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A palindrome is a number that reads the same forward and backward. For example - 1331. How many 4-digit palindromes can be formed using two of the five digits - 1, 3, 5, 7, and 9?
- a)10
- b)20
- c)30
- d)40
- e)60
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A palindrome is a number that reads the same forward and backward. For...
Understanding 4-Digit Palindromes
A 4-digit palindrome has the form ABBA, where A and B are digits. The first and last digits (A) must be the same, and the second and third digits (B) must also be the same.
Choosing Digits from the Set
We are provided with five digits: 1, 3, 5, 7, and 9. We need to form our palindrome using two of these digits.
Step 1: Selecting the Digits
1. **Choose A (the first and last digit)**
- A can be any of the five digits: 1, 3, 5, 7, 9.
- There are 5 options for A.
2. **Choose B (the second and third digit)**
- B can also be any of the five digits: 1, 3, 5, 7, 9.
- There are 5 options for B.
Step 2: Combining the Choices
- When forming the palindrome ABBA, the selections for A and B are independent of each other.
- Therefore, the total number of combinations can be calculated as follows:
- Total combinations = (Choices for A) × (Choices for B)
- Total combinations = 5 × 5 = 25.
Step 3: Accounting for Unique Combinations
However, since the problem specifies using **two of the five digits**, we need to consider the unique pairs of digits.
1. **Select 2 distinct digits** from the 5 available:
- The number of ways to choose 2 digits from 5 is given by the combination formula \(C(n, k)\):
- \(C(5, 2) = \frac{5!}{2!(5-2)!} = 10\).
2. **Forming Palindromes**:
- For each unique pair of digits (A, B), there are 2 configurations: A can be the first digit or B can be the first digit.
- Thus, each pair forms 2 unique palindromes.
Final Calculation
- Total 4-digit palindromes = Unique pairs × 2 configurations
- Total 4-digit palindromes = 10 × 2 = 20.
Thus, the correct answer is option **B) 20**.
A 4-digit palindrome has the form ABBA, where A and B are digits. The first and last digits (A) must be the same, and the second and third digits (B) must also be the same.
Choosing Digits from the Set
We are provided with five digits: 1, 3, 5, 7, and 9. We need to form our palindrome using two of these digits.
Step 1: Selecting the Digits
1. **Choose A (the first and last digit)**
- A can be any of the five digits: 1, 3, 5, 7, 9.
- There are 5 options for A.
2. **Choose B (the second and third digit)**
- B can also be any of the five digits: 1, 3, 5, 7, 9.
- There are 5 options for B.
Step 2: Combining the Choices
- When forming the palindrome ABBA, the selections for A and B are independent of each other.
- Therefore, the total number of combinations can be calculated as follows:
- Total combinations = (Choices for A) × (Choices for B)
- Total combinations = 5 × 5 = 25.
Step 3: Accounting for Unique Combinations
However, since the problem specifies using **two of the five digits**, we need to consider the unique pairs of digits.
1. **Select 2 distinct digits** from the 5 available:
- The number of ways to choose 2 digits from 5 is given by the combination formula \(C(n, k)\):
- \(C(5, 2) = \frac{5!}{2!(5-2)!} = 10\).
2. **Forming Palindromes**:
- For each unique pair of digits (A, B), there are 2 configurations: A can be the first digit or B can be the first digit.
- Thus, each pair forms 2 unique palindromes.
Final Calculation
- Total 4-digit palindromes = Unique pairs × 2 configurations
- Total 4-digit palindromes = 10 × 2 = 20.
Thus, the correct answer is option **B) 20**.
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A palindrome is a number that reads the same forward and backward. For example - 1331. How many 4-digit palindromes can be formed using two of the five digits - 1, 3, 5, 7, and 9?a)10b)20c)30d)40e)60Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A palindrome is a number that reads the same forward and backward. For example - 1331. How many 4-digit palindromes can be formed using two of the five digits - 1, 3, 5, 7, and 9?a)10b)20c)30d)40e)60Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A palindrome is a number that reads the same forward and backward. For example - 1331. How many 4-digit palindromes can be formed using two of the five digits - 1, 3, 5, 7, and 9?a)10b)20c)30d)40e)60Correct answer is option 'B'. Can you explain this answer?.
A palindrome is a number that reads the same forward and backward. For example - 1331. How many 4-digit palindromes can be formed using two of the five digits - 1, 3, 5, 7, and 9?a)10b)20c)30d)40e)60Correct answer is option 'B'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A palindrome is a number that reads the same forward and backward. For example - 1331. How many 4-digit palindromes can be formed using two of the five digits - 1, 3, 5, 7, and 9?a)10b)20c)30d)40e)60Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A palindrome is a number that reads the same forward and backward. For example - 1331. How many 4-digit palindromes can be formed using two of the five digits - 1, 3, 5, 7, and 9?a)10b)20c)30d)40e)60Correct answer is option 'B'. Can you explain this answer?.
Solutions for A palindrome is a number that reads the same forward and backward. For example - 1331. How many 4-digit palindromes can be formed using two of the five digits - 1, 3, 5, 7, and 9?a)10b)20c)30d)40e)60Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
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