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Algebraic Simplification

CAT 1995 Slot 1 · Quantitative Ability · Easy · Algebra

This is an easy Quantitative Ability question from the CAT 1995 Slot 1 paper. It tests Algebra. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Find the value of: 553+453552−55×45+452\frac{55^3 + 45^3}{55^2 - 55 \times 45 + 45^2}

  1. A.

    100

  2. B.

    105

  3. C.

    125

  4. D.

    75

Answer

A

Explanation

Using the algebraic identity a3+b3=(a+b)(a2−ab+b2)a^3 + b^3 = (a + b)(a^2 - ab + b^2): a3+b3a2−ab+b2=a+b\frac{a^3 + b^3}{a^2 - ab + b^2} = a + b Here a=55a = 55 and b=45b = 45, so the value is 55+45=10055 + 45 = 100.

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