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# an integer > 1 that is not prime is called composite. If

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an integer > 1 that is not prime is called composite. If [#permalink]

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26 Nov 2006, 16:07
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an integer > 1 that is not prime is called composite. If the 2 digit integer n is greater than 20, is n composite?

1. the ten digits of n is a factor of the units digit of n
2. the ten digit of n is 2.
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26 Nov 2006, 16:36
From 1) There are no prime numbers between 20 and 100 where the tens digit is a factor of the units digit therefore n must be composite. SUFF

From 2) n could be 23 and therefore prime or 24 and therefore composite so INSUFF.

A for me
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26 Nov 2006, 19:24
For eg 13, The 10th place (1) is a factor of units place(3)
Statements 1 and 2 together give the answer
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26 Nov 2006, 20:01
A for me too.

imagine the number is xy.
x >= 2, y > 0.

if x is a prime, then y must also be the same prime. so 11 is a factor.

if x is not a prime, then x has a factor which is also a factor of y. and hence a factor of this number xy.

so xy must have another factor other than itself and 1. so xy is a composite.

2. is Insuff. take 23. 24.
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26 Nov 2006, 23:44
This is a good one..
A for me too
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27 Nov 2006, 00:35
an integer > 1 that is not prime is called composite. If the 2 digit integer n is greater than 20, is n composite?

1. the ten digits of n is a factor of the units digit of n
2. the ten digit of n is 2.

A?

From 1. 99 / 99 / 33 / 22 /66 etc.... meets the rule, the tens digit 9 is a factor of the units digit 9? But we cannot consider 13, since the integer is greater than 20. SUFF

From 2. n could be 24 (composite) or 23 (prime) INSUFF
27 Nov 2006, 00:35
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