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OG If x is a multiple of 4

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AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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OG If x is a multiple of 4

Post Tue Jul 25, 2017 8:22 pm
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

B

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Post Mon Aug 14, 2017 1:11 pm
AbeNeedsAnswers wrote:
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

B
Since x is a multiple of 4, x = 4k for some positive integer k. Similarly, since y is a multiple of 6, y = 6m for some positive integer m. Thus, xy = (4k)(6m) = 24km. We see that regardless what k and m are, 24km will always be divisible by 8 and 12, but not necessarily by 18.

Answer: B

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Post Fri Aug 18, 2017 2:18 pm
If x is a multiple of m and y is a multiple of n, then x*y must be a multiple of the LCM of m and n and ALL FACTORS of that LCM. Here the LCM of 4 and 6 is 12, so that's our answer: all factors of 12.

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Post Mon Aug 14, 2017 1:11 pm
AbeNeedsAnswers wrote:
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

B
Since x is a multiple of 4, x = 4k for some positive integer k. Similarly, since y is a multiple of 6, y = 6m for some positive integer m. Thus, xy = (4k)(6m) = 24km. We see that regardless what k and m are, 24km will always be divisible by 8 and 12, but not necessarily by 18.

Answer: B

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Post Fri Aug 18, 2017 2:18 pm
If x is a multiple of m and y is a multiple of n, then x*y must be a multiple of the LCM of m and n and ALL FACTORS of that LCM. Here the LCM of 4 and 6 is 12, so that's our answer: all factors of 12.

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Post Wed Jul 26, 2017 6:48 pm
Hi AbeNeedsAnswers,

This question can be solved by TESTing VALUES.

We're told that X and Y are both POSITIVE INTEGERS, that X is a multiple of 4 and that Y is a multiple of 6. We're asked what (X)(Y) MUST be a multiple of (meaning every time, no matter what values we use for X and Y).

With Roman Numeral questions, it's often useful to use the Roman Numerals 'against' the prompt, but for this question I'm going to do a bit of 'brute force' work first to define the patterns involved.

X could be 4, 8, 12, 16, 20, etc.
Y could be 6, 12, 18, 24, 30, etc.

So (X)(Y) could be 24, 48, 72, 96, etc. Starting with the smallest possibility, notice that ALL the possible values are multiples of 24. That means that (X)(Y) would have to be a multiple of both 8 and 12 (since both of those numbers divide into any multiple of 24). 18 does NOT divide evenly into 24 though, so that option is not part of the correct answer.

Final Answer: B

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