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Number Property

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Number Property [#permalink] New post 19 Sep 2006, 16:04
Can someone explain?

An integer greater than 1 that is not prime is called composite. If the two digit integer n is greater than 20, is n composite?

1) The tens digit of n is a factor of the units digit of n.

2) The tens digit of n is 2
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Re: Number Property [#permalink] New post 19 Sep 2006, 16:14
govinam wrote:
Can someone explain?

An integer greater than 1 that is not prime is called composite. If the two digit integer n is greater than 20, is n composite?

1) The tens digit of n is a factor of the units digit of n. In other words, the units digit is a nonzero multiple of the tens digit.

2) The tens digit of n is 2


(1) Let 10>m>1 be the tens digit of n, then the units digit of n is km for some positive integer k<10

Thus n=10m+km=(10+k)m. Clearly n is composite (i.e non-prime) SUFF

(2) n could be 23 (prime) or 24 (composite) among other possibilities N SUFF


I get A

We could also mentally check (1) by examining the possilbities:

22 24 ..28 all composite

33 36 39

44 48

55 66 77 88 99
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 [#permalink] New post 20 Sep 2006, 08:39
OA is A. Thanks for the method. It was helpful.
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 [#permalink] New post 20 Sep 2006, 08:58
1) Bottomline: unit digit can factorize. Hence the number is NOT prime. BINGO.

2) That can give both. So wont work.

A is the answer.
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 [#permalink] New post 20 Sep 2006, 09:07
asaf one is factor of all intigers ... did u overlooked this??
  [#permalink] 20 Sep 2006, 09:07
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