DIRECTIONS for the question: Solve the following question and mark the best possible option.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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DIRECTIONS for the question: Solve the following question and mark the best possible option.

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?

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DIRECTIONS for the question: Solve the following question and mark th...

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 th...

Solution:

To find the maximum number of employees using this coding system, we need to consider the restrictions given in the question.

Restrictions:
1. Employee identification is a 3-digit number (first digit is non-zero).
2. No two employees can have identical identifications when written in reverse order.

Step 1: Count the number of possible 3-digit numbers
Since the first digit cannot be zero, there are 9 options (1-9) for the first digit. For the second and third digits, any number from 0-9 can be chosen. Therefore, the total number of possible 3-digit numbers is 9 * 10 * 10 = 900.

Step 2: Eliminate numbers that are identical when written in reverse order
Let's analyze the possible reverse order scenarios for the 3-digit numbers:

1. If the first and third digits are the same, there are 9 options for the first digit and 10 options for the second digit. The third digit will be the same as the first digit. Therefore, there are 9 * 10 = 90 possibilities.

2. If the first and third digits are different, there are 9 options for the first digit, 10 options for the second digit, and 10 options for the third digit. However, the first and third digits cannot be the reverse of each other. This means that for each possibility, there is only one valid reverse possibility. Therefore, there are 9 * 10 * 10 / 2 = 450 possibilities.

Step 3: Calculate the maximum number of employees
To find the maximum number of employees, we need to subtract the eliminated possibilities from the total number of possible 3-digit numbers.

Maximum number of employees = Total number of possible 3-digit numbers - Eliminated possibilities
= 900 - (90 + 450)
= 900 - 540
= 360

Therefore, the maximum number of employees who can use this coding system is 360.

Correct answer: Option C) 540

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DIRECTIONS for the question: Solve the following question and mark the best possible option.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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