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How many five digit palindrome numbers (which reads same forwards as backward, e.g. 12321) are multiples of 5?
- a)81
- b)100
- c)200
- d)90
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
How many five digit palindrome numbers (which reads same forwards as ...
Solution:
To form a 5-digit palindrome number, we can take the following steps:
- Choose the first two digits (from 1 to 9)
- Choose the third digit (from 0 to 9)
- The fourth digit is the same as the second digit
- The fifth digit is the same as the first digit
So, the total number of 5-digit palindrome numbers is 9 x 10 x 10 = 900.
Now, to find the number of palindrome numbers that are multiples of 5, we need to check the last digit. The last digit can be 0 or 5.
Case 1: Last digit is 0
- The first digit can be any of the 9 digits (1 to 9)
- The second digit can be any of the 10 digits (0 to 9)
- The third digit can be any of the 10 digits (0 to 9)
- The fourth digit is the same as the second digit
- The fifth digit is the same as the first digit
So, the total number of palindrome numbers with last digit 0 is 9 x 10 x 10 = 900.
Case 2: Last digit is 5
- The first digit can be any of the 9 digits (1 to 9)
- The second digit can be any of the 10 digits (0 to 9)
- The third digit can be any of the 10 digits (0 to 9)
- The fourth digit is the same as the second digit
- The fifth digit is 5
So, the total number of palindrome numbers with last digit 5 is 9 x 10 = 90.
Therefore, the total number of palindrome numbers that are multiples of 5 is 900 + 90 = 990.
Answer: Option B (100) is incorrect.
To form a 5-digit palindrome number, we can take the following steps:
- Choose the first two digits (from 1 to 9)
- Choose the third digit (from 0 to 9)
- The fourth digit is the same as the second digit
- The fifth digit is the same as the first digit
So, the total number of 5-digit palindrome numbers is 9 x 10 x 10 = 900.
Now, to find the number of palindrome numbers that are multiples of 5, we need to check the last digit. The last digit can be 0 or 5.
Case 1: Last digit is 0
- The first digit can be any of the 9 digits (1 to 9)
- The second digit can be any of the 10 digits (0 to 9)
- The third digit can be any of the 10 digits (0 to 9)
- The fourth digit is the same as the second digit
- The fifth digit is the same as the first digit
So, the total number of palindrome numbers with last digit 0 is 9 x 10 x 10 = 900.
Case 2: Last digit is 5
- The first digit can be any of the 9 digits (1 to 9)
- The second digit can be any of the 10 digits (0 to 9)
- The third digit can be any of the 10 digits (0 to 9)
- The fourth digit is the same as the second digit
- The fifth digit is 5
So, the total number of palindrome numbers with last digit 5 is 9 x 10 = 90.
Therefore, the total number of palindrome numbers that are multiples of 5 is 900 + 90 = 990.
Answer: Option B (100) is incorrect.
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Community Answer
How many five digit palindrome numbers (which reads same forwards as ...
Let the 5 digit palindrome be abcba
If it is a multiple of 5, then a should be 5.
Hence, b and c can be any of the 10 digits from 0 to 9
Total number of five digit palindrome numbers which are multiple of 5 = 1 × 10C1 × 10C1 = 100
Hence, the correct option is (b).
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How many five digit palindrome numbers (which reads same forwards as backward, e.g. 12321) are multiples of 5?a)81b)100c)200d)90Correct answer is option 'B'. Can you explain this answer?
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