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A Palindromic number reads the same forward and backward,
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03 Mar 2016, 09:08
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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
Re: A Palindromic number reads the same forward and backward,
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Updated on: 07 Nov 2016, 05:38
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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)
Re: A Palindromic number reads the same forward and backward,
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03 Mar 2016, 10:46
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The hundred-thousand's digit won't be zero or else it's no longer a 6 digit integer (you could form a palindromic number with five digits though). The subesquent two digits, ten-thousand's and thousand's digit, can be 10 different numbers each, zero - nine. Thus, \(9 * 10 * 10 * 1 * 1 * 1 = 900\) Answer D
Plus, it won't be 1,000 since the first three digits can't be more than 999 and the first three must be the same as the last three..
Re: A Palindromic number reads the same forward and backward,
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05 Mar 2016, 11:30
GMATPrepNow wrote:
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 ten-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 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 hundreds 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 tens digit This digit must be the SAME as the thousands digit (which we already chose in stage 2) So, we can complete this stage in 1 way.
Stage 5: Select the units digit This digit must be the SAME as the ten-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 5 stages (and thus build a 5-digit palindrome) in (9)(10)(10)(1)(1) ways (= 900 ways)
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.
A Palindromic number reads the same forward and backward,
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Updated on: 18 Aug 2019, 05:19
Top Contributor
Nezdem wrote:
GMATPrepNow wrote:
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)
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.
The basic idea is that, once we have selected the first 3 digits of the number, the last 3 digits automatically follow. For example, if the first 3 digits are 356---, then (to be a palindrome), the last 3 digits must be ---653, so we get the number 356653. Likewise, if the first 3 digits are 197---, then (to be a palindrome), the last 3 digits must be ---791, so we get the number 197791.
A Palindromic number reads the same forward and backward,
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18 Aug 2019, 00:21
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GMATPrepNow wrote:
Nezdem wrote:
GMATPrepNow wrote:
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)
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.
The basic idea is that, once we have selected the first 3 digits of the number, the last 3 digits automatically follow. For example, if the first 3 digits are 356---, then (to be a palindrome), the last 3 digits must be ---652, so we get the number 356652. Likewise, if the first 3 digits are 197---, then (to be a palindrome), the last 3 digits must be ---791, so we get the number 197791.
I hope that helps.
Cheers, Brent
Hi Brent,
Should the number in the highlighted portion not be 356653?
Also, may be the example used in the question stem does not provide complete clarity into the concept of Palindrome numbers. I was trying hard to replicate a 6-digit number that has first and second digits repeated in the remaining 4 positions. But now I understand from Brent's solution that Palindromes are of the form:
In case of 6-digit integers -> A B C C B A e.g. 123321 In case of 5-digit integers -> A B C B A e.g. 18981 In case of 4-digit integers -> A B B A e.g. 9889 In case of 3-digit integers -> A B A e.g. 989
Re: A Palindromic number reads the same forward and backward,
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18 Aug 2019, 00:36
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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
\(Asked:\) How many 6-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 12121.
Let the 6-digit Palindromic number be xyzzyx
Options for x = 9 Options for y = 10 Options for z = 10
Number of 6-digit Palindromic numbers = 9*10*10 = 900
IMO D
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Re: A Palindromic number reads the same forward and backward,
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18 Aug 2019, 10:18
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
this pallindrome would exists as ; xyzzyx ; so x= 9 ; y=10 & z= 10 total pairs ; 9*10*10 ; 900 IMO D
gmatclubot
Re: A Palindromic number reads the same forward and backward,
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18 Aug 2019, 10:18
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62% (01:13) correct 
