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An integer greater than 1 that is not prime is called

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An integer greater than 1 that is not prime is called [#permalink]

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20 Jun 2008, 00:14
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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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Director
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20 Jun 2008, 00:20
ritula wrote:
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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

its a yes / no question,

statement 1 : possible options where tens digit is a factor of unit digit, 21,22,31,33,41,42,44......... we can see that we have both prime (23, 31, 41....) and composite in the set. Not Suff
statement 2 : 21,22,23,24..... again Not Suff

Combine, we have only 21 and 22, both composite ... Suff

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CEO
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20 Jun 2008, 03:29
A.

"tens digit is a factor of the units digit" now that means if n > 20 the following will work :
22 24 26 28 33 36 39 44 48 and so on. I feel A is SUFFICIENT.

B doesnt tell us anything, both 23 and 24 can be values according to be so INSUFFICIENT.

This problem is commonly referred to as a C trap ....

OA ?

ritula wrote:
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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Intern
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20 Jun 2008, 05:32
In the case of 21 ,2 is not a factor of 1.

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Director
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20 Jun 2008, 08:45
bsd_lover wrote:
A.

"tens digit is a factor of the units digit" now that means if n > 20 the following will work :
22 24 26 28 33 36 39 44 48 and so on. I feel A is SUFFICIENT.

B doesnt tell us anything, both 23 and 24 can be values according to be so INSUFFICIENT.

This problem is commonly referred to as a C trap ....

OA ?

ritula wrote:
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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

oops ..... my bad..... you should never try to solve a PS question after a heavy north indian lunch .......

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Intern
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20 Jun 2008, 09:06
What about 139? That is prime and shows that A is not sufficient either. There has to be a way to so this simply without having to go so high for an example.

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Director
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20 Jun 2008, 09:07
jmaynardj wrote:

the question talks about only two digit number greater than 20

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20 Jun 2008, 09:09
durgesh79 wrote:
jmaynardj wrote:

the question talks about only two digit number greater than 20

heh, read the question for the win. I just preached about it in a different thread too

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20 Jun 2008, 09:15
Easiest way to not have to guess for two digits where "The tens digit of n is a factor of the units digit of n." To show insufficient we would have to show both a composite and a prime.

As it seems that they are all composite we look for a prime. So all odd ones digits. Also ruling out all number <20.
9 - 3,9 => 39, 99
7 - 7 => 77
5 - 5 => 55
3 - 3 => 33

Those are the only ones potentially a prime following the rule and they are all composite. Would love to have time to do the proof of this, but number will suffice for now.

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Senior Manager
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20 Jun 2008, 09:38
ritula wrote:
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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

A.

statement (1) is sufficient. any tens digit of n is a factor of the units digit that means the number is divisible by more than 2 factors (1 and itself ) so there is no way it can be prime. Sufficient. (e.g. 36, 24, 33, etc. )

remember a factor of a number should be either less than or equal to that number.

statement 2 is insufficient. It doesn't explain anything.

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20 Jun 2008, 09:57
Vavali wrote:
ritula wrote:

statement (1) is sufficient. any tens digit of n is a factor of the units digit that means the number is divisible by more than 2 factors (1 and itself ) so there is no way it can be prime. Sufficient. (e.g. 36, 24, 33, etc. )

remember a factor of a number should be either less than or equal to that number.

This sounds good but is not a proof, at least as far as I can see. You jump from saying "any tens digit of n is a factor of the units digit" OK that is given
But that is not proof that "the number is divisible by more than 2 factors"

In fact if the problem was not limited to 2 digits it would counter your reasoning. (ex. 139 above)

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Re: DS- Composite integer   [#permalink] 20 Jun 2008, 09:57
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