chetan2u wrote:
How many 6-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 12121.
A) 100
B) 610
C) 729
D) 900
E) 1000
OA after 3 days
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
--------------------------
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:
http://www.gmatprepnow.com/module/gmat-counting?id=775Cheers,
Brent
Why were the last two digits tied to one possible value? why the sudden change of rule?
I know you guys are right. you are pro. but I need to get it. I'm the learner. pls elucidate.