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Inequalities for a fraction between 0 and 1

CMAT 2018 · Quantitative Techniques & Data Interpretation · Easy · Algebra

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If aa is between 0 and 1, which of the following statements is (are) true? (i) a2−1>0a^2 - 1 > 0 (ii) a2+1>0a^2 + 1 > 0 (iii) a2−a>0a^2 - a > 0

  1. A.

    only (ii)

  2. B.

    (i) & (ii)

  3. C.

    (iii) only

  4. D.

    All three

Answer

A

Explanation

Since 0<a<10 < a < 1:

  1. 0<a2<1  ⟹  a2−1<00 < a^2 < 1 \implies a^2 - 1 < 0 (False)
  2. 1<a2+1<2  ⟹  a2+1>01 < a^2 + 1 < 2 \implies a^2 + 1 > 0 (True)
  3. a2<a  ⟹  a2−a<0a^2 < a \implies a^2 - a < 0 (False) Thus, only statement (ii) is true.

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