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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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62% (01:13) correct 38% (01:43) wrong based on 255 sessions
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How many 6digits 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
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Re: A Palindromic number reads the same forward and backward,
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Updated on: 07 Nov 2016, 05:38
chetan2u wrote: How many 6digits 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 hundredthousands 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 tenthousands 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 tenthousands 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 hundredthousands 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 6digit 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/gmatcounting?id=775Cheers, Brent
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Originally posted by GMATPrepNow on 03 Mar 2016, 14:08.
Last edited by GMATPrepNow on 07 Nov 2016, 05:38, edited 2 times in total.




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Re: A Palindromic number reads the same forward and backward,
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03 Mar 2016, 10:46
The hundredthousand'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, tenthousand'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..
Kr, Ron



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Re: A Palindromic number reads the same forward and backward,
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05 Mar 2016, 11:21
trying to grab this.. Stem needs to get clearer to me. Palindromic numbers read the same way forward and backward. as in 100001 131313 555555 770077
They all read the same forward or backward. It didn't state it must be the alternating example given in the stem.
100001 200002 . . 900009 nine
101101 201102 301102 . . .
My!! There shud be a formulae for this. Gmatprepnow solution above isn't quite clear to me either. Thanks
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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 6digits 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 tenthousands 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 tenthousands 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 5digit palindrome) in (9)(10)(10)(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/gmatcounting?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.



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A Palindromic number reads the same forward and backward,
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Updated on: 18 Aug 2019, 05:19
Nezdem wrote: GMATPrepNow wrote: chetan2u wrote: How many 6digits 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 hundredthousands 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 tenthousands 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 tenthousands 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 hundredthousands 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 6digit 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/gmatcounting?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. 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. I hope that helps. Cheers, Brent
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Originally posted by GMATPrepNow on 07 Nov 2016, 05:38.
Last edited by GMATPrepNow on 18 Aug 2019, 05:19, edited 1 time in total.



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A Palindromic number reads the same forward and backward,
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18 Aug 2019, 00:21
GMATPrepNow wrote: Nezdem wrote: GMATPrepNow wrote: Take the task of building palindromes and break it into stages. Stage 1: Select the hundredthousands 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 tenthousands 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 tenthousands 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 hundredthousands 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 6digit 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/gmatcounting?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. 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 356 652. 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 6digit 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 6digit integers > A B C C B A e.g. 123321 In case of 5digit integers > A B C B A e.g. 18981 In case of 4digit integers > A B B A e.g. 9889 In case of 3digit integers > A B A e.g. 989 Warm Regards, Pritish
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Re: A Palindromic number reads the same forward and backward,
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18 Aug 2019, 00:36
chetan2u wrote: How many 6digits 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 6digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 12121. Let the 6digit Palindromic number be xyzzyx Options for x = 9 Options for y = 10 Options for z = 10 Number of 6digit 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, 05:20
Pritishd wrote: Hi Brent,
Should the number in the highlighted portion not be 356653?
You're absolutely right. Lazy error on my part. I've edited my response. Cheers and thanks, Brent
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Re: A Palindromic number reads the same forward and backward,
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18 Aug 2019, 08:32
1st digit can have 9 options. 2nd digit 10. 3rd digit also 10. 6th digit = 1st digit = 1 option 5th Digit = 2nd digit = 1 option 4th digit = 3rd digit = 1 option.
Multiply all cases = 9*10*10*1*1*1 = 900



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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 6digits 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




Re: A Palindromic number reads the same forward and backward,
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