Bunuel wrote:
paskorntt wrote:
A palindrome is a number that reads the same forward and backward. For example. 2442 and 111 are palindromes. If 5-digit palindromes are formed using one or more of the digits, 1, 2, 3, how many such palindromes are possible?
A) 12
B) 15
C) 18
D) 24
E) 27
XYZYX
X can be 1, 2, or 3, thus 3 options.
Y can be 1, 2, or 3, thus 3 options.
Z can be 1, 2, or 3, thus 3 options.
Total 3^3=27.
Answer: E.
Similar questions to practice:
https://gmatclub.com/forum/a-palindrome- ... 29898.htmlhttps://gmatclub.com/forum/a-palindrome- ... 59265.htmlHope this helps.
Hi experts
Bunuel IanStewartThis question took me about three minutes in my practice exam, but I still got it incorrectly.
I was not familiar with palindrome, and I did not see that the number of combinations could be obtained by 3*3*3. Instead, I tried to count the possibilities manually. (The answer choices range between 12 to 27, which is not too many to count. It is not the most efficient way, but I had no other ways then.) I failed because I only thought of three types of arrangements, AAAAA, ABCBA and ABBBA, ignoring other two, AABAA and ABABA.
I checked the solutions in this thread (they are smart) and practiced other two similar palindrome questions.
I hope to confirm two issues:
1. When a palindrome has an even number of digits, we only need to care about the first half. When the palindrome has an odd number of digits, we care about the first half and the middle one.
For example, for the 4-digit palindrome XYZW, we only chose numbers for X and Y, since Z and W just copy the preceding digits respectively.
For the 5-digit palindrome ABCDE, we only chose numbers for A,B and C, letting D and E copy A and B.
2. These palindrome questions may vary in constraints, such as "the number must be odd," "no digits can be repeated," "the digits could only be 1, 2 and 3." We just tackle each questions differently.
Thank you.