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DIRECTIONS for the question: Solve the following question and mark the best possible option.
Q. In a company XYZ, the employee Identification is a 3-digit number (first digit is non-zero). However no two employees can have Identification that are identical when written in reverse order (456 and 654 are identical and hence only one of them can exist). What is the maximum number of employees who are using this coding system?
  • a)
    435
  • b)
    495
  • c)
    540
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
DIRECTIONS for the question:Solve the following question and mark the ...
Total number of 3 digit numbers are 900.
Three digit numbers that are symmetrical will have the same first and last digit. This digit can be selected in 9 ways. The second digit can be selected in 10 ways. So Number of symmetrical 3 digit numbers= 9 x 10 = 90
These 90 IDs will not have a corresponding number when written in reverse order.
So consider all of these 90 numbers.
Now, numbers ending with a 0 will also not have a 3 digit number when written in reverse order.
No. of such numbers = 9 x 10 = 90.
So consider all of these 90 numbers.
Rest of the (900-180)=720 numbers can be divided into 2 groups of 360 numbers each, where corresponding pairs of numbers will be identical when written in reverse order.
Hence, consider only 360 of these numbers.
So required number = 90 + 90 +360 = 540.
Hence (C).
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DIRECTIONS for the question:Solve the following question and mark the best possible option.Q. In a company XYZ, the employee Identification is a 3-digit number (first digit is non-zero). However no two employees can have Identification that are identical when written in reverse order (456 and 654 are identical and hence only one of them can exist). What is the maximum number of employees who are using this coding system?a)435b)495c)540d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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