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An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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

Given: $$n>20$$ --> two digit integer can be written as follows: $$n=10b+a>20$$ --> $$2\leq{b}\leq{9}$$, $$0\leq{a}\leq{9}$$.

(1) The tens digit of n is a factor of the units digit of n. This statement implies that $$a=kb$$, ($$0\leq{k}\leq{4}$$) --> $$n=10b+a=10b+kb=b(10+k)$$ --> as $$b\geq{2}$$, $$n$$ will always be composite and factor of $$b$$. Sufficient

(2) The tens digit of n is 2. This statement implies that $$b=2$$, but $$n$$ can be for instance composite 25 or prime 29. Not sufficient.

Answer: A.

chetan2u wrote:
A..
SI tells us that the tens digit is a factor of units digit so possible values of units digit are 4,6,8,9.....all would be even nos except no ending with digit 9, which will be 39... so all r composite....
SII.. no can be any of 21,22,23.....29..ie mix of composite and prime

Actually units digit of $$n$$ can be any digit but 1, meaning that 0, 2, 3, 5, 7 too. And for 9: 99 also fits: eg . 30, 40, 50, 60, 70, 80, 90, 22, 33, 55, 77, 99.
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Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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me too A.

considering A, the number can be written as

a(ak)

where a is the tens digit and ak is the unit digit, k is some constant.

= 10a + ak
= a(10+k)

this is always divisible by a and hence composite since a is not equal to 1
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Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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X & Y wrote:
An integer grater 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

Plz Explain..

(1) 24 (2 is a factor of 4), 39 (3 is a factor of 9), 48 (4 is a factor of 8) ... sufficient

(2) 22 composite, 23 not composite - not sufficient
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Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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A..
SI tells us that the tens digit is a factor of units digit so possible values of units digit are 4,6,8,9.....all would be even nos except no ending with digit 9, which will be 39... so all r composite....
SII.. no can be any of 21,22,23.....29..ie mix of composite and prime
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Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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ajit257 wrote:
Q13:
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.

Not sure about the ans

The moment I hear two digit prime number, I think of numbers having 1/3/7/9 as unit's digit. A two digit number ending in 0/2/4/5/6/8 cannot be prime since they are either even or a multiple of 5 (if it is a single digit, 5 is prime)

Stmnt 1: Ten's digit is a factor of the unit's digit.
It is easy to see that there are many such composite numbers e.g. 24, 26 etc.

I will try to find if there are any such prime numbers: The only factor of 1 is 1; of 3 are 1 and 3; of 7 are 1 and 7; of 9 are 1, 3 and 9.
11, 13, 17 and 19 are not allowed since the number should be greater than 20.
33, 77, 39 and 99 are all composite. So there is no such prime number. All such number will be composite so n is composite. Hence sufficient.

Stmnt 2: The tens digit of n is 2.
21 is not prime while 23 is. Hence not sufficient.

Answer (A).
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Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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Hi Bunuel,

I got the answer by other way. However, i would like to understand your explanation on (1) where you stated that a=kb, (0<=k<=4) --> n=10b+a=10b+kb=b(10+k) --> as b>=2, n will always be composite and factor of b.

Can you please explain in detail this a=kb part? why (0<=k<=4)?

Regards,
Mitesh
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Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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mrvora wrote:
Hi Bunuel,

I got the answer by other way. However, i would like to understand your explanation on (1) where you stated that a=kb, (0<=k<=4) --> n=10b+a=10b+kb=b(10+k) --> as b>=2, n will always be composite and factor of b.

Can you please explain in detail this a=kb part? why (0<=k<=4)?

Regards,
Mitesh

(1) says that the tens digit of n, which is b, is a factor of the units digit of n, which is a. So, b is a factor of a --> $$a=kb$$, for some integer k.

As for $$0\leq{k}\leq{4}$$: the least value of b is 2, thus if k is 5 or more, then a becomes 10 or more, which is not possible since we know that a is a digit ($$0\leq{k}\leq{4}$$).

Hope it's clear.
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GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37 Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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A two digit number comprised of two composite numbers is always composite. (1) is sufficient.

B is not sufficient. With thens digit as 2, the number could be 29, which is prime and 24, which is composite.
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Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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hdwnkr wrote:
A two digit number comprised of two composite numbers is always composite. (1) is sufficient.

B is not sufficient. With thens digit as 2, the number could be 29, which is prime and 24, which is composite.

Hi,
the statement may not be correct... 89 is a prime number, which has both digits composite..
stat 1 is suff but not for the reason you have mentioned..
there is no prime number till 100 satisfying the condition of 1
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Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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

Given: $$n>20$$ --> two digit integer can be written as follows: $$n=10b+a>20$$ --> $$2\leq{b}\leq{9}$$, $$0\leq{a}\leq{9}$$.

(1) The tens digit of n is a factor of the units digit of n. This statement implies that $$a=kb$$, ($$0\leq{k}\leq{4}$$) --> $$n=10b+a=10b+kb=b(10+k)$$ --> as $$b\geq{2}$$, $$n$$ will always be composite and factor of $$b$$. Sufficient

(2) The tens digit of n is 2. This statement implies that $$b=2$$, but $$n$$ can be for instance composite 25 or prime 29. Not sufficient.

Answer: A.

chetan2u wrote:
A..
SI tells us that the tens digit is a factor of units digit so possible values of units digit are 4,6,8,9.....all would be even nos except no ending with digit 9, which will be 39... so all r composite....
SII.. no can be any of 21,22,23.....29..ie mix of composite and prime

Actually units digit of $$n$$ can be any digit but 1, meaning that 0, 2, 3, 5, 7 too. And for 9: 99 also fits: eg . 30, 40, 50, 60, 70, 80, 90, 22, 33, 55, 77, 99.

Hi ,

What about No. 71 .
it is a prime number and
7 is factor of 1.
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Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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munishrattanpal wrote:
Bunuel wrote:
An integer grater than 1 that is not prime is called composite. If the two-digit integer n is greater than 20, is n composite?

Given: $$n>20$$ --> two digit integer can be written as follows: $$n=10b+a>20$$ --> $$2\leq{b}\leq{9}$$, $$0\leq{a}\leq{9}$$.

(1) The tens digit of n is a factor of the units digit of n. This statement implies that $$a=kb$$, ($$0\leq{k}\leq{4}$$) --> $$n=10b+a=10b+kb=b(10+k)$$ --> as $$b\geq{2}$$, $$n$$ will always be composite and factor of $$b$$. Sufficient

(2) The tens digit of n is 2. This statement implies that $$b=2$$, but $$n$$ can be for instance composite 25 or prime 29. Not sufficient.

Answer: A.

chetan2u wrote:
A..
SI tells us that the tens digit is a factor of units digit so possible values of units digit are 4,6,8,9.....all would be even nos except no ending with digit 9, which will be 39... so all r composite....
SII.. no can be any of 21,22,23.....29..ie mix of composite and prime

Actually units digit of $$n$$ can be any digit but 1, meaning that 0, 2, 3, 5, 7 too. And for 9: 99 also fits: eg . 30, 40, 50, 60, 70, 80, 90, 22, 33, 55, 77, 99.

Hi ,

What about No. 71 .
it is a prime number and
7 is factor of 1.

7 is not a factor of 1, 7 is a multiple of 1.
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Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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Please explain, why can't we consider 31( or 41) number for statement 1.

Is 3 a factor of 1?
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Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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20043856 wrote:
Please explain, why can't we consider 31( or 41) number for statement 1.

Is 3 a factor of 1?

In 31, 3 is the tens digit and 1 is the units digit. (1) says that the tens digit of n is a factor of the units digit of n but 3 is NOT a factor of 1, 1 is a factor of 3, or in another way 3 is a multiple of 1.

Hope it's clear.
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Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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For condition one - They have mentioned that ten's digit is a factor of one's digit.
Implying that numbers are - 22 ( 2 is factor of 2 ) , 24 ( 2 is a factor of 4 ) , 26, 28, 33, 36, 39 etc. Thus these numbers are composite as they are not prime.

Condition 2 , gives us 21,22,23,24....29. Of which 23, 29 are prime . Thus insufficient.

IMO - A .
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Re: An integer grater than 1 that is not prime is called composite. If the  [#permalink]

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gmatmba wrote:
X & Y wrote:
An integer grater 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

Plz Explain..

(1) 24 (2 is a factor of 4), 39 (3 is a factor of 9), 48 (4 is a factor of 8) ... sufficient

(2) 22 composite, 23 not composite - not sufficient

This isn't a good way to do it because really you should be looking at primes and not composites. If one prime had a factor where the tens digit was a factor of its units then your answer is destroyed. All you did was prove that composites have some tens digits which are factors of units digits--it is impossible above 5 really for the tens to be a factor of the units because 6 doesn't go into 1,2,3,4,5,7,8,9. And we know 66,77,88 and 99 aren't prime as they have factors of 11 .
(1) It's better to list the prime. The prime between 20-60--you should memorize. Are: 23,29,31,37,41,43,49,53,59 and 61. Notice how none of the Tens are factors of the units number. So we know for a prime that the tens digit is not a factor of the units digit. For a composite we can have one example 22, in which we see the tens is a factor of the units. (2 is a factor of 2). So we can see primes don't have tens that are factors of units between 20-100 and composites can. Therefore it is not a prime and therefore is a composite

(2) If the 10's digit is 2, the number could be 22 or 23. NS

Answer is therefore A
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