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We can see that xy is a multiple of both 8 and 12, but not 18.

Option (B)

@GyanOne - LCM of 4 and 6 = 12 or if I compare as mentioned in the below series... I can see only multiple of 12. Multiple of 4 - 4, 8, [highlight]12[/highlight], 16, 20, [highlight]24[/highlight]... Multiple of 6 - 6, [highlight]12[/highlight], 18, [highlight]24[/highlight]...

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so all factors of x has to have 2*2 in it and y has to have 2*3 in it.

lets look at our options

i) 8= 2*2*2. If we look at our prime factor boxes above we see that we have to have at least three 2's. (two in 4 and one in 6) so yes 8 is a multiple.

ii) 12= 2*2*3. Again if we look at our prime factor boxes above we see that it contains 2*2*3.

iii) 18= 2*3*3. For 18 we need two 3's and if you look at your prime factor boxes you see that we only have one 3, therefore 18 is not an option.

Re: If the positive integer x is a multiple of 4? [#permalink]

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05 May 2012, 02:11

Hello,

quick question, I got the answer right, though I am having some problems with the "plug in numbers" approach here. Can anybody help real quick with an example?

Re: If the positive integer x is a multiple of 4? [#permalink]

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05 May 2012, 03:40

2

This post received KUDOS

Expert's post

andih wrote:

Hello,

quick question, I got the answer right, though I am having some problems with the "plug in numbers" approach here. Can anybody help real quick with an example?

Thanks in advance!

If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 6, then xy must be a multiple of which of the following? I. 8 II. 12 III 18

A. II only B. I and II only C. I and III only D. II and III only E. I, II and III

First of all notice that we are asked \(xy\) MUST be a multiple of which of the following, not COULD be a multiple.

\(x\) is a multiple of 4 --> \(x=4m\), for some positive multiple \(m\), so \(x\) can be: 4, 8, 12, ... \(y\) is a multiple of 6 --> \(y=6n\), for some positive multiple \(n\), so \(y\) can be: 6, 12, 18, ...

So, \(xy=(4m)*(6n)=24mn\), so \(xy\) is in any case a multiple of 24, which means it must be a multiple of 8 and 12, but not necessarily of 18. For example the least value of \(x\) is 4 and the least value of \(y\) is 6, so the least value of \(xy\) is 24, which is a multiple of both 8 and 12, but not 18.

Hello I try ! X can be written as X=2x2K where K is a whole number which belongs to R Y can be written as Y= 3X2 L where L is a whole number which belongs to R HENCE XY can BE WRITTEN as 2x2x3x2xKxL

Hence XY must be a multiple of 8 and 12 For 18 we misse a 3

Re: If the positive integer x is a multiple of 4? [#permalink]

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05 Aug 2014, 23:50

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Re: If the positive integer x is a multiple of 4? [#permalink]

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13 Mar 2016, 12:32

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