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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
Joined: 16 Aug 2015
Posts: 6028
GMAT 1: 760 Q51 V42
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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, 01:10
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Difficulty:

45% (medium)

Question Stats:

58% (01:04) correct 42% (01:22) wrong based on 83 sessions

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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. $$4$$

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 6553 Re: When n is divided by 5, the remainder is 3, and when n is divided by [#permalink] ### Show Tags 08 Dec 2017, 01:27 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 _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Intern Joined: 26 Mar 2017 Posts: 18 Location: India Schools: Great Lakes '19 GMAT 1: 580 Q47 V23 GPA: 3.1 Re: When n is divided by 5, the remainder is 3, and when n is divided by [#permalink] ### Show Tags 08 Dec 2017, 01:51 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 ) Sent from my iPhone using GMAT Club Forum VP Joined: 07 Dec 2014 Posts: 1069 Re: When n is divided by 5, the remainder is 3, and when n is divided by [#permalink] ### Show Tags 08 Dec 2017, 10:28 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6028 GMAT 1: 760 Q51 V42 GPA: 3.82 When n is divided by 5, the remainder is 3, and when n is divided by [#permalink] ### Show Tags Updated on: 10 Dec 2017, 23:25 1 1 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Originally posted by MathRevolution on 10 Dec 2017, 18:15.
Last edited by MathRevolution on 10 Dec 2017, 23:25, edited 2 times in total.
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Joined: 23 Jan 2016
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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, 19:31
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.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6028
GMAT 1: 760 Q51 V42
GPA: 3.82
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, 23:26
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 &nbs [#permalink] 10 Dec 2017, 23:26
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