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GATE 2017 CE (CE2) – Question 4

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

Find x when $81\times(16/25)^{x+2}\div(3/5)^{2x+4}=144$.

  1. 1
  2. −1
  3. −2
  4. Cannot be determined

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Correct answer: (B) −1

Explanation

Collect the common exponent: $81(16/9)^{x+2}=144$. Dividing by 81 gives $(16/9)^{x+2}=16/9$. Since the base is positive and different from 1, $x+2=1$, hence $x=-1$ (B).