Number Properties: The Rules You FORGOT You Knew

Say it's 9:40 on a Tuesday night. You finished work an hour ago, you opened your Executive Assessment prep, and you hit a Quant question that says x and y are integers and xy + x is odd. Which of the following MUST be true? You stare at it. You start pushing algebra around. Three minutes later you have half a page of symbols and no answer. Here's the verdict: that question is NOT hard. It just LOOKS hard. It's built on a rule you learned when you were about eleven and then filed away with your old locker combination.

I'll bet you already know at least half of the rules in this post. The problem isn't knowledge. It's recall under pressure, at night, after a full workday. So let's dig those rules back up and put them to work.

Why this matters on THIS test

The Quantitative Reasoning section of the EA gives you 14 questions in 30 minutes. It's scored from 0 to 20, and it counts exactly as much as Verbal and Integrated Reasoning toward your 100 to 200 total. You can see the full layout on GMAC's assessment structure page. Do the quick math: that's a little over 2 minutes per question on AVERAGE. A question you can finish in 40 seconds because you know the rule buys you time for the wordy one later. Number properties questions are exactly where those 40 second wins live.

A quick term: number properties means the built-in behavior of numbers. Is it odd or even? Is it prime? What divides into it? The test hides these rules inside questions that look like algebra.

The dozen rules you FORGOT you knew

Don't just read these. Grab paper and write each one down as you go.

1. Even means it splits into pairs with nothing left over. Odd means one is left over.
2. Zero is even. It splits into zero pairs with nothing left over. People forget this constantly.
3. Adding: even + even = even, odd + odd = even, even + odd = odd.
4. Multiplying: if ANY factor is even, the product is even. The only way to get an odd product is odd × odd.
5. Powers keep the type. An odd number raised to a positive whole number power stays odd. An even one stays even.
6. A prime is a positive whole number with exactly two factors: 1 and itself.
7. 1 is NOT prime. It only has one factor.
8. 2 is the only even prime. Every other even number has 2 as a factor, so it has too many factors.
9. Know the primes under 30 cold: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
10. Divisible by 3 (or 9): add the digits. If the sum divides by 3 (or 9), so does the number. 4,815 has digits that sum to 18, so it divides by both.
11. Divisible by 4: check only the last two digits. 7,316 ends in 16, so yes. By 5: it ends in 0 or 5. By 6: it must divide by BOTH 2 and 3.
12. Consecutive integers (whole numbers in a row, like 7, 8, 9): any two in a row include an even, so their product is even. Any three in a row include a multiple of 3 AND an even, so their product divides by 6.

Now watch a 'hard' question get quick

This is a Problem Solving question: a regular math question with five answer choices, one of them right.

Stop for a second. How long did that take once you tested values? Now think about the version of you writing algebra at 9:40 at night. Which one would you rather send into the test center?

The same rules, in Data Sufficiency

Data Sufficiency questions give you a question and two statements. You don't solve for the answer. You decide whether the statements give you ENOUGH information to answer it. The five answer choices are always the same, so learn them once and save time on every DS question.

The mistakes I watch people make every week

1. Doing the odd/even work in your head. It feels fast. It's where the silly mistakes live. INSTEAD: write E and O under every variable as you figure it out. Five seconds of ink saves a wrong answer.
2. Testing only one set of values on a "must be true" question. One set can make two wrong answers look right. INSTEAD: test once to knock out choices, then test a second set on whatever survives.
3. Forgetting the weird numbers. Zero, 1, 2 and negative numbers are where the test hides its traps. INSTEAD: when the question says "integer" and not "positive integer," ALWAYS try 0 and a negative before you commit.
4. Reaching for algebra first. You're a strategist now, not a math student. INSTEAD: test values, test the answers, and when the numbers get ugly, estimate, because the test wants you to.
5. Skipping past the word "integer." That word is not decoration. It's the whole question. INSTEAD: circle it in your notes. Then ask which of the twelve rules it unlocks.
6. Missing the rule because it's buried in a story. Number properties show up inside word problems about teams, boxes and budgets. INSTEAD: translate the words into math first, then look for the odd, even, prime or divisibility rule hiding underneath.

This is training, not cramming

Knowing a rule and USING it at speed are different skills. A tennis player knows what a backhand is. She still hits a thousand of them. You need the same reps. These rules should fire the instant you see "integer," "odd" or "divisible," without you hunting through memory.

And don't get down on yourself if you forgot that 0 is even or that 1 isn't prime. Most people did. That's the good news: this is one of the most fixable gaps on the whole test.

Here's your challenge for today. Take a blank sheet. From memory, write all twelve rules. Then check yourself against this post. For every rule you missed or fumbled, make up two test values that prove it, and write those down too. Then redo both examples above WITHOUT looking at the solutions. If you can't do that in under 15 minutes, you just found exactly where your next study session starts.