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# Number Property

Author Message
Manager
Joined: 20 May 2006
Posts: 96

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19 Sep 2006, 16:04
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1262

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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
Manager
Joined: 20 May 2006
Posts: 96

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20 Sep 2006, 08:39
OA is A. Thanks for the method. It was helpful.
Director
Joined: 06 Sep 2006
Posts: 736

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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.

SVP
Joined: 05 Jul 2006
Posts: 1747

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20 Sep 2006, 09:07
asaf one is factor of all intigers ... did u overlooked this??
20 Sep 2006, 09:07
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