CAT Quantitative Ability Questions | CAT Permutation, Combination and Probability questions
CAT/1997
Question . 63
ABC is a three-digit number in which A > 0. The value of ABC is equal to the sum of the factorials of its three digits. What is the value of B?
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Explanatory Answer
Method of solving this CAT Quantitative Ability Question from Permutation, Combination and Probability question
(c) Seeing the options. Since 7! = 5040 and 9! = 362880 are four and 6 digit numbers respectively,
hence, B can’t be 7 or 9. 3 digits number will be of the form 100 A + 10 B + C.
∴ 100A + 10B + C = A! + B! + C!
Now by hit & trial method i.e., with B = 2 and B = 4 find which one is better.
Hence, B = 4, A = 1 , C = 5