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# Is 1,000 a factor of k? a) 2,000 is a factor of 4k b) 8 is a

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CEO
Joined: 15 Aug 2003
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Is 1,000 a factor of k? a) 2,000 is a factor of 4k b) 8 is a [#permalink]  09 Oct 2003, 15:00
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Is 1,000 a factor of k?

a) 2,000 is a factor of 4k

b) 8 is a factor of k
Manager
Joined: 26 Aug 2003
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[#permalink]  10 Oct 2003, 05:08
My guess is C as well.

Reasoning:

(1) In other words 500 is a multiple of K.
(2) This says 8 is multiple of K but that has nothing to do with 1000.
(combined) If 500 is multiple of K then you can divide further and see how far you can go with a multiple of 2 in the denominator. You end up with 125, this is where (2) comes in the picture, and you can see that K has to be divisible by at least by twice the 500, which is 1000.
Intern
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[#permalink]  10 Oct 2003, 06:24
The answer is D. 2000 and 8 both go by 1,000.
Manager
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Re: D [#permalink]  10 Oct 2003, 06:44
watchdog wrote:
The answer is D. 2000 and 8 both go by 1,000.

(1) Let's say K is 500, thus 4K = 2000. 4K divisible by 2000. But 1000 is not a factor of 500.
(2) K = 320. K/8 = 40. Doesn't say anything about 1000 being a factor.
(combined) Since K has to be at least 2*500 = 1000, you can say 1000/8 = 125. And 1000/1000 = 1.
Intern
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[#permalink]  14 Oct 2003, 20:53
I would pick C. Here is the reasoning:

Statement in other words: Is 2^3 x 5^3 factors of K?

1. 2^4 x 5^3 is a factor of 4k, therefore, 2^2 x 5^3 is a factor of K. -Not sufficient since we need one more 2 to affirm the statement.

2. 2^3 is a factor of K, not enough.

Having both, 2^2 x 5^3 and 2^3 as factor of k is enough to say that 2^3 x 5^3 are factors of K
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SVP
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[#permalink]  14 Oct 2003, 22:14
got C as well

(1) k=500p NOT SUFF
(2) k=8q NOT SUFF

Combine: k=LCM(500, 8)*r=1000r
SVP
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[#permalink]  14 Oct 2003, 22:32
YES!!!
CEO
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Kudos [?]: 697 [0], given: 781

[#permalink]  14 Oct 2003, 22:48
stolyar wrote:
YES!!!

Stolyar

can we say ,in general, that..

If two numbers are factors of k, then their LCM is also a factor of K.
SVP
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[#permalink]  14 Oct 2003, 22:57
I think yes.
If two numbers A and B are both factors of X, then X is either LCM(A, B) itself or a multiple of LCM(A, B)
[#permalink] 14 Oct 2003, 22:57
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# Is 1,000 a factor of k? a) 2,000 is a factor of 4k b) 8 is a

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