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CAT Questions – Numbers (divisibility) with VIDEO Solution

QUESTION 1
If 23!=25852016738abc976640000, where a, b, and c are digits, then find the sum a+b+c?
  1. 2
  2. 20
  3. 11
  4. None of these
Option: 2
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QUESTION 2
Let n=abc be a three digit number which is NOT divisible by 10. If the sum of the numbers abc and cba is divisible by 11, find the largest value of n.
Answer: 979
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QUESTION 3
Let n be a positive integer and n<100. If ${n^{200}} - 1$ is divisible by ${\left( {n - 1} \right)^2}$, what could be the largest possible value of n.
Answer: 51
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QUESTION 4
If n is a positive integer, find the smallest value of n such that $n!$ is divisible by ${{n}^{4}}-5{{n}^{2}}+4$
Answer: 13
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QUESTION 5
18222 + 12222 – 5222 – 1 is divisible by
  1. 189
  2. 221
  3. 289
  4. None of these
Option: 2
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