 $\displaystyle BC = 1$,

or, equivalently,

$C = \frac{1}{B}$ $\displaystyle C = \frac{1}{B}$.

By way of substitution and the distributive property,

$\displaystyle A (B + C)$

$\displaystyle = AB + AC$

$= AB + A \cdot \frac{1}{B}$ $\displaystyle = AB + A \cdot \frac{1}{B}$

$= AB + \frac{A}{B}$ $\displaystyle = AB + \frac{A}{B}$

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Example Question #34 : Real Numbers

$\displaystyle A$ is the multiplicative inverse of $\displaystyle C$.

Which of the following is equivalent to

$A\left (BC \right )$ $\displaystyle A\left (BC \right )$

for all values of the variables?

Possible Answers:

$\displaystyle 0$

$-A^{2}B$ $\displaystyle -A^{2}B$

$A^{2}B$ $\displaystyle A^{2}B$

$\displaystyle 1$

$\displaystyle B$

Correct answer:

$\displaystyle B$

Explanation:

If $\displaystyle A$ is the multiplicative inverse of $\displaystyle C$, then

CA = 1 $\displaystyle CA = 1$.

By way of the commutative and associative properties, substitution, and the identity property of multiplication:

$A\left (BC \right ) = \left (BC \right ) A = B (CA) = B \cdot 1 = B$ $\displaystyle A\left (BC \right ) = \left (BC \right ) A = B (CA) = B \cdot 1 = B$

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Example Question #431 : Arithmetic

When evaluating each of the following expressions, which one(s) require you to multiply first?

I) $12 + 45 \times 23$ $\displaystyle 12 + 45 \times 23$

II) $\left (12 + 45 \right ) \times 23$ $\displaystyle \left (12 + 45 \right ) \times 23$

III) $12 + \left (45 \times 23 \right )$ $\displaystyle 12 + \left (45 \times 23 \right )$

Possible Answers:

I only

II and III only

I and II only

I and III only

III only

Correct answer:

I and III only

Explanation:

According to the order of operations, any operations within parentheses must be performed first. In expression (II), this is the addition; in expression (III), this is the multiplication.

Expression (I) does not have any parentheses, so, by the order of operations, in the absence of grouping symbols, multiplication precedes addition.

Therefore, the correct response is I and III only.

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Example Question #36 : Real Numbers

$\displaystyle A$ is the multiplicative inverse of $\displaystyle C$. Which of the following expressions is equivalent to

$\displaystyle A (B + C)$

for all values of the variables?

Possible Answers:

$\displaystyle AB$

$\displaystyle B$

AB + 1 $\displaystyle AB + 1$

$AB - A^{2}$ $\displaystyle AB - A^{2}$

$AB + A^{2}$ $\displaystyle AB + A^{2}$

Correct answer:

AB + 1 $\displaystyle AB + 1$

Explanation:

By the distributive property,

$\displaystyle A (B + C) = AB + AC$

$\displaystyle A$ is the multiplicative inverse of $\displaystyle C$, meaning that, by defintion, AC = 1 $\displaystyle AC = 1$, so

$\displaystyle AB + AC = AB + 1$.

AB + 1 $\displaystyle AB + 1$ is the correct choice.

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GMAT Math : Arithmetic

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1982 : Problem Solving Questions

Example Question #1983 : Problem Solving Questions

Example Question #1984 : Problem Solving Questions

Example Question #30 : Real Numbers

Example Question #431 : Arithmetic

Example Question #31 : Understanding Real Numbers

Example Question #1982 : Problem Solving Questions

Example Question #34 : Real Numbers

Example Question #431 : Arithmetic

Example Question #36 : Real Numbers

All GMAT Math Resources

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