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When the positive integer n is divided by 8, the remainder is 3, and w

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Math Revolution GMAT Instructor
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When the positive integer n is divided by 8, the remainder is 3, and w  [#permalink]

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New post 10 Jul 2018, 02:38
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[GMAT math practice question]

When the positive integer n is divided by 8, the remainder is 3, and when n is divided by 5, the remainder is 2. What is the remainder when the smallest possible value of n is divided by 6?

A. 0
B. 1
C. 2
D. 3
E. 4

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Re: When the positive integer n is divided by 8, the remainder is 3, and w  [#permalink]

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New post 10 Jul 2018, 02:58
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MathRevolution wrote:
[GMAT math practice question]

When the positive integer n is divided by 8, the remainder is 3, and when n is divided by 5, the remainder is 2. What is the remainder when the smallest possible value of n is divided by 6?

A. 0
B. 1
C. 2
D. 3
E. 4


n = 8x + 3 (3,11,19,27)
n = 5x + 2 (2,7,12,17,22,27)

Therefore, the smallest value of n is 27.
When divided by 6, it will give a remainder of 3(Option D)
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Re: When the positive integer n is divided by 8, the remainder is 3, and w  [#permalink]

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New post 10 Jul 2018, 02:59
1
MathRevolution wrote:
[GMAT math practice question]

When the positive integer n is divided by 8, the remainder is 3, and when n is divided by 5, the remainder is 2. What is the remainder when the smallest possible value of n is divided by 6?

A. 0
B. 1
C. 2
D. 3
E. 4


n=8p+3
n=5q+2

8p+3=5q+2
p=(5q-1)/8
for p to be divisible by 8 , q can be 5,13..
therefore n = 27,67..
remainder when 27(smallest value of n) is divided by 6 is 3
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Re: When the positive integer n is divided by 8, the remainder is 3, and w  [#permalink]

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New post 10 Jul 2018, 05:06
MathRevolution wrote:
[GMAT math practice question]

When the positive integer n is divided by 8, the remainder is 3, and when n is divided by 5, the remainder is 2. What is the remainder when the smallest possible value of n is divided by 6?

A. 0
B. 1
C. 2
D. 3
E. 4


When the positive integer \(n\) is divided by 8, the remainder is 3.
In other words, \(n\) is 3 more than a multiple of 8:
\(n = 8a + 3\), where \(a\) is a nonnegative integer.
Options for \(n\):
3, 11, 19, 27...

When n is divided by 5, the remainder is 2.
In other words, n is 2 more than a multiple of 5:
\(n = 5b + 2\), where \(b\) is a nonnegative integer.
Options for \(n\):
2, 7, 12, 17, 22, 27...

The smallest value common to the two lists is 27.
When 27 is divided by 6, the remainder is 3.


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Re: When the positive integer n is divided by 8, the remainder is 3, and w  [#permalink]

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New post 10 Jul 2018, 07:21
MathRevolution wrote:
[GMAT math practice question]

When the positive integer n is divided by 8, the remainder is 3, and when n is divided by 5, the remainder is 2. What is the remainder when the smallest possible value of n is divided by 6?

A. 0
B. 1
C. 2
D. 3
E. 4


Possible Values when divided by 8 are { 3 , 11 , 19 , 27......................}
Possible Values when divided by 5 are { 2 , 7 , 12, 17, 22, 27..........}

Thus when 27 is divided by 6 we have the remainder as 3, Answer must be (D)
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Re: When the positive integer n is divided by 8, the remainder is 3, and w  [#permalink]

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New post 10 Jul 2018, 20:41
MathRevolution wrote:
[GMAT math practice question]

When the positive integer n is divided by 8, the remainder is 3, and when n is divided by 5, the remainder is 2. What is the remainder when the smallest possible value of n is divided by 6?

A. 0
B. 1
C. 2
D. 3
E. 4


n=8q+3
n=5p+2
8q+3=5p+2→
5p-8q=1
so we need to find a multiple of 5 that is one greater than a multiple of 8
least possibilities are 25 and 24
thus, p=5; q=3; least possibility of n=27
27/6 leaves a remainder of 3
D
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Re: When the positive integer n is divided by 8, the remainder is 3, and w  [#permalink]

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New post 12 Jul 2018, 01:10
=>

If \(n\) has remainder \(3\) when it is divided by \(8\), then \(n = 8a + 3\) for some integer \(a\). The possible positive integer values of \(n\) are \(3, 11, 19, 27, 35, … .\)
If \(n\) has remainder \(2\) when it is divided by \(5\), then \(n = 5b + 2\) for some integer \(b\). The possible positive integer values of \(n\) are \(2, 7, 12, 17, 22, 27, 32, … .\)
The smallest value of \(n\) that appears in both lists is \(27\). Therefore, the smallest possible value for \(n\) is \(27\).
\(27 = 6*4 + 3, 27\) has remainder \(3\) when it is divided by \(6\).

Therefore, the answer is D.
Answer: D
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Re: When the positive integer n is divided by 8, the remainder is 3, and w  [#permalink]

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New post 14 Jul 2018, 19:36
MathRevolution wrote:
[GMAT math practice question]

When the positive integer n is divided by 8, the remainder is 3, and when n is divided by 5, the remainder is 2. What is the remainder when the smallest possible value of n is divided by 6?

A. 0
B. 1
C. 2
D. 3
E. 4


Since when the positive integer n is divided by 8, the remainder is 3, we see that n could be:

3, 11, 19, 27, ...

Since when the positive integer n is divided by 5, the remainder is 2, n couold be:

2, 7, 12, 17, 22, 27, ...

Thus, the smallest value of n is 27, and 27/6 = 4 remainder 3.

Answer: D
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Re: When the positive integer n is divided by 8, the remainder is 3, and w &nbs [#permalink] 14 Jul 2018, 19:36
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