Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
First, figure out how many possible five-digit codes there are in general. Since there are ten digits (0 through 9) and five different positions, the number of possible codes is 10 × 10 × 10 × 10 × 10, or 105 = 100,000.
Now, what must be true about five-digit codes that could be interpreted correctly either way (left to right or right to left)? These codes must be palindromes—they must be the same forward and backwards. If you represent each digit with a letter, then the code must be of the form xyzyx. The first and last digits must be the same (x), and the second and fourth digits must be the same (y). The middle digit can be anything.
Since you now only can determine three digits independently, you only have 10 × 10 × 10, or 103 = 1,000 possible palindromic codes.
The chance of choosing such a code at random is 1,000/100,000, or 1/100.
The correct answer is B.