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A threedigit number is such that when its reverse is subtra [#permalink]
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10 Feb 2010, 05:42
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A threedigit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number? (A) 4 (B) 5 (C) 7 (D) 8
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Last edited by Bunuel on 25 Feb 2014, 06:16, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



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Re: Solve  Simple Equations Q#1 [#permalink]
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cleetus wrote: Plz illustrate how to solve this equation question 1) A threedigit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?
A) 4 B) 5 C) 7 D) 8 Hi, welcome to the Gmat Club. Solution to your question is as follows: Three digit number \(abc\) can be represented as \(100a+10b+c\), its reverse number would be \(cba\) or \(100c+10b+a\). Given: \(100a+10b+c(100c+10b+a)=297\) > \(ac=3\), this gives us 7 values for \(a\) and \(c\): {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}. Also given: \(3b=ac\), from above we know \(ac=3\), hence \(3b=3\) > \(b=1\), only one value for \(b\). So total of 7 such numbers are possible: {916}{815}{714}{613}{512}{411}{310}. Answer: C.
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Re: Solve  Simple Equations Q#1 [#permalink]
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Re: A threedigit number is such that when its reverse is subtra [#permalink]
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abc  cba = 297 100a+10b+c  100c  10b  a = 297 99a99c = 297 ac = 3 also, 3b = ac b=1 Numbers abc a1c ac can take (9,6),(8,5),(7,4),(6,3),(5,2),(4,1),(3,0) Hence 7
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Re: A threedigit number is such that when its reverse is subtra [#permalink]
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Re: A threedigit number is such that when its reverse is subtra [#permalink]
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cleetus wrote: A threedigit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?
(A) 4 (B) 5 (C) 7 (D) 8 You can also use reasoning to solve it. "thrice the tens digit is equal to the difference between its hundreds and units digits." The difference between any two digits cannot be more than 90 = 9. So the tens digit can be 3 at most. But if the difference between the other two digits is 9, their subtraction will give us something around 900. We need something around 300 so the tens digit must be 1 and the difference between the other two digits must be 3. So the first such number you can have is 310. If you subtract 013 out of it, you get 297  Correct. Next you can have is 411. If you subtract 114 out of it, you will get 297  Correct. Next you can have is 512. If you subtract 215 out of it, you will get 297  Correct. and so on goes the pattern till you have 916. So in all, you have 7 numbers. Answer (C)
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Re: A threedigit number is such that when its reverse is subtra [#permalink]
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16 Aug 2015, 23:54
Bunuel wrote: cleetus wrote: Plz illustrate how to solve this equation question 1) A threedigit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?
A) 4 B) 5 C) 7 D) 8 Hi, welcome to the Gmat Club. Solution to your question is as follows: Three digit number \(abc\) can be represented as \(100a+10b+c\), its reverse number would be \(cba\) or \(100c+10b+a\). Given: \(100a+10b+c(100c+10b+a)=297\) > \(ac=3\), this gives us 7 values for \(a\) and \(c\): {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}. Also given: \(3b=ac\), from above we know \(ac=3\), hence \(3b=3\) > \(b=1\), only one value for \(b\). So total of 7 such numbers are possible: {916}{815}{714}{613}{512}{411}{310}. Answer: C. this gives us 7 values for a and c: {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}. Can you please write how we get 7 possible values? I understood your solution but only 7 possible probability part is unclear.



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Re: A threedigit number is such that when its reverse is subtra [#permalink]
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17 Aug 2015, 01:19
sashibagra wrote: Bunuel wrote: cleetus wrote: Plz illustrate how to solve this equation question 1) A threedigit number is such that when its reverse is subtracted from it, the result is 297. Also, thrice the tens digit is equal to the difference between its hundreds and units digits. How many possible values are there for the number?
A) 4 B) 5 C) 7 D) 8 Hi, welcome to the Gmat Club. Solution to your question is as follows: Three digit number \(abc\) can be represented as \(100a+10b+c\), its reverse number would be \(cba\) or \(100c+10b+a\). Given: \(100a+10b+c(100c+10b+a)=297\) > \(ac=3\), this gives us 7 values for \(a\) and \(c\): {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}. Also given: \(3b=ac\), from above we know \(ac=3\), hence \(3b=3\) > \(b=1\), only one value for \(b\). So total of 7 such numbers are possible: {916}{815}{714}{613}{512}{411}{310}. Answer: C. this gives us 7 values for a and c: {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}. Can you please write how we get 7 possible values? I understood your solution but only 7 possible probability part is unclear. We got that a  c = 3: the positive difference between the hundreds and units digits of the number is 3. If a = 9 (max possible value of a), then c is 6, if a = 8, then c = 5, ..., if a = 3, then c = 0 (min possible value of c). Hope it's clear.
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A threedigit number is such that when its reverse is subtra [#permalink]
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17 Aug 2015, 21:57
Quote: Hi, welcome to the Gmat Club.
Solution to your question is as follows:
Three digit number \(abc\) can be represented as \(100a+10b+c\), its reverse number would be \(cba\) or \(100c+10b+a\).
Given: \(100a+10b+c(100c+10b+a)=297\) > \(ac=3\), this gives us 7 values for \(a\) and \(c\): {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}.
Also given: \(3b=ac\), from above we know \(ac=3\), hence \(3b=3\) > \(b=1\), only one value for \(b\).
So total of 7 such numbers are possible: {916}{815}{714}{613}{512}{411}{310}.
Answer: C. Quote: this gives us 7 values for a and c: {9,6}{8,5}{7,4}{6,3}{5,2}{4,1}{3,0}. Can you please write how we get 7 possible values? I understood your solution but only 7 possible probability part is unclear. Quote: We got that a  c = 3: the positive difference between the hundreds and units digits of the number is 3. If a = 9 (max possible value of a), then c is 6, if a = 8, then c = 5, ..., if a = 3, then c = 0 (min possible value of c).
Hope it's clear. I am sorry, it was really a silly question and I shouldn't asked it. It was very easy topic but I was just thinking it complicatedly so it was unclear to me. now it's clear , thanks



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Re: A threedigit number is such that when its reverse is subtra [#permalink]
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Re: A threedigit number is such that when its reverse is subtra [#permalink]
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14 Sep 2017, 23:29
Hmm, had 6 been one of the choices, I would have fallen for it. I basically used the same process to solve this problem  ABC  CBA = 297, so Here I saw that A>C, AC = 3 3B= AC Hence 1 is the only possible value for 1. And possible values for A & C are: (9,6), (8,5), (7,4) (6,3) (5,2), (4,1) (3,0)I was initially looking for 6, because I didn't think C could be 0 as CBA would be a two digit number.. but nowhere in the question stem say that the reverse of the three digit number ABC also has to be a three digit number.




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