Q.If $a > b$ and $c < 0$, then which of the following is true ? (A) $a + c < b + c$ (B) $a - c < b - c$ (C) $ac > bc$ (D) $a - c > b + c$

Integer Comparison: What It Means and Why It Matters

Imagine you have two piles of stones. One pile has 5 stones, the other has 3. Without counting, you can see the first pile is bigger. That's comparison in the real world — you're asking "which is larger?" or "are they equal?"

Integer comparison is just that same question, but asked about whole numbers (…, -3, -2, -1, 0, 1, 2, 3, …). The only twist is that integers include negative numbers, so the "bigger" pile might actually be a debt or a temperature below zero.

The Intuition: The Number Line

Picture a horizontal line. In the middle is 0. To the right are positive numbers (1, 2, 3, …), getting larger as you go right. To the left are negative numbers (-1, -2, -3, …), getting more negative (smaller) as you go left.

So:

• 5 is to the right of 3 → 5 > 3
• -2 is to the right of -5 → -2 > -5
• 0 is to the right of -1 → 0 > -1

The Precise Statement

For any two integers $a$ and $b$:

• $a > b$ (a is greater than b) if $a$ lies to the right of $b$ on the number line.
• $a < b$ (a is less than b) if $a$ lies to the left of $b$ on the number line.
• $a = b$ if $a$ and $b$ are the same point on the number line.

Equivalently, in terms of subtraction:

• $a > b$ means $a - b$ is positive.
• $a < b$ means $a - b$ is negative.
• $a = b$ means $a - b = 0$.

Common Pitfalls

Another trap: comparing a negative and a positive. Any positive integer is always greater than any negative integer. For example, -100 < 1, even though 100 is a large number.

Quick Reference Table

The Big Idea

Integer comparison is just "which way on the number line?" The number farther right wins. That's it. Once you internalize the number line, you never need to memorize rules — you just picture the line and see the answer.