EA PrepProTheory Guide
Data Sufficiency
Data Sufficiency · Quantitative

Don't solve it.
Decide if you can.

Data Sufficiency is unlike any question you've seen on other tests. You're never asked to find the answer — only a sharper question: do you have enough information to find it? Once that clicks, DS becomes one of the most learnable parts of the exam. This guide builds it from zero.

01
How Data Sufficiency works
What it is

Every DS question gives you a question and two clues (the test calls them "statements"), labeled (1) and (2). Your job is not to find the final answer. It's to decide a different thing: is the information enough to answer the question for certain?

Then you choose from five answer options that are exactly the same on every DS question. They sound like jargon at first — so let's translate each one into plain language.

The five options, in plain language

Think of statements (1) and (2) as two clues. Each option is simply a verdict on which clue (or clues) turned out to be enough to answer the question:

  • A Only clue (1) is enough — (2) alone isn't.
  • B Only clue (2) is enough — (1) alone isn't.
  • C Neither alone, but the two together are enough.
  • D Each clue alone is enough — either one answers it.
  • E Not even both together are enough.

But to actually choose among these five, you need to know one thing precisely: what "enough" really means. That single word does all the work — so it's where we go next.

02
What "enough" really means

Here's the single idea the whole section rests on. A clue is "enough" (the test says sufficient) only when it forces exactly one possible answer. If the clue still allows two or more different answers, it is not enough — no matter how helpful it looks.

Sufficient = the clue leaves only one possible answer.
Not sufficient = the clue still allows two or more different answers.

So the smartest way to test a clue is not to trust it — it's to try to break it. Ask: "Can I find two different situations that both fit this clue but give different answers to the question?" If you can, the clue is not enough. If you genuinely can't, it is.

Question: Is x greater than 10?   Clue: x² = 144.

A hurried solver thinks "x = 12, which is greater than 10 — enough!" But try to break it: x² = 144 is true for x = 12 and for x = −12 (because −12 × −12 = 144 too).

So two situations fit the clue: x = 12 (answer: yes, >10) and x = −12 (answer: no). Two different answers survive → the clue is not enough. The trap was assuming x had to be the positive 12.

If you look for a reason a clue works, you'll usually find one — and stop too early, missing the second case that ruins it. Most DS traps are exactly that hidden second case: a negative number, a zero, a fraction you didn't consider.

Hunting for a way to break the clue forces you to go looking for that second case on purpose. If you find it, the clue is not enough — proven. If you honestly can't find one after trying the usual troublemakers, you can trust it. It's the more reliable habit.

The five options aren't a list to memorize — they're a process

Now that you know what "enough" means, you never have to memorize the five letters. Just follow one process: check whether each clue is enough, then read off the letter. Here's the whole logic in one picture:

Does clue (1) alone answer it? YES NO Does clue (2) alone also answer it? Does clue (2) alone answer it? YES NO YES NO D A B Both together enough? C YES E NO
Now try it — does each clue pin down one answer?

No math tricks needed yet — just the logic of "is this enough?" Read the question and the two clues, decide whether each one leaves a single answer, and pick the option.

Try it · DS format
How old is Maria?
(1) Maria is exactly 30 years old.
(2) Maria is older than 25.

Clue (1) "exactly 30" answers the question completely on its own → enough. Clue (2) "older than 25" could mean 26, 40, 55 — many answers remain, so it's not enough on its own. One clue works, the other doesn't → A. This is the whole game: you didn't calculate anything, you judged whether each clue pins down a single answer.

03
Factor to zero (and don't lose answers)

Many DS questions hinge on an equation, and there's one mistake the test sets the same trap for again and again: dividing both sides of an equation by a variable. Doing that secretly throws away a valid answer — and in DS, a thrown-away answer changes everything.

First, what "factoring" means

Factoring just means rewriting an expression as a multiplication. For example, x² − 5x can be rewritten as x(x − 5) — that is, "x times (x − 5)." It's the same expression, written as a product of two pieces.

Why is that useful? Because of one simple rule: if two things multiply to give zero, at least one of them must be zero. If x(x − 5) = 0, then either x = 0, or (x − 5) = 0 (which means x = 5). That single rule hands you all the answers at once.

The method: when an equation has the variable on both sides, don't divide. Move everything to one side so it equals zero, factor it into a product, then set each piece to zero. That captures every answer.

The tempting (wrong) way — divide by x:
x² = 5x → divide both sides by x → x = 5. Just one answer. But dividing by x quietly assumed x isn't zero.

The safe way — factor to zero:
x² − 5x = 0 → x(x − 5) = 0 → x = 0 or x = 5. Two answers.

Dividing by x deleted the perfectly valid answer x = 0. In a yes/no DS question, that missing answer is often the exact case that makes a clue "not enough."

Try it · DS format
Is the number k positive?
(1) k² = 7k
(2) k is less than 9

Clue (1): factor to zero → k² − 7k = 0 → k(k − 7) = 0 → k = 0 or k = 7. Since 0 is not positive but 7 is, the answer could be "no" or "yes" → not enough. Clue (2) k < 9: allows tons of values → not enough. Together: k is still 0 or 7, and both are less than 9, so clue (2) rules out neither. Still "no or yes" → E. (Dividing by k would have wrongly deleted k = 0 and made clue 1 look enough.)

04
Combining the two clues

If neither clue is enough on its own, you check whether they're enough together — that's the difference between option C ("both together work") and option E ("not even together"). But there's a catch most beginners fall for.

Combining only helps if the second clue actually rules out the leftover possibilities that made the first clue not enough. Don't assume that putting two clues together magically settles things — sometimes the second clue adds nothing that matters.

A simple order to stay organized — "AD / BCE"

Check clue (1) first. If it's enough on its own, the answer must be A or D. If it's not, the answer must be B, C, or E. Making that one split early — before you even look at the other clue — keeps the five options from blurring together.

Is the number x positive?   (1) x² = 4x   (2) x is less than 10

(1): factor → x(x − 4) = 0 → x = 0 or 4. "No" or "yes," so not enough. (2): many values, not enough. Combine them: x is 0 or 4 — and both are less than 10, so clue (2) eliminates neither. You're still stuck between 0 ("no") and 4 ("yes") → E. Combining looked promising but changed nothing.

05
Two kinds of questions

DS questions come in two flavors, and "enough" means something slightly different in each.

"What is the value?" questions ("What is x?", "How many employees?") → a clue is enough only if it pins down exactly one number.

"Yes or no?" questions ("Is x positive?", "Is n even?") → a clue is enough if it gives one consistent answer (always yes, or always no) — even if you never learn the exact number.

Here's the subtlety beginners miss: on a yes/no question, a clue that always gives "no" is enough — because the question is answered (the answer is "no, for certain"). What makes a clue not enough is when it gives "yes" in one case and "no" in another. Don't throw away a yes/no clue just because you couldn't find the exact value — you didn't need it.

"Enough" means the question is answered — not that the answer is "yes." If every situation the clue allows gives "no," then you can answer with confidence: "no, definitely." That's a settled, single answer to a yes/no question, which is the whole bar. Beginners lose points by discarding such clues because they "couldn't find the number" — but a yes/no question never asked for the number.

06
Testing cases

When you're not sure whether a clue is enough, don't just stare at it — test numbers. Plug in a value that fits the clue, note the answer, then try to find a second value that also fits but gives a different answer. If you find one, the clue is not enough (you just broke it).

Test the troublemakers, not random numbers

Some numbers are far more likely to expose a hidden second case. Reach for these first:

  • 0 — breaks assumptions about sign and about products
  • 1 — behaves unusually with multiplication and powers
  • a negative number — breaks "everything is positive" assumptions
  • a fraction between 0 and 1 — breaks "multiplying makes things bigger" assumptions

Is x × y greater than 0?   Clue: x + y is greater than 0.

Try x = 3, y = 1: fits the clue (sum is 4), and x × y = 3 (greater than 0) → "yes." Now try to break it: x = 5, y = −1: still fits (sum is 4), but x × y = −5 (not greater than 0) → "no." Two answers from one clue → not enough. The deliberately mixed-sign case broke it on the second try.

Break fast, then confirm with logic

Two numbers that disagree prove "not enough" instantly — stop there. Proving a clue is enough is harder (you can't test every number), so confirm those with reasoning. Use number-testing to break clues; use logic to confirm the ones that survive.

07
Number facts worth memorizing

Finally, a short reference of the number facts the test leans on most. Keep these handy — they're the raw material the traps above are built from.

Zero — the most weaponized number
  • Zero is an integer, and it counts as even.
  • Zero is neither positive nor negative — so for "is x positive?", x = 0 means "no," and it's a legal value unless the problem rules it out.
  • You cannot divide by zero — which is exactly why dividing an equation by a variable is dangerous.
Sign and powers

Squaring or taking absolute value erases the sign: x² = 9 means x = 3 or −3. But odd powers keep the sign: if x³ is positive, x is positive. This even-vs-odd difference is a constant DS edge.

Even and odd (parity)
  • even ± even = even;   odd ± odd = even;   even ± odd = odd
  • even × anything = even;   odd × odd = odd
  • n(n + 1) — two consecutive integers — is always even, because one of any two neighbors is even.
Integer vs. not

If a problem doesn't say "integer," fractions and decimals are allowed — and they break many clues. Always check whether you're restricted to integers before assuming it.

Try it · DS format
Is x positive?
(1) x³ is greater than 0
(2) x² is greater than 4

Clue (1) x³ > 0: an odd power keeps the sign, so x³ positive means x is positive — always "yes" → enough. Clue (2) x² > 4: an even power hides the sign, so x could be 3 (yes) or −3 (no) → not enough. One clue works, the other doesn't → A. This is the even-vs-odd-power edge in action.

The DS habit
  • Read precisely: is this a "what is the value?" or a "yes or no?" question?
  • Clue (1) alone — try to break it with a second case. Enough or not?
  • Clue (2) alone — same, judged on its own.
  • Combine only if needed — does clue (2) rule out clue (1)'s leftover cases?
  • Watch the traps: dividing by a variable, zero, negatives, fractions, even powers hiding the sign.
  • Use AD / BCE to keep the five options organized, and choose.

Internalize this routine and Data Sufficiency stops being a guessing game — it becomes the disciplined judgment the Executive Assessment is built to reward.

This is a preview of the DS section

The full theory guide covers Data Sufficiency, Problem Solving, Critical Reasoning, Sentence Correction, and Integrated Reasoning — each with interactive practice — and is included with every EA Prep Pro plan.