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 Post subject: GMAT Number Theory
PostPosted: Mon Apr 29, 2013 8:39 am 
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How many two-digit 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 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.


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 Post subject: Re: GMAT Number Theory
PostPosted: Mon Apr 29, 2013 8:45 am 
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43 = 40 + 3 = 4 × 10 + 3

When we divide 43 by 4 the remainder is 3, NOT 1.


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 Post subject: Re: GMAT Number Theory
PostPosted: Mon Apr 29, 2013 8:46 am 
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What about 15? 15 = 14 × 1 + 1


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 Post subject: Re: GMAT Number Theory
PostPosted: Mon Apr 29, 2013 8:46 am 
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Quote:
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


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 Post subject: Re: GMAT Number Theory
PostPosted: Mon Apr 29, 2013 8:51 am 
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Why not 99?


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 Post subject: Re: GMAT Number Theory
PostPosted: Mon Apr 29, 2013 8:52 am 
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Quote:
Why not 99?
99 = 4 × 24 + 3
So 99 does not give 1 as a remainder when divided by 4.


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