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Number properties

by Carloselopez » Sun Sep 08, 2013 5:10 pm
Hi all,

This problem could be easy for some of you, but it was very tricky for me:

If x is an integer, is 15 a factor of x?

1) 15 is a factor of 10x.
2) 15 is a factor of 11x.

I appreciate your help.
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by Java_85 » Sun Sep 08, 2013 8:27 pm
IMO B is the answer.

1) 15 is a factor of 10x ==> 10x have 3 and 5 factors ==> x should have the 3 because 10 just have the 2 and 5 factors. ==> answer could be B C E.

2) 15 is a factor of 11x. ==> 11x have 3 and 5 factors ==> x should have both 3 and 5 factors because 11 just have the factor 11. ==> B alone is sufficient because x has both 3 and 5 factors i.e. 15 is a factor of x.
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by Carloselopez » Mon Sep 09, 2013 10:10 am
Java_85 wrote:IMO B is the answer.

1) 15 is a factor of 10x ==> 10x have 3 and 5 factors ==> x should have the 3 because 10 just have the 2 and 5 factors. ==> answer could be B C E.

2) 15 is a factor of 11x. ==> 11x have 3 and 5 factors ==> x should have both 3 and 5 factors because 11 just have the factor 11. ==> B alone is sufficient because x has both 3 and 5 factors i.e. 15 is a factor of x.

Hi Java_85,

Thabk you for your reply, but I'm sorry I don't get your explanation....
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by Java_85 » Mon Sep 09, 2013 10:35 am
Hi Carloselopez,
I'll rephrase my explanation:

Rule: if a number want to have a factor of 15, it should have both 3 and 5 factors.

10x = 1*2*5*x --> But for 10x to have the factor 15 it should have the 3 too, which is in x, so we just know that x has the factor 3
Does x has the factor 5? We don't know ==> (1) is not sufficient.

11x= 1*11*x --> But for 11x to have the factor 15 it should have factors 3 and 5, which are in x, so x has both 3 and 5 factors --> (2) is sufficient.

hope this helps.
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by TheGmatTutor » Tue Sep 10, 2013 8:30 am
For 15 to be a factor of x, x needs to have both 3 and 5 as factors.

1) 15 is a factor of 10x

- This proves that 10x has both 3 and 5 as factors
- However, 10 has 2 and 5 as factors. So you don't know if x itself has 5 as a factor. Therefore, statement 1 is insufficient

2) 15 is a factor of 11x

- This proves that x itself must have 3 and 5 as factors. Since 11 is prime, it only supplies 11 as a factor. Therefore statement 2 is sufficient

Answer: B
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by Mike@Magoosh » Tue Sep 10, 2013 3:34 pm
Carloselopez wrote:Hi all,
This problem could be easy for some of you, but it was very tricky for me:

If x is an integer, is 15 a factor of x?
1) 15 is a factor of 10x.
2) 15 is a factor of 11x.

I appreciate your help.
Hello Carloselopez,
I'll just add my two cents.

If this problem struck you as difficult, then this suggests to me that you would really benefit from learning more about prime factorization. See this post:
https://magoosh.com/gmat/2012/gmat-math-factors/

You may also find this more general blog informative:
https://magoosh.com/gmat/2013/gmat-number-properties/

I hope you find all this helpful. Let me know if you have any more questions along these lines.
Mike :-)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
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by Carloselopez » Thu Sep 12, 2013 5:27 am
Java_85 wrote:Hi Carloselopez,
I'll rephrase my explanation:

Rule: if a number want to have a factor of 15, it should have both 3 and 5 factors.

10x = 1*2*5*x --> But for 10x to have the factor 15 it should have the 3 too, which is in x, so we just know that x has the factor 3
Does x has the factor 5? We don't know ==> (1) is not sufficient.

11x= 1*11*x --> But for 11x to have the factor 15 it should have factors 3 and 5, which are in x, so x has both 3 and 5 factors --> (2) is sufficient.

hope this helps.
Thank you Java, now it's clear for me!
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by Carloselopez » Thu Sep 12, 2013 5:33 am
Mike@Magoosh wrote:
Carloselopez wrote:Hi all,
This problem could be easy for some of you, but it was very tricky for me:

If x is an integer, is 15 a factor of x?
1) 15 is a factor of 10x.
2) 15 is a factor of 11x.

I appreciate your help.
Hello Carloselopez,
I'll just add my two cents.

If this problem struck you as difficult, then this suggests to me that you would really benefit from learning more about prime factorization. See this post:
https://magoosh.com/gmat/2012/gmat-math-factors/

You may also find this more general blog informative:
https://magoosh.com/gmat/2013/gmat-number-properties/

I hope you find all this helpful. Let me know if you have any more questions along these lines.
Mike :-)
Thabk you Mike, it is really helpful! Carlos
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