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The sum of the digits of a two digit number..

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The sum of the digits of a two digit number.. [#permalink] New post 14 Nov 2012, 07:34
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Difficulty:

  25% (medium)

Question Stats:

88% (02:03) correct 12% (02:13) wrong based on 26 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


[Reveal] Spoiler:
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)
[Reveal] Spoiler: OA

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Re: The sum of the digits of a two digit number.. [#permalink] New post 14 Nov 2012, 07:43
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


[Reveal] Spoiler:
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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Re: The sum of the digits of a two digit number.. [#permalink] New post 14 Nov 2012, 09:14
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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Re: The sum of the digits of a two digit number.. [#permalink] New post 14 Nov 2012, 18:29
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


[Reveal] Spoiler:
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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Re: The sum of the digits of a two digit number.. [#permalink] New post 14 Nov 2012, 19:47
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


[Reveal] Spoiler:
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, 19:47
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