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The difference between a two-digit number and the number obtained by r

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The difference between a two-digit number and the number obtained by r  [#permalink]

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New post 19 Mar 2019, 07:06
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Question Stats:

55% (02:36) correct 45% (03:02) wrong based on 31 sessions

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The difference between a two-digit number and the number obtained by revers-ing its digits is 5 times the sum of the digits of either number. What is the sum of the two digit number and its reverse?

(A) 44

(B) 55

(C) 77

(D) 99

(E) 110
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Re: The difference between a two-digit number and the number obtained by r  [#permalink]

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New post 19 Mar 2019, 08:18
Noshad wrote:
The difference between a two-digit number and the number obtained by revers-ing its digits is 5 times the sum of the digits of either number. What is the sum of the two digit number and its reverse?

(A) 44

(B) 55

(C) 77

(D) 99

(E) 110


Let, Number = ab = 10a+b
Number after reversing digits = ba = 10b+a


(10a+b)-(10b+a) = 5*(a+b)

i.e. 9a - 9b = 5a + 5b

i.e. 9(a-b) = 5(a+b)

which is possible only when a+b = 9 and a-b = 5
i.e. a = 7 and b = 2

Requires sum = 72+27 = 99

Answer: Option D
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Re: The difference between a two-digit number and the number obtained by r  [#permalink]

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New post 19 Mar 2019, 10:47
Noshad wrote:
The difference between a two-digit number and the number obtained by revers-ing its digits is 5 times the sum of the digits of either number. What is the sum of the two digit number and its reverse?

(A) 44

(B) 55

(C) 77

(D) 99

(E) 110


we know that the difference between any two digit reversals xy and yx will be 9(x-y)
so 9(x-y)=5(x+y)→
x/y=7/2
72+27=99
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Re: The difference between a two-digit number and the number obtained by r  [#permalink]

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New post 19 Mar 2019, 11:16
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The difference of the two digit number itself and it's reversal is always divisible by 9.
And the resulting number = 9(larger digit- smaller digit)
For example, difference between 18 and 81 = 9(8-1)=63.


The summation of the two digit number itself and it's reversal is always divisible by 11. And the resulting number = 11(larger digit+smaller digit)
For example, difference between 18 and 81 = 11(8+1)=99.

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Re: The difference between a two-digit number and the number obtained by r  [#permalink]

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New post 19 Mar 2019, 11:32
Noshad wrote:
The difference between a two-digit number and the number obtained by revers-ing its digits is 5 times the sum of the digits of either number. What is the sum of the two digit number and its reverse?

(A) 44

(B) 55

(C) 77

(D) 99

(E) 110


given
10a+b-10b-a= 5a+5b
we get
2a=7b
a= 7 ; b = 2
so sum = 99
IMO D
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Re: The difference between a two-digit number and the number obtained by r   [#permalink] 19 Mar 2019, 11:32
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