An integer is a whole number with no fractional part: …, −3, −2, −1, 0, 1, 2, 3, … . Note what is not an integer — 2.5, 3/4 and √2 are numbers but not integers, and the GRE deliberately blurs "number" and "integer" to bait you. The number line orders every real number from left (smaller) to right (larger), so −7 < −2 even though 7 > 2; on the negative side, the bigger the digit, the smaller the value. Distance on the line is always positive and equals the absolute difference |a − b|. Zero is an integer, is neither positive nor negative, and sits exactly between the two sides. When a GRE question says "x is a number" without saying "integer", you must allow fractions and negatives — that single word changes the answer to many Quantitative Comparison items.
✅ Solved examples
1. List the integers strictly between −3.5 and 2.
Integers greater than −3.5 and less than 2: −3, −2, −1, 0, 1. That is 5 integers. (2 is excluded because "strictly between" is open.)
2. On the number line, which is greater: −8 or −3?
−3 lies to the RIGHT of −8, so −3 > −8. On the negative side the number closer to zero is larger.
3. Quantitative Comparison. Quantity A: the distance between −5 and 6 on the number line. Quantity B: 10. Which is greater?
Distance = |6 − (−5)| = |11| = 11. Quantity A (11) > Quantity B (10), so Quantity A is greater.
4. How many integers x satisfy −4 ≤ x < 3?
x can be −4, −3, −2, −1, 0, 1, 2 — that is 7 values. (Include −4 because of ≤; exclude 3 because of <.)
✏️ Practice — try these, take hints as needed
1. How many integers lie strictly between −2 and 5?
Strictly means exclude both ends.
List −1, 0, 1, 2, 3, 4.
Count them.
6
2. Order from least to greatest: 0, −4, 3, −1.
Most negative is smallest.
−4 sits farthest left.
Then −1, 0, 3.
−4, −1, 0, 3
3. What is the distance between −12 and −4 on the number line?
Distance = |a − b|.
|−4 − (−12)|.
= |8|.
8
4. Which is larger, −0.5 or −1/3?
−1/3 ≈ −0.333.
Closer to zero is larger.
−1/3 is right of −0.5.
−1/3
5. How many integers satisfy −3 < x ≤ 2?
Exclude −3, include 2.
List −2, −1, 0, 1, 2.
Count.
5
📝 Topic test — 8 questions
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