Real Numbers

Practice Questions

GMAT Quantitative Reasoning › Real Numbers

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1

is a real number. True or false: is a rational number.

Statement 1: $N^{2} - 1$ is a rational number.

Statement 2: is a rational number.

2

Evaluate .

Statement 1: is the multiplicative inverse of .

Statement 2: is the additive inverse of .

3

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

If both and are both positive, then $a \bigstar b = a-b$ .

If both and are not both positive, then $a \bigstar b = a+b$ .

Evaluate $M \bigstar N$ .

Statement 1: .

Statement 2: .

4

Is z a negative number?

(1) $\dpi{100} \small 13z>14z$

(2) $\dpi{100} \small 4+z$ is positive

5

Which of the following is the decimal representation of an irrational number? (Assume any observed patterns continue)

6

Define an operation $\bigstar$ on the positive integers as follows:

If and are both prime integers, then $a \bigstar b = 1$ .

If and are not both prime integers, then $a \bigstar b = 2$ .

Evaluate $M \bigstar N$ .

Statement 1: .

Statement 2: is a factor of .

7

Define an operation $\bigstar$ on the positive integers as follows:

If and are both prime integers, then $a \bigstar b =|a- b|$ .

If and are not both prime integers, then $a \bigstar b = 0$ .

Evaluate $M \bigstar N$ .

Statement 1: .

Statement 2: is a factor of .

8

Evaluate .

Statement 1: is the multiplicative inverse of .

Statement 2: is the additive inverse of .

9

$\small a + 8 = b+12$

$\small c+ 5 = d + 11$

$\small a + 4 = d + 3$

Order $\small a,b, c,d$ from least to greatest.

10

Evaluate $A \cdot (B + C)$ .

Statement 1:

Statement 2:

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