Today’s paper

Algebra

Ten quantitative aptitude questions, each marked as you answer.

  1. If x + 1⁄x = 8, what is x² + 1⁄x²?
    Answer and working

    Answer

    Square both sides: x² + 2 + 1/x² = 64, so x² + 1/x² = 62.

  2. Solve for x: 5x + 5 = 3x + 31
    Answer and working

    Answer

    5x − 3x = 31 − 5, so 2x = 26 and x = 26 ÷ 2. x = 13.

  3. If x + 1⁄x = 3, what is x² + 1⁄x²?
    Answer and working

    Answer

    Square both sides: x² + 2 + 1/x² = 9, so x² + 1/x² = 7.

  4. If x + 1⁄x = 9, what is x³ + 1⁄x³?
    Answer and working

    Answer

    x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 729 − 27 = 702.

  5. If a − b = 1 and ab = 56, what is a³ − b³?
    Answer and working

    Answer

    a³ − b³ = (a − b)³ + 3ab(a − b) = 1 + 168 = 169.

  6. If x + 1⁄x = 6, what is x³ + 1⁄x³?
    Answer and working

    Answer

    x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 216 − 18 = 198.

  7. If x + 1⁄x = 6, what is x³ + 1⁄x³?
    Answer and working

    Answer

    x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 216 − 18 = 198.

  8. If a + b = 16 and ab = 60, what is a² + b²?
    Answer and working

    Answer

    a² + b² = (a + b)² − 2ab = 256 − 120 = 136.

  9. If x + 1⁄x = 9, what is x² + 1⁄x²?
    Answer and working

    Answer

    Square both sides: x² + 2 + 1/x² = 81, so x² + 1/x² = 79.

  10. If x + 1⁄x = 6, what is x³ + 1⁄x³?
    Answer and working

    Answer

    x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 216 − 18 = 198.

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More quantitative aptitude: Percentages, Profit, loss and discount, Simple interest, Compound interest, Ratio and proportion, Averages.