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Mathematical Reasoning Arithmetic and Number Sense Flashcards

6 cards from real GED practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. What is the value of −3² + (−3)²?

    Answer: 0

    These two expressions look similar but follow different rules. −3² means the negative sign is applied AFTER squaring: −(3²) = −9. But (−3)² means the negative is inside the parentheses and gets squared too: (−3)(−3) = +9. So −9 + 9 = 0.

  2. A store raises the price of a jacket by 20%, then one month later reduces the new price by 20%. Compared to the original price, the final price is:

    Answer: 4% lower than the original

    Start with $100. After a 20% increase: $100 × 1.20 = $120. After a 20% decrease on the NEW price: $120 × 0.80 = $96. The final price is $96, which is $4 less than $100 — a 4% decrease. The percentages don't cancel because they apply to different base amounts.

  3. What is the greatest common factor (GCF) of 252 and 180?

    Answer: 36

    Use prime factorization. 252 = 2² × 3² × 7. 180 = 2² × 3² × 5. The GCF is the product of the common prime factors at their lowest powers: 2² × 3² = 4 × 9 = 36. The factors 5 and 7 are not shared, so they are excluded.

  4. Which of the following expressions results in an irrational number?

    Answer: √3 + √12

    √4 + √9 = 2 + 3 = 5 (rational). √2 × √8 = √16 = 4 (rational). π − (π − 1) = 1 (rational). But √3 + √12 = √3 + 2√3 = 3√3, which remains irrational because √3 has no exact decimal form. The key is that adding two irrational numbers with the same radical component doesn't make them rational.

  5. On a number line, point A is at −7 and point B is at 4. Point C is located exactly 3/5 of the way from A to B. What is the coordinate of point C?

    Answer: −0.4

    The total distance from A to B is 4 − (−7) = 11 units. Moving 3/5 of the way: (3/5) × 11 = 6.6 units from point A. Starting at −7 and moving 6.6 units toward B: −7 + 6.6 = −0.4. Point C is at −0.4.

  6. Simplify: (3.6 × 10⁴) − (8.2 × 10³)

    Answer: 2.78 × 10⁴

    To subtract numbers in scientific notation, first express them with the same exponent. Convert 3.6 × 10⁴ to 36 × 10³. Now subtract: (36 × 10³) − (8.2 × 10³) = 27.8 × 10³. Convert back to proper scientific notation: 2.78 × 10⁴. A common error is subtracting the exponents or failing to realign the powers of ten.