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Manager
Joined: 03 Sep 2012
Posts: 245
Location: United States
Concentration: Healthcare, Strategy
GMAT Date: 02-20-2013
GPA: 3.65
WE: Medicine and Health (Health Care)
Followers: 8
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The sum of the digits of a two digit number.. [#permalink]
 14 Nov 2012, 08:34
Question Stats:
100% (01:38) correct
0% (00:00) wrong based on 1 sessions
The sum of the digits of a two digit number is 10. When the digits are reversed, the number decreases by 54. Find the changed Number. (A) 28 (B) 19 (C) 37 (D) 46 Let the Units digit of the Number be Y and the Tens digit be X. The number can be represented as 10X + Y
According to the Question Stem: X + Y = 10
When the number is reversed we get 10Y+X as the new number.
According to the question stem: (10x+Y) - (10 Y + X) = 54 , Simplifying we get 9X - 9Y = 54 or 9 (X-Y) = 54 or X-Y = 6.
Putting this in the original equation we get two equations ; X + Y = 10 (1) and X - Y = 6 (2)
Solving 1 & 2 we get X = 8. Y comes out to 2 , and the Original Number is 82. The new number is 28 (A) _________________
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Director
Status: Disappointed devil..
Joined: 15 Sep 2012
Posts: 592
Location: India
Concentration: Strategy, General Management
WE: Information Technology (Computer Software)
Followers: 20
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223
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Re: The sum of the digits of a two digit number.. [#permalink]
14 Nov 2012, 08:43
vomhorizon wrote: The sum of the digits of a two digit number is 10. When the digits are reversed, the number decreases by 54. Find the changed Number. (A) 28 (B) 19 (C) 37 (D) 46 Let the Units digit of the Number be Y and the Tens digit be X. The number can be represented as 10X + Y
According to the Question Stem: X + Y = 10
When the number is reversed we get 10Y+X as the new number.
According to the question stem: (10x+Y) - (10 Y + X) = 54 , Simplifying we get 9X - 9Y = 54 or 9 (X-Y) = 54 or X-Y = 6.
Putting this in the original equation we get two equations ; X + Y = 10 (1) and X - Y = 6 (2)
Solving 1 & 2 we get X = 8. Y comes out to 2 , and the Original Number is 82. The new number is 28 (A) Reversing digits gives a number 54 less than original => difference in digits =54/9 = 6 Only option A satsifies this. Ans A it is.
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Director
Joined: 02 Jul 2012
Posts: 752
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 19
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Re: The sum of the digits of a two digit number.. [#permalink]
14 Nov 2012, 10:14
a+b = 10 10a + b - 10b - a = 54 a-b = 6 a= 8, b = 2. Reversed number is 28. Kudos Please... If my post helped.
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Intern
Status: wants to beat the gmat
Joined: 18 Jul 2012
Posts: 20
Location: United States
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Re: The sum of the digits of a two digit number.. [#permalink]
14 Nov 2012, 19:29
Vips0000 wrote: vomhorizon wrote: The sum of the digits of a two digit number is 10. When the digits are reversed, the number decreases by 54. Find the changed Number. (A) 28 (B) 19 (C) 37 (D) 46 Let the Units digit of the Number be Y and the Tens digit be X. The number can be represented as 10X + Y
According to the Question Stem: X + Y = 10
When the number is reversed we get 10Y+X as the new number.
According to the question stem: (10x+Y) - (10 Y + X) = 54 , Simplifying we get 9X - 9Y = 54 or 9 (X-Y) = 54 or X-Y = 6.
Putting this in the original equation we get two equations ; X + Y = 10 (1) and X - Y = 6 (2)
Solving 1 & 2 we get X = 8. Y comes out to 2 , and the Original Number is 82. The new number is 28 (A) Reversing digits gives a number 54 less than original => difference in digits =54/9 = 6 Only option A satsifies this. Ans A it is. Can you further explain this in detail? How did you get 54/9 ? Where did the 9 come from?
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Director
Status: Disappointed devil..
Joined: 15 Sep 2012
Posts: 592
Location: India
Concentration: Strategy, General Management
WE: Information Technology (Computer Software)
Followers: 20
Kudos [?]:
223
[0], given: 23
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Re: The sum of the digits of a two digit number.. [#permalink]
14 Nov 2012, 20:47
watwazdaquestion wrote: Vips0000 wrote: vomhorizon wrote: The sum of the digits of a two digit number is 10. When the digits are reversed, the number decreases by 54. Find the changed Number. (A) 28 (B) 19 (C) 37 (D) 46 Let the Units digit of the Number be Y and the Tens digit be X. The number can be represented as 10X + Y
According to the Question Stem: X + Y = 10
When the number is reversed we get 10Y+X as the new number.
According to the question stem: (10x+Y) - (10 Y + X) = 54 , Simplifying we get 9X - 9Y = 54 or 9 (X-Y) = 54 or X-Y = 6.
Putting this in the original equation we get two equations ; X + Y = 10 (1) and X - Y = 6 (2)
Solving 1 & 2 we get X = 8. Y comes out to 2 , and the Original Number is 82. The new number is 28 (A) Reversing digits gives a number 54 less than original => difference in digits =54/9 = 6 Only option A satsifies this. Ans A it is. Can you further explain this in detail? How did you get 54/9 ? Where did the 9 come from? This 9 is logical derivation. Difference between a 2 digit number and number with reversed digit is always 9 times the difference between digits. Any number 10a+b when reversed would be 10b+a , the difference would be 9(b-a)
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Re: The sum of the digits of a two digit number..
[#permalink]
14 Nov 2012, 20:47
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