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# An integer greater than 1 that is not a prime is called

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Senior Manager
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An integer greater than 1 that is not a prime is called [#permalink]  03 May 2006, 14:41
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An integer greater than 1 that is not a prime is called composite.
If the two digit integer n is greater than 20, is n composite ?

1. The tenths digit of n is a factor of the unit digits of n
2. The tenths digit of n is 2

I've a confusion, whether "tenths" and tens" digit is are same
Manager
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Re: DS - Number theory [#permalink]  03 May 2006, 14:52
gmat_crack wrote:
An integer greater than 1 that is not a prime is called composite.
If the two digit integer n is greater than 20, is n composite ?

1. The tenths digit of n is a factor of the unit digits of n
2. The tenths digit of n is 2

from the statement we know n is between 21-99

from (1)
we get that n can be 2x, 3x, 4x

so the numbers can be 22, 24, 26, 28, 33, 36,39, 44, 48

so (1) is sufficient

from (2) not enough could be 23 or 24 or whatever

so I'll go with A on this one
Manager
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Re: DS - Number theory [#permalink]  03 May 2006, 20:00
gmat_crack wrote:
An integer greater than 1 that is not a prime is called composite.
If the two digit integer n is greater than 20, is n composite ?

1. The tenths digit of n is a factor of the unit digits of n
2. The tenths digit of n is 2

I've a confusion, whether "tenths" and tens" digit is are same

'tenths' digit is the first digit after the decimal point (right of decimal point)
'tens' digit is the second digit before the decimal point (left of the decimal pont) 24, in this case 2 is the tens digit. hope this helps.
Manager
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Re: DS - Number theory [#permalink]  03 May 2006, 20:04
shampoo wrote:
gmat_crack wrote:
An integer greater than 1 that is not a prime is called composite.
If the two digit integer n is greater than 20, is n composite ?

1. The tenths digit of n is a factor of the unit digits of n
2. The tenths digit of n is 2

I've a confusion, whether "tenths" and tens" digit is are same

'tenths' digit is the first digit after the decimal point (right of decimal point)
'tens' digit is the second digit before the decimal point (left of the decimal pont) 24, in this case 2 is the tens digit. hope this helps.

Note: the above is a general rule, however, in this problem it seems that tenths refers to tens. someone correct me if I am wrong. thanks
Senior Manager
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indeed A
From st 1 it can be only such integers as 24, 36, 48 etc….all of them are composite. Suff.
From st 2 it can be 26 or 29. So insuff.
Director
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Statement 1 is insufficient
Eg 13, 17 etc.
1 is a factor of 3.

Statement 2 is insufficient
23 is a prime no

Taking 1 and 2 together,
It can only be composite

Ans = C
VP
Joined: 29 Dec 2005
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remgeo wrote:
Statement 1 is insufficient
Eg 13, 17 etc.
1 is a factor of 3.

Statement 2 is insufficient
23 is a prime no

Taking 1 and 2 together,
It can only be composite

Ans = C

hmm...
A is sufficient. the question stem says n is greater than 20.
Quote:
An integer greater than 1 that is not a prime is called composite. If the two digit integer n is greater than 20, is n composite ?

1. The tenths digit of n is a factor of the unit digits of n
2. The tenths digit of n is 2
Director
Joined: 24 Oct 2005
Posts: 660
Location: London
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Yes...

God!! Help me ..........
Manager
Joined: 27 Jan 2006
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Location: Europe
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anybody who can break it??
VP
Joined: 29 Apr 2003
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jeunesis wrote:
:shock:

anybody who can break it??

Okay let me take a stab!

Let the number be of digits xy where x is the 10th digit and y the units. BOTH positive numbers as n>20!

Thus the number: n = 10*x+y

now the stem says that x is a multiple of y!!!
Thus we can rephrase y=mx

Substitute this in the number, we get:

n = 10*x + y
= 10*x + mx
= x(10+m)

Thus, the number n is divisible by some number x!
Since, the number is greater than 20, x is NOT 1!

Thus the number is divisible by some number that is not 1 and hence is not a PRIME number!

One might argue what if n=x! In such a scenario, we get the value of m as -ve!

Hence, I still favor option A!
VP
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Using brute force

from A:
22, 24, 26, 28
33, 36, 39
44, 48
55
66
77
88
99

All of them are composite!
Manager
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I agree with A
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