SOLUTION: Can someone please explain in detail this question: If A, B, and C are positive integers, and A is a factor of B, then which of the following must be true ? (A) 2A = 4B (B) BC >

Question 976005: Can someone please explain in detail this question:
If A, B, and C are positive integers, and A is a factor of B, then which of the following must be true ?
(A) 2A = 4B
(B) BC > AC
(C) BC is a multiple of A
(D) AC is a factor of B
(E) AB is a multiple of C
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
2*A = 4*B
A = 2*B

the last equation implies that A is larger than B, but it's actually the other way around.

So choice A is false.

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"A is a factor of B" means
B = k*A
where k is some integer

Eg: B = 2*A or B = 7*A

Since A,B,C are positive, and because A is a factor of B, this makes A < B

A < B
A*C < B*C
BC > AC

So choice B is true.

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B = k*A
B*C = k*A*C
BC = (k*C)*A

so that proves BC is a multiple of A. Put another way, A is a factor of BC

That makes choice C true.

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"AC is a factor of B" is only true if C is also a factor. But we don't know if C is a factor of B or not. So we can't say it's true.

Therefore, choice D is false.

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This is similar to choice D. We would have to know if C is factor of either A or B. But we're not given this info.

Choice E is false.
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The only true statements are
(B) BC > AC
(C) BC is a multiple of A

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Jim
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