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

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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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[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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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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New post 08 Dec 2017, 00:51
Answer is 3

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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New post 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
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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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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 \(7\).
Therefore, the answer is D.

Answer : D
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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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New post 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 \(7\).
Therefore, the answer is D.

Answer : D



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

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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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New post 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 \(7\).
Therefore, the answer is D.

Answer : D



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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