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

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Senior Manager
Joined: 02 Sep 2006
Posts: 254
If x, y and z are positive integers, is xyz divisible by 3? [#permalink]

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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
VP
Joined: 25 Jun 2006
Posts: 1166

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13 Nov 2006, 01:35
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.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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13 Nov 2006, 02:04
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
Senior Manager
Joined: 02 Sep 2006
Posts: 254

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17 Nov 2006, 00:47
OA is A and E.

I get it now. Thanks.
17 Nov 2006, 00:47
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If x, y and z are positive integers, is xyz divisible by 3?

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