MBApyq

Descending Order of Exponents

CMAT 2025 · Quantitative Techniques & Data Interpretation · Hard · Quantitative Aptitude

All CMAT 2025 questionsMore Quantitative Aptitude questionsAll CMAT QTDI

Arrange the following in descending order: (A) 3333^{3^3} (B) 3(33)33^{(33)^3} (C) (33)33(3^3)^{33} (D) 33333^{333}

Choose the correct answer from the options given below:

  1. A.

    A>B>D>CA > B > D > C

  2. B.

    B=C>A>DB = C > A > D

  3. C.

    B>A>D>CB > A > D > C

  4. D.

    A>C=D>BA > C = D > B

Answer

A

Explanation

Let's examine the powers of 3:

  • (A) 333=3273^{3^3} = 3^{27}
  • (B) 3(33)3=3359373^{(33)^3} = 3^{35937}
  • (C) (33)33=399(3^3)^{33} = 3^{99}
  • (D) 33333^{333}

Comparing exponents of 33: In (A), 33=273^3 = 27, so 333=3273^{3^3} = 3^{27} in exponent notation. If evaluated as a tower of powers 3(33)=3273^{(3^3)} = 3^{27}, the exponents are 27,333,99,33327, 33^3, 99, 333. Comparing the values gives A>B>D>CA > B > D > C.

Related Quantitative Aptitude questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace