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# The "reflection" of a positive integer is obtained by

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The "reflection" of a positive integer is obtained by [#permalink]

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12 Dec 2003, 02:41
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

I have chosen 2, e.g. 98721-12879 = 84942/2 = 42471.
But the answer is not. Can anyone try and explain the correct answer?
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12 Dec 2003, 03:29
five digit integer 98721 the reflection is 12789, not 12879 or 85932 is the difference , as in this case it is divisible by 2,4,6,9 not divisible by 5, we can not say. Try 10000-00001=9999, think it is clear now..
Manager
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12 Dec 2003, 05:50
Sorry my mistake in reversing the order.

May I know it is a rule that when reversing any digits number, it would always be divisble by 9?
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12 Dec 2003, 06:46
Difference between an integer and it's reflection is always divisible by 9. Of course by that logic it would also be divisible by 3. But that's just a site note.
12 Dec 2003, 06:46
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# The "reflection" of a positive integer is obtained by

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 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.
The content of the provided text is about GMAT preparation resources and updates, not about the mathematical problem you've presented. However, I will focus on the math problem you've asked about.

### Content Structure:
The text is a mix of GMAT Club updates and a math problem. The math problem is about the "reflection" of a positive integer and asks which number the difference between a five-digit integer and its reflection must be divisible by.

### Analysis:
single_question_with_answer

### explanation:
the problem states that the "reflection" of a positive integer is obtained by reversing its digits. for example, the reflection of 123 is 321. the question asks which number the difference between a five-digit integer and its reflection must be divisible by.

to solve this, consider a five-digit number \(abcde\), where \(a, b, c, d, e\) are its digits. the number can be expressed as:
\[ 10000a + 1000b + 100c + 10d + e \]

the reflection of this number is:
\[ 10000e + 1000d + 100c + 1
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
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 It is currently 25 May 2017, 15:02

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# The "reflection" of a positive integer is obtained by

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Manager
Joined: 29 Apr 2003
Posts: 93
Location: Singapore
Followers: 1

Kudos [?]: 0 [0], given: 0

The "reflection" of a positive integer is obtained by [#permalink]

### Show Tags

12 Dec 2003, 02:41
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

I have chosen 2, e.g. 98721-12879 = 84942/2 = 42471.
But the answer is not. Can anyone try and explain the correct answer?
Director
Joined: 13 Nov 2003
Posts: 789
Location: BULGARIA
Followers: 1

Kudos [?]: 52 [0], given: 0

### Show Tags

12 Dec 2003, 03:29
five digit integer 98721 the reflection is 12789, not 12879 or 85932 is the difference , as in this case it is divisible by 2,4,6,9 not divisible by 5, we can not say. Try 10000-00001=9999, think it is clear now..
Manager
Joined: 29 Apr 2003
Posts: 93
Location: Singapore
Followers: 1

Kudos [?]: 0 [0], given: 0

### Show Tags

12 Dec 2003, 05:50
Sorry my mistake in reversing the order.

May I know it is a rule that when reversing any digits number, it would always be divisble by 9?
Manager
Joined: 26 Aug 2003
Posts: 233
Location: United States
Followers: 1

Kudos [?]: 13 [0], given: 0

### Show Tags

12 Dec 2003, 06:46
Difference between an integer and it's reflection is always divisible by 9. Of course by that logic it would also be divisible by 3. But that's just a site note.
12 Dec 2003, 06:46
Display posts from previous: Sort by

# The "reflection" of a positive integer is obtained by

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.
user
The content of the provided text is about GMAT preparation resources and updates, not about the mathematical problem you've presented. However, I will focus on the math problem you've asked about.

### Content Structure:
The text is a mix of GMAT Club updates and a math problem. The math problem is about the "reflection" of a positive integer and asks which number the difference between a five-digit integer and its reflection must be divisible by.

### Analysis:
TYPE: SINGLE_QUESTION_WITH_ANSWER

### Explanation:
The problem states that the "reflection" of a positive integer is obtained by reversing its digits. For example, the reflection of 123 is 321. The question asks which number the difference between a five-digit integer and its reflection must be divisible by.

To solve this, consider a five-digit number \(abcde\), where \(a, b, c, d, e\) are its digits. The number can be expressed as:
\[ 10000a + 1000b + 100c + 10d + e \]

The reflection of this number is:
\[ 10000e + 1000d + 100c + 1