If A = log 1 + log 2 + log 3 + .......... log n and B = log ((n - 1)!), which of the following must be true? n is a natural number.
  • a)
    A > B
  • b)
    A < B
  • c)
    A = B
  • d)
    A > B
  • e)
    A < B
Correct answer is option 'D'. Can you explain this answer?
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CAT Question

By Memta Devi · Feb 28, 2020 ·CAT
3 Answers
Lakshya Gupta answered Feb 28, 2020
A=logn! which is greater then B

Krishna answered Apr 02, 2020
A = log 1 + log 2 + log 3 + ..........+ log n = log (1 * 2 * 3 x 4 x ... x n) = log(n!)
B = log ((n - 1)!)
Since n is a natural number,
for any n > 1, A > B
For n = 1, A = log (1!) = log 1 and B = log (0!) = log 1
i.e. A = B
Thus, A > B
Hence, option 4.

Akash Singh answered Mar 04, 2020
Log xy = log x + log y
A = log1 + log 2 .... + log n
A = log(1.2.3....n)
A = log(n!)
A = log(n.(n-1)!)
A = log n + log ((n-1)!)
A = log n + B

Since log n >= 0
A >= B

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