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# Solve - Simple Equations Q#1

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Joined: 25 Jan 2010
Posts: 114
Location: Calicut, India
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Solve - Simple Equations Q#1 [#permalink]  10 Feb 2010, 05:42
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Difficulty:

5% (low)

Question Stats:

50% (00:00) correct 50% (00:00) wrong based on 2 sessions
Plz illustrate how to solve this equation question
1) A three-digit 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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Math Expert
Joined: 02 Sep 2009
Posts: 15072
Followers: 2519

Kudos [?]: 15463 [2] , given: 1552

Re: Solve - Simple Equations Q#1 [#permalink]  10 Feb 2010, 06:00
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Expert's post
cleetus wrote:
Plz illustrate how to solve this equation question
1) A three-digit 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 --> a-c=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=a-c, from above we know a-c=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}.

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Re: Solve - Simple Equations Q#1   [#permalink] 10 Feb 2010, 06:00
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