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# If x, y and z are positive integers, is xyz divisible by 3?

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If x, y and z are positive integers, is xyz divisible by 3? [#permalink]  13 Nov 2006, 01:01
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I got both questions the same answer but it's wrong. I will explain the details after OA.

If x, y and z are positive integers, is xyz divisible by 3?
1. x is a multiple of 3
2. xyz<27

If x and y are both positive integers, how many different positive integers are factors of xy?

1. x is a prime number
2. y is divisible by 3
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A
E.

For the 2nd question, y could be the multiplication of 3 and any other numbers, so you can't determine the no of factors, because you don't know y.
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St1:
x is a multiple of 3. So we can represent xyz with 3(n)yz where n = 1,2,3...

So xyz is divisible by 3. Sufficient.

St2:
If xyz = 25, then it's not divisible by 3.
If xyz = 9, then it's divisible by 3.
Insufficient.

Ans A

If x and y are both positive integers, how many different positive integers are factors of xy?

1. x is a prime number
2. y is divisible by 3

St1:
no information for y

St2:
no information for x

Using st1 and st2:
insufficient. x will contribute two integers, 1 and itself. y can be any multiple of 3. So there can be a number of different answers.

Ans E
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OA is A and E.

I get it now. Thanks.
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