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If a twodigit positive integer has its digits reversed, the
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27 Dec 2012, 07:29
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If a twodigit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7
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Re: If a twodigit positive integer has its digits reversed, the
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27 Dec 2012, 07:31




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Re: If a twodigit positive integer has its digits reversed, the
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13 Oct 2013, 13:45
Bunuel wrote: Walkabout wrote: If a twodigit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Given that (10a + b)  (10b + a) = 27 > 9a  9b =27 > a  b = 3. Answer: A. Do we use 10 because of the tens digit??



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13 Oct 2013, 13:49
runningguy wrote: Bunuel wrote: Walkabout wrote: If a twodigit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Given that (10a + b)  (10b + a) = 27 > 9a  9b =27 > a  b = 3. Answer: A. Do we use 10 because of the tens digit?? Yes, any twodigit integer ab can be expressed as 10a+b, for example: 45 = 10*4 + 5. The same for 3, 4, 5, ... digit numbers. For example, 4digit number 5,432 can be written as 5*1,000 + 4*100 + 3*10 + 2 = 5,432. Hope it's clear.
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Re: If a twodigit positive integer has its digits reversed, the
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12 Jan 2014, 14:28
Walkabout wrote: If a twodigit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 The answer has to be a factor of 27, the only option that's a factor of 27 is 3. Sice \((10x + y)  (10y + x) = 27\), you can simplify this relationship by subtracting with a common factor > 9x  9y = 27 > 9(x  y) = 27 > here, you already notice that the difference has to be a factor of both 9 and 27, but you can simplify further > x  y = 3, and thus we have the answer. But these last steps are superfluous if you already notice that the answer has to be a factor of 27, this way you save time without having to calculate.



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Re: If a twodigit positive integer has its digits reversed, the
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18 Feb 2015, 21:12
Hi All, Even though this question might seem a little strange, you do NOT need to do any excessive math to get to the correct answer. With just a bit of 'playing around' you can use 'brute force' to get to the answer. We're told that a 2digit number has its digits reversed and the difference between those two numbers is 27. IF we use.... 11 and 11, then the difference is 0  this is NOT a match 12 and 21, then the difference = 9  this is NOT a match 13 and 31, then the difference = 18  this is NOT a match (notice the pattern though? The difference keeps increasing by 9!!!!! I wonder what the next one will be???) 14 and 41, then the difference = 27 = this IS a match The question asks for the difference in the two DIGITS. The difference between 1 and 4 is 3. Final Answer: There are actually several ways to get to this answer: 14 and 41, 25 and 52, 36 and 63, 47 and 74, 58 and 85, 69 and 96. GMAT assassins aren't born, they're made, Rich
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Re: If a twodigit positive integer has its digits reversed, the
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24 Nov 2015, 03:21
Hey guys, I was wondering if it is true to say that for any AB and BA ==> 9 is always a factor of (AB) or (BA) which ever is bigger, and so we can directly divide 27/9 to yield 3 then we can check numbers for a match: 4114 = 27 ==>So if we were given AB  BA = 54 ==> 54/9 = 6 check numbers: 71 17 = 54 Is this reasoning always correct?
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Re: If a twodigit positive integer has its digits reversed, the
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07 Jan 2018, 04:21
Bunuel wrote: Walkabout wrote: If a twodigit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 Given that (10a + b)  (10b + a) = 27 > 9a  9b =27 > a  b = 3. Answer: A. Hello Bunuel, did you divide both sides of equation 9a  9b =27 by 9 to get a  b = 3 ?



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Re: If a twodigit positive integer has its digits reversed, the
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07 Jan 2018, 04:23



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If a twodigit positive integer has its digits reversed, the
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07 Jan 2018, 11:59
Walkabout wrote: If a twodigit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7 let d=the difference between any two twodigit reversals d will always be a multiple of 9 d/9 will always be the difference between the two digits 27/9=3 A




If a twodigit positive integer has its digits reversed, the &nbs
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