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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]...
Can you pls elaborate more? _________________
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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]
05 May 2012, 01:11
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]
05 May 2012, 02:40
1
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]
05 Aug 2014, 22:50
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