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 Author: questioner [ Sat Dec 25, 2010 6:23 pm ] Post subject: GMAT Number Theory How many two-digit numbers yield a remainder of 1 when divided by both 4 and 14?A. 0B. 1C. 2D. 3E. 4(D) Let’s use n to denote a two-digit number that fits the requirement in the question.Since we are looking for a remainder of 1 when n is divided by 4 or 14, then (n – 1) must be divisible by both 4 and 14. All numbers divisible by both 4 and 14 must be divisible by their least common multiple, which is 28.So n – 1 can equal any two-digit multiple of 28. These possible values are:n – 1 = 28, 56, or 84.Therefore, n = 29, 57, or 85 (3 different two-digit numbers).The correct answer is choice (D).----------43 is also another number that yeild a remainder of 1 when divided by both 4 and 14. So the answer should be D.

 Author: Gennadiy [ Sat Dec 25, 2010 6:24 pm ] Post subject: Re: GMAT Number Theory 43 = 40 + 3 = 4 × 10 + 3When we divide 43 by 4 the remainder is 3, NOT 1.

 Author: robertian23 [ Fri Feb 03, 2012 10:49 am ] Post subject: Re: GMAT Number Theory What about 15? 15 = 14 × 1 + 1

 Author: Gennadiy [ Tue Feb 07, 2012 8:00 am ] Post subject: Re: GMAT Number Theory robertian23 wrote:What about 15? 15 = 14 × 1 + 115 does NOT yield 1 as a remainder, when it is divided by 4.15 = 3 × 4 + 3

 Author: questioner [ Mon Feb 04, 2013 1:46 pm ] Post subject: Re: GMAT Number Theory Why not 99?

 Author: Gennadiy [ Mon Feb 04, 2013 1:49 pm ] Post subject: Re: GMAT Number Theory Quote:Why not 99?99 = 4 × 24 + 3So 99 does not give 1 as a remainder when divided by 4.

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