Is Zero Even Integer or Odd Integer? GMAT Problem Solving

Question: Is zero even integer or odd integer? Is zero +ve or -ve?

1. Even Number
2. ​​Odd Number
3. Neither Even nor odd

“Is Zero Even Integer or Odd Integer? GMAT Problem Solving” - is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. The GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer: A

Explanation:

What is an Integer?

Mathematically, we can split up all integers into two categories: even numbers and odd numbers. An integer is colloquially defined as a number that can be written without a fractional component—is as simple as asking one question: Is the number divisible by 2? If yes, then it is even; if no, then it is odd.

Now, we need to know where exactly does 0 fall into these categories? Most people are confused by the number 0. They are unsure if it’s an integer, to begin with, and unaware of its placement as a number because it technically signifies an empty set. Under the rules of parity, is zero even or odd?

To answer the question, we can follow the below example:

Mathematically, a set of Even numbers
= {2x; for all x belonging to integers}, whereas an odd number is an integer of the form n = 2x + 1.

For example,
At x = 0
2x = 2(0) = 0 (Even number)

In other words, a number is divisible by 2 if the result of its division by 2. It has no remainder or fractional component—in other terms, if the result is an integer. Let us look at another example:

A simple division by two: 10÷2=5.

In this division statement, the number 10 is the dividend; the number 2 is the divisor; and the number 5 is the quotient or the result of the equation. Because the quotient of this division by 2 is an integer, the number 10 is proved to be even.

If you were to divide, say, 101 by 2, the quotient would be 50.5—not an integer, thereby classifying 101 as an odd number.
In the same way, when 0 is divided by 2, the resulting quotient turns out to also be 0—an integer, thereby classifying it as an even number.
Any number that can be divided by two to create another whole number is even. Zero passes this test because if you have zero you get zero.

Hence, 0 is an even integer, making A the correct answer.

Now, is zero +ve or -ve?

Zero is neither positive nor negative. The reason of that is explained in the below image.

Integers which lie right to zero on the number line are positive integers.
Integers which lie left to zero on the number line are negative integers.
Zero is neither a negative integer nor a positive integer.

Hence, 0 or zero is neither negative nor positive. It is a reference to the positive and negative sides of integers.

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