GATE 2017 CS (CS2) – Question 8

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice

X is a 30-digit positive integer starting with digits 4 then 7. How many digits does X³ have?

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Correct answer: (A) 90

Explanation

The prefix gives $4.7\times10^{29}\le X<4.8\times10^{29}$. Cubing yields $1.03823\times10^{89}\le X^3<1.10592\times10^{89}$. These values are at least 10⁸⁹ and below 10⁹⁰, hence have 90 digits, A.

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