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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7612
GMAT 1: 760 Q51 V42 GPA: 3.82
When the positive integer n is divided by 8, the remainder is 3, and w  [#permalink]

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1 00:00

Difficulty:   25% (medium)

Question Stats: 77% (01:23) correct 23% (01:40) wrong based on 82 sessions

### HideShow timer Statistics [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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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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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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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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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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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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GMAT 1: 760 Q51 V42 GPA: 3.82
Re: When the positive integer n is divided by 8, the remainder is 3, and w  [#permalink]

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=>

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 $$6$$.

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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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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.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: When the positive integer n is divided by 8, the remainder is 3, and w   [#permalink] 14 Jul 2018, 19:36
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