Source: Manhattan GMAT
Question: A palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?
Because we need odd number so we have only 1, 3, 5, 7, 9 = 5 choices for outer numbers(palindrome will have same outer and same inner numbers such as 1221)
inner numbers can be even or odd, so we have 10 choices.
So total number = 5*10*1*1 = 50
2. Now I want to form a palindrome for even, 4-digit numbers, my approach is:
again we have 5 even choices = 0, 2, 4, 6, 8, but we can not use 0 in first place so we only 4 choices.
for inner number again we have 10 choices.
so even 4-digit numbers: 4*10*1*1* = 40
Please correct me if I am wrong.
Question: A palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?
Because we need odd number so we have only 1, 3, 5, 7, 9 = 5 choices for outer numbers(palindrome will have same outer and same inner numbers such as 1221)
inner numbers can be even or odd, so we have 10 choices.
So total number = 5*10*1*1 = 50
2. Now I want to form a palindrome for even, 4-digit numbers, my approach is:
again we have 5 even choices = 0, 2, 4, 6, 8, but we can not use 0 in first place so we only 4 choices.
for inner number again we have 10 choices.
so even 4-digit numbers: 4*10*1*1* = 40
Please correct me if I am wrong.
