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# The sum of the digits of a standard two-digit numeral is 9.

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Manager
Joined: 10 Jun 2004
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The sum of the digits of a standard two-digit numeral is 9. [#permalink]  30 Jun 2004, 15:56
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The sum of the digits of a standard two-digit numeral is 9. if the digits are reversed, the numeral represents a numberthat is 45 less. What is the original numeral?
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-Genius is one percent inspiration, and ninety-nine percent perspiration.

Senior Manager
Joined: 21 Mar 2004
Posts: 444
Location: Cary,NC
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Kudos [?]: 20 [0], given: 0

let the number be xy.

its value = 10x+y
when digits are reversed ,value = 10y+x

given
1. x+y = 9
2. 10x+y = 10y+x +45 simplifies to x-y=5

solve
x=7, y=2 : the number is 72

- ash
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ash
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I'm crossing the bridge.........

GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4313
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Same method as Ash. Wow, this problem bogged me for a while until I realized the subtlety of the 2nd sentence.
Sentence says: if the digits are reversed, the numeral represents a number that is 45 less
I misread that as: if the digits are reversed, the numeral represents a number that is less than 45 --> This would have given 81, 72 or 63!
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Best Regards,

Paul

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Joined: 19 May 2004
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For small numbers like these (ie 2 digit numbers), the trial-and -error method works well...
you could fix the tens digit, put a unit's digit 5 more than that and check. The calculations are simple and the answer can be reached easily.

Cheerio!!
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Don't drink and derive!

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