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GMAT Number Theory http://www.800score.com/forum/viewtopic.php?f=3&t=113 
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Author:  questioner [ Sat Dec 25, 2010 6:23 pm ] 
Post subject:  GMAT Number Theory 
How many twodigit numbers yield a remainder of 1 when divided by both 4 and 14? A. 0 B. 1 C. 2 D. 3 E. 4 (D) Let’s use n to denote a twodigit 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 twodigit multiple of 28. These possible values are: n – 1 = 28, 56, or 84. Therefore, n = 29, 57, or 85 (3 different twodigit 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 + 3 When 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 + 1 15 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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