Quantitative Aptitude Ques 1509

Question: If $ {{(2000)}^{10}}=1.024\times 10^{k}, $ then the value of k is

Options:

A) 33

B) 30

C) 34

D) 31

Show Answer

Answer:

Correct Answer: A

Solution:

  • (a) $ {{(2000)}^{10}}=1024\times 10^{k} $

$ \Rightarrow $ $ {{(2\times 1000)}^{10}}=1.024\times 10^{k} $
$ \Rightarrow $ $ {{(2\times 10^{3})}^{10}}=\frac{1024}{1000}\times 10^{k} $

$ \Rightarrow $ $ 2^{10}\times 10^{30}=1024\times {10^{k-3}} $ $ [\because {{(PQ)}^{n}}=P^{n}\times Q^{n}] $

$ \Rightarrow $ $ 2^{10}\times 10^{30}=2^{10}\times {10^{k-3}} $ On comparing the powers, we get $ 30=k-3 $
$ \Rightarrow $ $ k=33 $

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