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How many integers n greater than 10 and less than 100 a
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23 Nov 2018, 07:41
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68% (02:04) correct 32% (02:20) wrong based on 314 sessions
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How many integers n greater than 10 and less than 100 are such that, if the digits of n are reversed, the resulting integer is n+9 ? (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 Project PS Butler : Question #36 Subscribe to get Daily Email  Click Here  Subscribe via RSS  RSS
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How many integers n greater than 10 and less than 100 a
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23 Nov 2018, 10:51
Let A be tens digit & B be units digit \(X = 10A + B\) After reversing digits, \(X _{new}\) \(= 10B + A\) Difference between \(X\) and \(X_{new}\) is \(9\), so I get following equation \((10A + B)  (10B + A) = 9\) \(9A – 9B = 9\) \(9(AB) = 9\) \(AB = 1\) \(A = B+1\) Since units digit X is +1 more than tens digit, I get following numbers 12, 23, 34, 45, 56, 67, 78, 89 IMO: D




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Re: How many integers n greater than 10 and less than 100 a
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23 Nov 2018, 07:55
HKD1710 wrote: How many integers n greater than 10 and less than 100 are such that, if the digits of n are reversed, the resulting integer is n+9 ? (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 Project PS Butler : Question #36 Subscribe to get Daily Email  Click Here  Subscribe via RSS  RSSLet n=ab(as it is 2 digit number bcz >10 and less than 100) so reverse will be =ba now as per qsn reverseorgn=9(1) we know ab can be written as 10*a+b(54=10*5+4) ba=10*b+a now substituting in 1 10b+a10ab=9 9b9a=9 ba=1 so this condition will hold true only if diff of two digits is 1 so from 11 to 20 this is true only for 12(21=1) then from 2130 true for 23(32=1) make sure 21 is not valid as(12=1 not 1) ba=1 so this way each set of 10 numbers has 1 number for which ba=1 total we have 9 such sets (1120,2130,9199) so 8 such numbers bcz in 9199 we cant have this condition i.e 12,23,34,45,56,67,78,89, so 8 such numbers



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Re: How many integers n greater than 10 and less than 100 a
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09 Feb 2019, 20:26
The two digit number (assume) = 10a+b then by the given condition 10a+b = 10b+a+9 (digits are reversed and 9 added) => 9a  9b = 9 => a  b =1
we have following number between 10 and 100 which satisfy above condition 12, 23 , 34, 45, 56,67,78,89



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Re: How many integers n greater than 10 and less than 100 a
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09 Feb 2019, 19:44
HKD1710 wrote: How many integers n greater than 10 and less than 100 are such that, if the digits of n are reversed, the resulting integer is n+9 ?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9
First of all i didn't understand the question and when i did understood it, lot of time had passed, so marked it incorrect. Lets see, 10<n<100, digits of n are reversed, resulting number will be n+9 10x +y = 10y+x +9 9 (xy) = 9 xy = 1 This means that the difference between the tens digit and units digit is 1 I messed up where ??, i had to consider these as well 12 2334 4556 6778 89 Now if i took 98 it wont give 108 after reversing, so out
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How many integers n greater than 10 and less than 100 a
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Updated on: 10 Feb 2019, 10:39
HKD1710 wrote: How many integers n greater than 10 and less than 100 are such that, if the digits of n are reversed, the resulting integer is n+9 ?
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9 note pattern: 12/21, 23/32, 34/43... 12+11(n1)<100 11n<99 n<9 n=8 D
Originally posted by gracie on 09 Feb 2019, 20:39.
Last edited by gracie on 10 Feb 2019, 10:39, edited 2 times in total.



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How many integers n greater than 10 and less than 100 a
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09 Feb 2019, 22:46
10A+B=n 10B+A=n+9
10B+A=10A+B+9 9B9A=9 BA=1 Integers between 11 and 99, that have unit digit 1 greater than tenths digit12, 23, 34, 45 ..... = total 8
Ans  D  Kudos if helpful!



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Re: How many integers n greater than 10 and less than 100 a
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02 Jan 2020, 02:58
dave13 wrote: Let A be tens digit & B be units digit \(X = 10A + B\) After reversing digits, \(X _{new}\) \(= 10B + A\) Difference between \(X\) and \(X_{new}\) is \(9\), so I get following equation \((10A + B)  (10B + A) = 9\) \(9A – 9B = 9\) \(9(AB) = 9\) \(AB = 1\) \(A = B+1\) Since units digit X is +1 more than tens digit, I get following numbers 12, 23, 34, 45, 56, 67, 78, 89 IMO: D and range of a and b is 1 to 10?



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Re: How many integers n greater than 10 and less than 100 a
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28 Mar 2020, 09:42
HKD1710 wrote: How many integers n greater than 10 and less than 100 are such that, if the digits of n are reversed, the resulting integer is n+9 ? (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 Project PS Butler : Question #36 Subscribe to get Daily Email  Click Here  Subscribe via RSS  RSSAsked: How many integers n greater than 10 and less than 100 are such that, if the digits of n are reversed, the resulting integer is n+9 ? Let the number be xy where x is tenth digit and y is unit digit. (10y+x)  (10x+y) = 9(yx) = 9 yx = 1 Numbers = {12,23,34,45,56,67,78,89} IMO D




Re: How many integers n greater than 10 and less than 100 a
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