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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
Joined: 16 Aug 2015
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When the positive integer n is divided by 8, the remainder is 3, and w  [#permalink]

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10 Jul 2018, 02:38
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Question Stats:

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

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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior PS Moderator Joined: 26 Feb 2016 Posts: 3359 Location: India GPA: 3.12 Re: When the positive integer n is divided by 8, the remainder is 3, and w [#permalink] ### Show Tags 10 Jul 2018, 02:58 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 = 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) _________________ You've got what it takes, but it will take everything you've got Director Joined: 20 Feb 2015 Posts: 790 Concentration: Strategy, General Management Re: When the positive integer n is divided by 8, the remainder is 3, and w [#permalink] ### Show Tags 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 Senior Manager Joined: 04 Aug 2010 Posts: 435 Schools: Dartmouth College Re: When the positive integer n is divided by 8, the remainder is 3, and w [#permalink] ### Show Tags 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. _________________ GMAT and GRE Tutor Over 1800 followers GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4512 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: When the positive integer n is divided by 8, the remainder is 3, and w [#permalink] ### Show Tags 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) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) VP Joined: 07 Dec 2014 Posts: 1207 Re: When the positive integer n is divided by 8, the remainder is 3, and w [#permalink] ### Show Tags 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7612 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] ### Show Tags 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 _________________ 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$79 for 1 month Online Course"
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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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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.

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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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