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# The "reflection" of a positive integer is obtained by reversing its di

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Math Expert
Joined: 02 Sep 2009
Posts: 52905
The "reflection" of a positive integer is obtained by reversing its di  [#permalink]

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06 Feb 2019, 23:56
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Difficulty:

45% (medium)

Question Stats:

57% (02:16) correct 43% (01:56) wrong based on 35 sessions

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The "reflection" of a positive integer is obtained by reversing its digits. For example 321 is the reflection of 123 The difference between a five-digit integer and its reflection must be divisible by which of the following?

A. 2
B. 4
C. 5
D. 6
E. 9

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Re: The "reflection" of a positive integer is obtained by reversing its di  [#permalink]

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07 Feb 2019, 00:07
Bunuel wrote:
The "reflection" of a positive integer is obtained by reversing its digits. For example 321 is the reflection of 123 The difference between a five-digit integer and its reflection must be divisible by which of the following?

A. 2
B. 4
C. 5
D. 6
E. 9

eg = 12345 and reflection 54321 , 45789 , reflection 98754

testing the values , difference would always be divisible by 9
IMO E
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Joined: 25 Jan 2019
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Re: The "reflection" of a positive integer is obtained by reversing its di  [#permalink]

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09 Feb 2019, 09:55
Number = abcde = 10^4 ( a ) + 10^3 (b) + 10^2 (c) + 10 (d) + e
Reflection = edcba = 10^4 ( e ) + 10^3 (d) + 10^2 (c) + 10 (b) + a

Number - Reflection = 10^4 ( a - e ) + 10^3 ( b -d ) + 10 (d- b) + e - a

= (a-e) ( 10 ^ 4 - 1) + (b-d) ( 10^3 - 10)
= (a-e) (99999) + (b-d) (990)
= 9* (something)

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Joined: 09 Mar 2018
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Re: The "reflection" of a positive integer is obtained by reversing its di  [#permalink]

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09 Feb 2019, 10:19
Bunuel wrote:
The "reflection" of a positive integer is obtained by reversing its digits. For example 321 is the reflection of 123 The difference between a five-digit integer and its reflection must be divisible by which of the following?

A. 2
B. 4
C. 5
D. 6
E. 9

when the number is taken as 54321, reflection will be 12345, difference will be / by 2 4 and 9

when the number is taken as 76432, reflection will be 23467, difference will be / 9

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Re: The "reflection" of a positive integer is obtained by reversing its di   [#permalink] 09 Feb 2019, 10:19
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