Number Properties

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hariharakarthi: Master | Next Rank: 500 Posts; Posts: 131; Joined: Tue Apr 22, 2008 1:54 pm; Thanked: 3 times; GMAT Score:550

by hariharakarthi » Mon Nov 09, 2009 7:09 am

If j and k are positive integers, is k a divisor of 24?

(1) The product jk is a divisor of 48

(2) j =3

Please Explain in detail.

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Source: Beat The GMAT — Data Sufficiency | Mon Nov 09, 2009 7:09 am

palvarez: Master | Next Rank: 500 Posts; Posts: 199; Joined: Sat Oct 24, 2009 4:43 pm; Thanked: 22 times; GMAT Score:710

by palvarez » Mon Nov 09, 2009 7:21 am

1. 48 divides jk. 24 divides k only when gcd(24, j) = 1, which we don't know.

2. j = 3. Insuff.

Combining:

gcd(24,j) = 3. Insufficient.

OR
jk = 48m ==> k = 16m. k is a multiple of 24 when m is a multiple of 3. Insufficient.

E is the answer.

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antondesh: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Tue Aug 18, 2009 9:46 am; Thanked: 4 times

by antondesh » Mon Nov 09, 2009 7:35 am

I think it's C... The question is basically asking whether 24 divided by k gives us an integer.

(1) Insufficient. Let's say j=6, k=8. That way jk=48 and k is the divisor of 24. But now let's say that j=1, k=48. That way jk=48, and k is not the divisor of 24.

(2) Insufficent, because we are told nothing about k.

Combined we get 3k=48 which means k=16. So k is not a divisor of 24. Sufficent.

What's the OA?

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2010gmat: Master | Next Rank: 500 Posts; Posts: 371; Joined: Fri Mar 06, 2009 2:48 am; Thanked: 27 times; GMAT Score:740

by 2010gmat » Mon Nov 09, 2009 9:55 am

E for me too

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Mon Nov 09, 2009 11:28 am

I agree with antondesh. If you guys think it is E, please use the same method of explaining as antondesh; please explain in a simple way so everyone can benefit from you.

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antondesh: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Tue Aug 18, 2009 9:46 am; Thanked: 4 times

by antondesh » Mon Nov 09, 2009 11:46 am

I'm changing my reply to E

Here's the reasoning:

Separately, the statements are insuffient (refer to my earlier post).

Now combined, we know that jk = a divisor of 48. We also know that j=3.

So our equation is 3k = divisor of 48.

What are the divisors of 48? 1, 48, 6, 8, 12, 24 etc...

So there are multiple values for k. Which means that both statements together are insuffient.

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Mon Nov 09, 2009 11:50 am

antondesh wrote:I'm changing my reply to E

Here's the reasoning:

Separately, the statements are insuffient (refer to my earlier post).

Now combined, we know that jk = a divisor of 48. We also know that j=3.

So our equation is 3k = divisor of 48.

What are the divisors of 48? 1, 48, 6, 8, 12, 24 etc...

So there are multiple values for k. Which means that both statements together are insuffient.

but k is 2*2*2*2. I can say E because 2 and 2*2 and 2*2*2 all devise 24 but 2*2*2*2 does not devise 24.

Am I right ? PLease expalin your answer more.

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pmFollowed by: 3 members; Location: California; Thanked: 13 times

by heshamelaziry » Mon Nov 09, 2009 12:08 pm

I take my last posting back. I do not understand at all. How can k be anything other than 16 ? PLease explain

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antondesh: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Tue Aug 18, 2009 9:46 am; Thanked: 4 times

by antondesh » Mon Nov 09, 2009 12:30 pm

Here are our two statements:

(1) The product jk is a divisor of 48

(2) j =3

Think about it. Statement (1) says that the product of j and k is a divisor of 48. Statement (2) says that j = 3.

So if we combine the two statements, we get:

"The product of 3 and k is a divisor of 48."

It's NOT saying that the product of 3 and k equals 48. It's saying that the product of 3 and k is a divisor of 48. So it's saying that if we take k and multiply it by 3, that result will divide 48 evenly.

So k could be equal to 16. In that case 3*16=48. And 48 is a divisor of 48.

Or k could be equal to 4. In which case 3*4=12. And 12 is a divisor of 48.

The bottom line, we just know what k equals. Therefore we don't know if it divides 24 evenly. (For example, 16 doesn't divide 24 evenly but 4 does).

Choice E

Let me know if this is clear.

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hariharakarthi: Master | Next Rank: 500 Posts; Posts: 131; Joined: Tue Apr 22, 2008 1:54 pm; Thanked: 3 times; GMAT Score:550

by hariharakarthi » Mon Nov 09, 2009 6:18 pm

Ans is E.

Rephrase the question: Find the value of K?
Two stmts alone are insuff.

Together:
jk is a divisor of 48. Moreover, j=3.
Prime factors of 48 = Four 2's and one 3.

48/jk = should be an integer as per stmt 1.

(2^4).3/3k = Integer
Here, k can take any values from 2,2^1,2^2, 2^3 and 2^4.
So, have multiple values of k. Hence, E is the answer.

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viju9162: Master | Next Rank: 500 Posts; Posts: 434; Joined: Mon Jun 11, 2007 9:48 pm; Location: Bangalore; Thanked: 6 times; GMAT Score:600

by viju9162 » Mon Nov 09, 2009 10:05 pm

Answer is E..

From A, the factors for 48 can be 2,3,8,16..

16 is not divisor of 24..

Therefore not sufficient..

From B, you cant determine and as well from C..

"Native of" is used for a individual while "Native to" is used for a large group

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