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Select All That Apply
Reasoning

Master the GRE's trickiest question format: where one, some, or all choices can be correct, and partial credit does not exist.

GRE Quantitative

What Is Select All That Apply?

On the GRE Quantitative section, Select All That Apply (SATA) questions present a prompt and a list of answer choices. You must identify every correct choice: there may be one correct answer, several, or even all of them.

Why SATA Is Different

Standard MCQ
Exactly one answer is correct. You can use elimination to narrow choices to a single option.
SATA
Any number of answers can be correct. You must evaluate every choice independently against the prompt.

The SATA Mindset

Question Prompt Evaluate Each Choice Independently A: True ✓ B: False ✕ C: True ✓ Select A and C only

Do not ask "Which one is correct?" Instead, ask "Is this particular choice correct?" for every option, one at a time.

The Core Rule of SATA

This means you often need to test boundary cases. A value that works for one example but fails for another is not a valid answer. The GRE rewards exhaustive checking, not intuition.

Must Be True vs. Could Be True

Must Be True
True in every valid scenario. No counterexample exists. This is what SATA typically asks for.
Could Be True
True in at least one scenario but not necessarily all. Not sufficient for SATA unless the question says "could."

GRE Quant Question Formats

Standard MCQ SATA Numeric Entry
Correct answers Exactly 1 1 or more Exactly 1
Partial credit N/A No N/A
Elimination useful? Very Limited No
Key strategy Eliminate wrong Test each choice Solve directly

How to Solve SATA Problems

1
Read the prompt carefully. Identify whether it asks "must be true," "could be true," or "which values satisfy."
2
Isolate each choice. Cover the others mentally. Ask: "Is this one true given the constraints?"
3
Test with values. Plug in boundary values, extremes, negatives, zero, and fractions to stress-test each choice.
4
Look for counterexamples. One valid counterexample disqualifies a "must be true" choice instantly.
5
Select all survivors. Only check the choices that passed every test. Then move on.

Example 1: Integer Properties

A
Always true. \(\text{Even} \times \text{Even} = \text{Even}\). ✓
B
Always true. \(\text{Even} + 1 = \text{Odd}\). ✓
C
Not always. If \( x = 2 \), then \( \frac{x}{2} = 1 \), which is odd. Counterexample found. ✕
D
Always true. \( x^2 \) is even, so \( x^2 - 1 \) is odd. ✓

Example 2: Inequality Reasoning

-3 0 3 x ranges here (open)
\( x^2 \) ranges: \( [0, 9) \)
0 9

Example 3: Divisibility Stress Test

Key insight: \( n(n^2 - 1) = (n-1) \cdot n \cdot (n+1) \), which is the product of three consecutive integers.

1
Three consecutive integers always include at least one multiple of 2 and at least one multiple of 3.
2
So the product is always divisible by \( 2 \), \( 3 \), and \( 6 \).
3
But is it always divisible by \( 12 \)? Try \( n = 2 \): \( 1 \cdot 2 \cdot 3 = 6 \). Since \( 6 \div 12 \) is not an integer: counterexample.

The Power of Boundary Testing

For SATA questions, always test these critical values against each choice:

\( 0 \) and \( 1 \)
The most common counterexample generators. Many "always true" claims fail here.
Negatives
Test \( -1 \), \( -\frac{1}{2} \). Signs flip, inequalities reverse, exponents behave differently.
Fractions
Values like \( \frac{1}{2} \) break assumptions: squaring shrinks them instead of growing.

When to Use Algebra

Plugging in values can disprove a statement quickly, but to confirm something must always be true, you often need algebraic proof.

Plug-In Values
Best for: eliminating wrong choices. One counterexample is enough to reject a "must be true" choice.
Algebraic Proof
Best for: confirming correct choices. Rewrite expressions, factor, apply known identities to show a statement always holds.

Common Mistakes

✕ Selecting Too Few
Stopping after finding one correct answer, assuming it's a standard MCQ. Always check every choice.
✕ Selecting Too Many
Choosing answers that could be true when the question asks what must be true. Read the wording.
✕ Testing Only Easy Values
Trying \( n = 2 \) and \( n = 4 \) but forgetting edge cases like \( n = 1 \), \( n = 0 \), or fractions.

SATA Strategy Summary

Step Action Purpose
1 Read the prompt wording "Must" vs. "could" vs. "which values"
2 Isolate each choice Treat as independent true/false
3 Plug in boundary values Find counterexamples to eliminate
4 Confirm algebraically Verify "must be true" choices
5 Select exact correct set No partial credit: precision matters

Question 1 of 5

If \( x \) is a negative number, which of the following must be positive? (In a real SATA, you would select all that apply. Here, pick the answer that lists the correct set.)

Question 2 of 5

If \( n \) is a positive integer, which of the following must be odd? (Pick the answer listing the complete correct set.)

Question 3 of 5

If \( 0 < a < 1 \), which of the following must be true? (Pick the answer listing the complete correct set.)

Question 4 of 5

What is the most important first step when encountering a SATA question on the GRE?

Question 5 of 5

If \( x \) and \( y \) are integers and \( xy = 12 \), which of the following could be the value of \( x + y \)? (Pick the answer listing the complete correct set.)