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# n is a positive integer less than 50. When n is divided by 6, the rem

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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n is a positive integer less than 50. When n is divided by 6, the rem  [#permalink]

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07 Aug 2018, 01:00
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[Math Revolution GMAT math practice question]

n is a positive integer less than 50. When n is divided by 6, the remainder is 2, and when n is divided by 7, the remainder is 6. What is the remainder when n is divided by 8?

A. 1
B. 2
C. 3
D. 4
E. 5

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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" NUS School Moderator Joined: 18 Jul 2018 Posts: 983 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) n is a positive integer less than 50. When n is divided by 6, the rem [#permalink] ### Show Tags 07 Aug 2018, 01:19 when N is divided by 6, remainder is 2 when N is divided by 7, remainder is 6 $$\frac{(7x+6)}{6}$$ should give remainder 2 x=2 satisfies the equation. Hence the general equation will be 7*6x + 20 = 42x+20 Since N is less than 50. Put x=0. Then N=20. $$\frac{20}{8}$$ will leave a remainder 4. D is the ans. _________________ Press +1 Kudos If my post helps! VP Joined: 31 Oct 2013 Posts: 1392 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) Re: n is a positive integer less than 50. When n is divided by 6, the rem [#permalink] ### Show Tags 07 Aug 2018, 04:47 MathRevolution wrote: [Math Revolution GMAT math practice question] n is a positive integer less than 50. When n is divided by 6, the remainder is 2, and when n is divided by 7, the remainder is 6. What is the remainder when n is divided by 8? A. 1 B. 2 C. 3 D. 4 E. 5 Note: n<50 when n is divided by 6 the reminder is 2. What could be the value of n. n = 4 , 8 , 14, 20, 26, 32, 38, 44. At the same when n is divided by 7 the reminder is 6. Among the numbers listed above only 20 confirms the condition. So, n = 20. When we divide 20 by 8 the reminder is 4. The best answer is D. 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: n is a positive integer less than 50. When n is divided by 6, the rem [#permalink] ### Show Tags 07 Aug 2018, 07:29 1 MathRevolution wrote: [Math Revolution GMAT math practice question] n is a positive integer less than 50. When n is divided by 6, the remainder is 2, and when n is divided by 7, the remainder is 6. What is the remainder when n is divided by 8? A. 1 B. 2 C. 3 D. 4 E. 5 $$n_6 = { 2 , 8 , 14, 20.....................}$$ $$n_7 = { 6, 13 , 20....................}$$ So, $$n = 20$$ $$\frac{20}{8}$$ = Remainder $$\ 4$$, 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 ) Math Expert Joined: 02 Aug 2009 Posts: 7764 Re: n is a positive integer less than 50. When n is divided by 6, the rem [#permalink] ### Show Tags 07 Aug 2018, 07:42 MathRevolution wrote: [Math Revolution GMAT math practice question] n is a positive integer less than 50. When n is divided by 6, the remainder is 2, and when n is divided by 7, the remainder is 6. What is the remainder when n is divided by 8? A. 1 B. 2 C. 3 D. 4 E. 5 n divided by 6 leaves remainder 2 means 'n' is even... First inference:- remainder should be EVEN, as n/8 will leave even remainder Only possibility 2 or 4 So 7*2k+6 is the number... So the first number is k=1, so number =7*2+6=20 Now 20 divided by 8 will leave 4 as remainder.. D _________________ VP Joined: 07 Dec 2014 Posts: 1206 n is a positive integer less than 50. When n is divided by 6, the rem [#permalink] ### Show Tags 07 Aug 2018, 08:08 MathRevolution wrote: [Math Revolution GMAT math practice question] n is a positive integer less than 50. When n is divided by 6, the remainder is 2, and when n is divided by 7, the remainder is 6. What is the remainder when n is divided by 8? A. 1 B. 2 C. 3 D. 4 E. 5 n/6=q+2 n/7=p+6 →6q-7p=4 plugging in increasing values, q=3 p=2 least value of n=20 20/8 leaves remainder of 4 D Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7609 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: n is a positive integer less than 50. When n is divided by 6, the rem [#permalink] ### Show Tags 09 Aug 2018, 01:32 => The positive integers less than $$50$$ that have a remainder of $$2$$ when they are divided by $$6$$ are $$n = 2, 8, 14, 20, 26, 32, 38$$ and $$44$$. The positive integers less than $$50$$ that have a remainder of $$6$$ when they are divided by $$7$$ are $$n = 6, 13, 20, 27, 34, 41$$ and $$48$$. The only integer in both lists is $$n = 20$$. $$20$$ has a remainder of $$4$$ when it is divided by $$8$$. 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: n is a positive integer less than 50. When n is divided by 6, the rem   [#permalink] 09 Aug 2018, 01:32
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