A Palindromic number reads the same forward and backward,

Take the task of building palindromes and break it into stages.

Stage 1: Select the hundred-thousands digit
We can choose 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 1 in 9 ways

Stage 2: Select the ten-thousands digit
We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 2 in 10 ways

Stage 3: Select the thousands digit
We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 2 in 10 ways

IMPORTANT: At this point, the remaining digits are already locked in.

Stage 4: Select the hundreds digit
This digit must be the SAME as the thousands digit (which we already chose in stage 3)
So, we can complete this stage in 1 way.

Stage 5: Select the tens digit
This digit must be the SAME as the ten-thousands digit (which we already chose in stage 2)
So, we can complete this stage in 1 way.

Stage 6: Select the units digit
This digit must be the SAME as the hundred-thousands digit (which we already chose in stage 1)
So, we can complete this stage in 1 way.
By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus build a 6-digit palindrome) in (9)(10)(10)(1)(1)(1) ways (= 900 ways)

Answer: D
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Note: the FCP can be used to solve the majority of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775

Cheers,
Brent