AAPL wrote: ↑Mon Feb 22, 2021 10:13 am

**GMAT Prep**
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. 28

E. 27

OA

E

Take the task of creating a 5-digit palindrome and break it into

stages.

Stage 1: Select a digit for the first position.

We can choose 1, 2 or 3, so we can complete stage 1 in

**3** ways

Stage 2: Select a digit for the second position.

We can choose 1, 2 or 3, so we can complete stage 2 in

**3** ways

Stage 3: Select a digit for the third position.

We can choose 1, 2 or 3, so we can complete stage 3 in

**3** ways

Stage 4: Select a digit for the fourth position.

**Important: In order to create a palindrome, the fourth digit must be the same as the second digit. **

For example, if the first three digits are 213, then fourth digit must be 1, and the fifth digit must be 2 to get the 5-digit palindrome 21312
Since the fourth digit must be the same as the second digit, we can complete stage 4 in

**1** way

Stage 5: Select a digit for the fifth position.

Since the fifth digit must be the same as the first digit, we can complete stage 5 in

**1** way

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus create a 5-digit palindrome) in

**(3)(3)(3)(1)(1)** ways (=

27 ways)

Answer: E