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Post subject: GMAT Number Theory Posted: Sat Dec 25, 2010 6:23 pm 

Joined: Sun May 30, 2010 3:15 am Posts: 424

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.


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Gennadiy

Post subject: Re: GMAT Number Theory Posted: Sat Dec 25, 2010 6:24 pm 

Joined: Sun May 30, 2010 2:23 am Posts: 498

43 = 40 + 3 = 4 × 10 + 3
When we divide 43 by 4 the remainder is 3, NOT 1.


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robertian23

Post subject: Re: GMAT Number Theory Posted: Fri Feb 03, 2012 10:49 am 

Joined: Fri Feb 03, 2012 10:47 am Posts: 1

What about 15? 15 = 14 × 1 + 1


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Gennadiy

Post subject: Re: GMAT Number Theory Posted: Tue Feb 07, 2012 8:00 am 

Joined: Sun May 30, 2010 2:23 am Posts: 498


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questioner

Post subject: Re: GMAT Number Theory Posted: Mon Feb 04, 2013 1:46 pm 

Joined: Sun May 30, 2010 3:15 am Posts: 424


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Gennadiy

Post subject: Re: GMAT Number Theory Posted: Mon Feb 04, 2013 1:49 pm 

Joined: Sun May 30, 2010 2:23 am Posts: 498


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