DSQ: Understanding the properties of integers

Practice Questions

GMAT Quantitative Reasoning › DSQ: Understanding the properties of integers

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1

Does the integer have at least 4 different positive prime factors?

(1) $\frac{x}{14}$ is an integer.

(2) $\frac{x}{15}$ is an integer.

2

If is a positive integer, is divisible by 6?

1. The sum of the digits of is divisible by 6

2. is even

3

Is $\dpi{100} \small x+y$ odd?

(1) $\dpi{100} \small x$ is odd

(2) $\dpi{100} \small x-y$ is even

4

A whole number has four digits. True or false: The integer is divisible by 9.

Statement 1: The sum of the digits is 26.

Statement 2: The last two digits are 98.

5

, , and are integers. Is odd?

(1) is a prime number and

(2) is odd

6

Is a positive integer a prime number or a composite number?

Statement 1: $n \in \left {5,10,15,20,25,30,... \right }$

Statement 2: $n \in \left {7,14,21,28,35,42,... \right }$

7

Let be positive integers. When is $M^{2} + 4 N^{2}$ an odd number?

8

If is an integer and $\dpi{100} \small 3<k<7$ , what is the value of ?

(1) $\dpi{100} \small k$ is a factor of 20.

(2) $\dpi{100} \small k$ is a factor of 24.

9

and are nonzero integers. Is $A ^{B}$ positive, negative, or zero?

Statement 1: is negative.

Statement 2: is even.

10

What is the area of a rhombus in square inches?

One of its angles measures $30^\circ$
One of its sides measures 10 inches

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