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# When n is divided by 5, the remainder is 3, and when n is divided by

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Math Revolution GMAT Instructor
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When n is divided by 5, the remainder is 3, and when n is divided by [#permalink]

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08 Dec 2017, 00:10
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[GMAT math practice question]

When $$n$$ is divided by $$5$$, the remainder is $$3$$, and when $$n$$ is divided by $$6$$, the remainder is $$3$$. What is the remainder when the smallest possible integer value of n is divided by $$7$$?

A. $$0$$
B. $$1$$
C. $$2$$
D. $$3$$
E. $$4$$
[Reveal] Spoiler: OA

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Re: When n is divided by 5, the remainder is 3, and when n is divided by [#permalink]

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08 Dec 2017, 00:27
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MathRevolution wrote:
[GMAT math practice question]

When $$n$$ is divided by $$5$$, the remainder is $$3$$, and when $$n$$ is divided by $$6$$, the remainder is $$3$$. What is the remainder when the smallest possible integer value of n is divided by $$7$$?

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

since the remainder is same, 3, and the divisors, 6 & 5, both are greater than 3, the smallest INTEGER will be 0.
And whatever be the divisor > 3, the Remainder will always be 3

D
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Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: When n is divided by 5, the remainder is 3, and when n is divided by [#permalink]

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08 Dec 2017, 00:51

If the options had answer 5, then it would have confused few ppl by taking 33 as n value ( missing to consider 0 )

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Re: When n is divided by 5, the remainder is 3, and when n is divided by [#permalink]

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08 Dec 2017, 09:28
MathRevolution wrote:
[GMAT math practice question]

When $$n$$ is divided by $$5$$, the remainder is $$3$$, and when $$n$$ is divided by $$6$$, the remainder is $$3$$. What is the remainder when the smallest possible integer value of n is divided by $$7$$?

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

n=5q+3
n=6p+3
q/p=6/5
n=33
33-(6*5)=3=least integer value of n
3/7 leaves a remainder of 3
D

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Math Revolution GMAT Instructor
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When n is divided by 5, the remainder is 3, and when n is divided by [#permalink]

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10 Dec 2017, 17:15
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Plugging in numbers is the recommended approach for remainder questions.
The integers that have a remainder of $$3$$ when they are divided by $$5$$ are $$3, 8, 13, 18, 23, 28, 33, 38, …$$
The integers that have a remainder of $$3$$ when they are divided by $$6$$ are $$3, 9, 15, 21, 27, 33, 39, …$$
The smallest integer $$n$$ that occurs in both lists is $$3$$.
Since $$3 = 7 ∙0 + 3$$, this value of n has a remainder of $$3$$ when it is divided by $$7$$.

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Last edited by MathRevolution on 10 Dec 2017, 22:25, edited 2 times in total.

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Re: When n is divided by 5, the remainder is 3, and when n is divided by [#permalink]

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10 Dec 2017, 18:31
MathRevolution wrote:
=>

Plugging in numbers is the recommended approach for remainder questions.
The integers that have a remainder of $$3$$ when they are divided by $$5$$ are $$3, 8, 13, 18, 23, 28, 33, 38, …$$
The integers that have a remainder of $$3$$ when they are divided by $$6$$ are $$3, 9, 15, 21, 27, 33, 39, 38, …$$
The smallest integer $$n$$ that occurs in both lists is $$38$$.
Since $$38 = 7 ∙5 + 3$$, this value of n has a remainder of $$3$$ when it is divided by $$7$$.

Is it a right solution? As per above, the smallest integer will be 33 not 38.

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Math Revolution GMAT Instructor
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Re: When n is divided by 5, the remainder is 3, and when n is divided by [#permalink]

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10 Dec 2017, 22:26
saleemc wrote:
MathRevolution wrote:
=>

Plugging in numbers is the recommended approach for remainder questions.
The integers that have a remainder of $$3$$ when they are divided by $$5$$ are $$3, 8, 13, 18, 23, 28, 33, 38, …$$
The integers that have a remainder of $$3$$ when they are divided by $$6$$ are $$3, 9, 15, 21, 27, 33, 39, 38, …$$
The smallest integer $$n$$ that occurs in both lists is $$38$$.
Since $$38 = 7 ∙5 + 3$$, this value of n has a remainder of $$3$$ when it is divided by $$7$$.

Is it a right solution? As per above, the smallest integer will be 33 not 38.

The solution is fixed. The smallest integer is 3.
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Re: When n is divided by 5, the remainder is 3, and when n is divided by   [#permalink] 10 Dec 2017, 22:26
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