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# When the even integer n is divided by 9, the remainder is 8.

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Intern
Joined: 08 Jan 2013
Posts: 38
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Kudos [?]: 17 [0], given: 5

When the even integer n is divided by 9, the remainder is 8. [#permalink]

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25 Apr 2013, 15:31
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Difficulty:

25% (medium)

Question Stats:

68% (01:45) correct 32% (00:29) wrong based on 127 sessions

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When the even integer n is divided by 9, the remainder is 8. Which of the following, when added to n, gives a number that is divisible by 18?

A. 1
B. 4
C. 9
D. 10
E. 17

[Reveal] Spoiler:
My working:

Step 1

$$\frac{n}{9}$$ = x remainder 8

For example,
$$\frac{17}{9}$$ = 1 remainder 8
$$\frac{26}{9}$$ = 2 remainder 8
$$\frac{35}{9}$$ = 3 remainder 8

Therefore, n can be even or odd is a member of the set {17, 26, 35, ... }.

Step 2

Substitute the possible answers (1, 4, 9, 10, 17) to find a sum that is divisible by 18.

For example,
17 + 1 = 18, which is divisible by 18. Therefore the answer is 1
17 + 4 = 21, which is not divisible by 18
17 + 9 = 26, which is not divisible by 18
17 + 10 = 27, which is not divisible by 18
17 + 17 = 34, which is not divisible by 18

Grrr... Where did I go wrong?
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Apr 2013, 15:36, edited 1 time in total.
Renamed the topic and edited the question.
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Kudos [?]: 1687 [5] , given: 219

Re: Which sum is divisible by 18? [#permalink]

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25 Apr 2013, 15:33
5
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stormbind wrote:
Grrr... Where did I go wrong?

When the even integer n is divided by 9, the remainder is 8. Which of the following, when added to n, gives a number that is divisible by 18?
17 is not even

Solution:

I use real numbers here I think it's easier

$$n=8$$ reminder when divided by 9 is 8, to make it divisible by 18 it's easy to see that 10 is necessary
$$8+10=18$$ divisible by $$18$$
D
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Joined: 02 Sep 2009
Posts: 32657
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Kudos [?]: 68768 [1] , given: 9818

Re: When the even integer n is divided by 9, the remainder is 8. [#permalink]

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25 Apr 2013, 15:50
1
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Expert's post
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stormbind wrote:
When the even integer n is divided by 9, the remainder is 8. Which of the following, when added to n, gives a number that is divisible by 18?

A. 1
B. 4
C. 9
D. 10
E. 17

[Reveal] Spoiler:
My working:

Step 1

$$\frac{n}{9}$$ = x remainder 8

For example,
$$\frac{17}{9}$$ = 1 remainder 8
$$\frac{26}{9}$$ = 2 remainder 8
$$\frac{35}{9}$$ = 3 remainder 8

Therefore, n can be even or odd is a member of the set {17, 26, 35, ... }.

Step 2

Substitute the possible answers (1, 4, 9, 10, 17) to find a sum that is divisible by 18.

For example,
17 + 1 = 18, which is divisible by 18. Therefore the answer is 1
17 + 4 = 21, which is not divisible by 18
17 + 9 = 26, which is not divisible by 18
17 + 10 = 27, which is not divisible by 18
17 + 17 = 34, which is not divisible by 18

Grrr... Where did I go wrong?

Given that $$n=9q+8$$ and n is even --> n could be 8, 26, 44, ...

What number from answer choices when added to 8 (for example) yields a multiple of 18? 10!

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Re: When the even integer n is divided by 9, the remainder is 8.   [#permalink] 25 Apr 2013, 15:50
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