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 Author: LM [ 24 Jan 2012, 10:01 ] Post subject: What is the value of length n<100 meter of wire? What is the value of length n<100 meter of wire?(1) When divided equal part of 10 meter each, a piece of 5 meter is left.(2) When divided equal of 6 meter each, a piece of 1 meter is left.

 Author: Bunuel [ 24 Jan 2012, 10:12 ] Post subject: Re: DS-Length of wire LM wrote:What is the value of length n<100 meter of wire?1) When divided equal part of 10 meter each, a piece of 5 meter is left.2) When divided equal of 6 meter each, a piece of 1 meter is left.What is the value of length n<100 meter of wire?(1) When divided equal part of 10 meter each, a piece of 5 meter is left --> $$n=10q+5$$: 5, 15, 25, ..., 95. Not sufficient.(2) When divided equal of 6 meter each, a piece of 1 meter is left --> $$n=6p+1$$: 1, 7, 13, 19, 25, ..., 97. Not sufficient.(1)+(2) General formula of $$n$$ based on $$n=10q+5$$ and $$n=6p+1$$ would be $$n=30m+25$$ --> $$n$$ can be: 25, 55 or 85. Not sufficient.Answer: E.To elaborate more. How to derive general formula of $$n$$ based on $$n=10q+5$$ and $$n=6p+1$$: divisor will be the least common multiple of above two divisors 6 and 10, hence 30. Remainder will be the first common integer in above two patterns, hence 25. So, to satisfy both conditions, $$n$$ must be of a type $$n=30m+25$$: 25, 55 or 85.For more about this concept see:manhattan-remainder-problem-93752.html#p721341when-positive-integer-n-is-divided-by-5-the-remainder-is-90442.html#p722552when-the-positive-integer-a-is-divided-by-5-and-125591.html#p1028654Hope it helps.

 Author: Runner2 [ 25 Jan 2012, 10:27 ] Post subject: Re: What is the value of length n<100 meter of wire? clear explanation

 Author: LM [ 25 Jan 2012, 20:39 ] Post subject: Re: DS-Length of wire Bunuel wrote:LM wrote:What is the value of length n<100 meter of wire?1) When divided equal part of 10 meter each, a piece of 5 meter is left.2) When divided equal of 6 meter each, a piece of 1 meter is left.What is the value of length n<100 meter of wire?(1) When divided equal part of 10 meter each, a piece of 5 meter is left --> $$n=10q+5$$: 5, 15, 25, ..., 95. Not sufficient.(2) When divided equal of 6 meter each, a piece of 1 meter is left --> $$n=6p+1$$: 1, 7, 13, 19, 25, ..., 97. Not sufficient.(1)+(2) General formula of $$n$$ based on $$n=10q+5$$ and $$n=6p+1$$ would be $$n=30m+25$$ --> $$n$$ can be: 25, 55 or 85. Not sufficient.Answer: E.To elaborate more. How to derive general formula of $$n$$ based on $$n=10q+5$$ and $$n=6p+1$$: divisor will be the least common multiple of above two divisors 6 and 10, hence 30. Remainder will be the first common integer in above two patterns, hence 25. So, to satisfy both conditions, $$n$$ must be of a type $$n=30m+25$$: 25, 55 or 85.For more about this concept see:manhattan-remainder-problem-93752.html#p721341when-positive-integer-n-is-divided-by-5-the-remainder-is-90442.html#p722552when-the-positive-integer-a-is-divided-by-5-and-125591.html#p1028654Hope it helps.To elaborate more. How to derive general formula of $$n$$ based on $$n=10q+5$$ and $$n=6p+1$$: divisor will be the least common multiple of above two divisors 6 and 10, hence 30. Remainder will be the first common integer in above two patterns, hence 25. So, to satisfy both conditions, $$n$$ must be of a type $$n=30m+25$$: 25, 55 or 85.Thanks very much. Above would have been very difficult to figure out in the real exam.

 Author: TGC [ 11 Aug 2013, 09:36 ] Post subject: Re: What is the value of length n<100 meter of wire? N<100What is N?(1).N =10A +5 ..... N can be 5,15,25,35 and so on INSUFFICIENT(2).N= 6B + 1 .... N can be 1,7,13,19,25 and so on INSUFFICIENTCombining (1).& (2).We get N = 30X + 25N can be 25,55,85Hence INSUFFICIENT(E) it is !!

 Author: smyarga [ 30 Jul 2014, 03:14 ] Post subject: Re: What is the value of length n<100 meter of wire? Actually, this problem you can solve at most in 10 seconds:)The main point here is that all numbers with exact remainder form arithmetic progression with difference=divisor.For example, all x such that "when x is divided by 5 the remainder is 1" form arithmetic progression with first element 1 and difference 5:1, 6, 11, 16, 21.....If 50

 Author: shreyast [ 10 Mar 2015, 11:59 ] Post subject: Re: What is the value of length n<100 meter of wire? smyarga wrote:Actually, this problem you can solve at most in 10 seconds:)The main point here is that all numbers with exact remainder form arithmetic progression with difference=divisor.For example, all x such that "when x is divided by 5 the remainder is 1" form arithmetic progression with first element 1 and difference 5:1, 6, 11, 16, 21.....If 5070, (1)+(2), could've been sufficient.

 Author: sudhirgupta93 [ 21 Jul 2016, 03:57 ] Post subject: Re: What is the value of length n<100 meter of wire? LM wrote:What is the value of length n<100 meter of wire?(1) When divided equal part of 10 meter each, a piece of 5 meter is left.(2) When divided equal of 6 meter each, a piece of 1 meter is left.How about this?n < 100 ----- (1)S1- When divided equal part of 10 meter each, a piece of 5 meter is left.implies n = 10k + 5, where k is some integer10k + 5 < 100 (from 1)solving k < 9.5 implies no unique solution for n as it can have multiple values. Therefore insufficient.S2- When divided equal part of 6 meter each, a piece of 1 meter is left.solving as above we get k < 16.5 which again means it is insufficient.Even combining S1 and S2 we don't reach a definite solution. Hence answer is E.

 Author: gracie [ 24 Jan 2020, 11:17 ] Post subject: Re: What is the value of length n<100 meter of wire? LM wrote:What is the value of length n<100 meter of wire?(1) When divided equal part of 10 meter each, a piece of 5 meter is left.(2) When divided equal of 6 meter each, a piece of 1 meter is left.n=10q+5n=6p+1→10q-6p=-4least values of q and p are 2 and 4 respectivelysubstituting, least value of n=25lcm of divisors 10 and 6=30so 3 possible <100 meter values of n: 25, 55, 85neither 1 nor 2 sufficientE

 Author: bumpbot [ 15 Jan 2023, 07:17 ] Post subject: Re: What is the value of length n<100 meter of wire? Hello from the GMAT Club BumpBot!Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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